Daily Papers

The key-value (KV) cache dominates memory bandwidth and footprint in long-context autoregressive inference. Recent rotation-preconditioned codecs (TurboQuant, PolarQuant) show that a structured random rotation followed by a per-coordinate scalar quantizer matched to an analytically tractable marginal is a near-optimal recipe for KV compression. OCTOPUS advances this paradigm through joint quantization of rotated coordinate triplets. Each triplet's direction is mapped to a square via an octahedral parameterization, and the two resulting coordinates and the triplet norm are Lloyd-Max quantized against implementation-matched marginals. Optimizing the per-triplet squared error gives a strictly non-uniform bit allocation depending only on the total dimensionality of the keys. We find the finite-dimensional quality optimum with sweeps to be constant on every real decoder we test. The codec is data-oblivious, online, and deterministic given a seed. Across text, video, and audio, OCTOPUS matches or beats every prior rotation codec at every reported bit width and metric, with a lead that grows as bits drop for extreme compression. Furthermore, a fused Triton implementation reconstructs keys on the fly without materializing the uncompressed key, so the codec adds no decode-time bandwidth or latency over the existing dequantization. Project Page: https://octopus-quant.github.io/

Vector quantization, a problem rooted in Shannon's source coding theory, aims to quantize high-dimensional Euclidean vectors while minimizing distortion in their geometric structure. We propose TurboQuant to address both mean-squared error (MSE) and inner product distortion, overcoming limitations of existing methods that fail to achieve optimal distortion rates. Our data-oblivious algorithms, suitable for online applications, achieve near-optimal distortion rates (within a small constant factor) across all bit-widths and dimensions. TurboQuant achieves this by randomly rotating input vectors, inducing a concentrated Beta distribution on coordinates, and leveraging the near-independence property of distinct coordinates in high dimensions to simply apply optimal scalar quantizers per each coordinate. Recognizing that MSE-optimal quantizers introduce bias in inner product estimation, we propose a two-stage approach: applying an MSE quantizer followed by a 1-bit Quantized JL (QJL) transform on the residual, resulting in an unbiased inner product quantizer. We also provide a formal proof of the information-theoretic lower bounds on best achievable distortion rate by any vector quantizer, demonstrating that TurboQuant closely matches these bounds, differing only by a small constant (approx 2.7) factor. Experimental results validate our theoretical findings, showing that for KV cache quantization, we achieve absolute quality neutrality with 3.5 bits per channel and marginal quality degradation with 2.5 bits per channel. Furthermore, in nearest neighbor search tasks, our method outperforms existing product quantization techniques in recall while reducing indexing time to virtually zero.

Weight quantization has become a standard tool for efficient LLM deployment, especially for local inference, where models are now routinely served at 2-3 bits per parameter. The state of the art is currently split into two sets of methods: simple scalar quantization techniques, such as GPTQ or AWQ, which are widely deployed but plateau in accuracy at 3-4 bits per parameter (bpp), and "second-generation" vector- or trellis-quantized methods, such as QTIP, GPTVQ and AQLM, which push the accuracy frontier at low bit-widths but are notoriously hard to implement and to scale, and have gained relatively less traction. In this paper, we ask whether this gap is fundamental, or whether a carefully optimized scalar quantizer can recover most of it. We answer in the affirmative, by introducing GSQ (Gumbel-Softmax Quantization), a post-training scalar quantization method which jointly learns the per-coordinate grid assignments and the per-group scales using a Gumbel-Softmax relaxation of the discrete grid. GSQ matches the cardinality of the relaxation to the small number of levels available in the target bit-width regime (e.g., 3-8 levels for ternary and 3 bpp, respectively), making the relaxation tight and the optimization tractable. Practically, on the standard Llama-3.1-8B/70B-Instruct models, GSQ closes most of the gap between scalar quantization and the QTIP frontier at 2 and 3 bits, while using a symmetric scalar grid with group-wise quantization, and thus fully compatible with existing scalar inference kernels. We further show that GSQ scales to trillion-scale Mixture-of-Experts models such as Kimi-K2.5, where vector-quantized methods are difficult to apply.

Post-training quantization (PTQ) has emerged as a practical approach to compress large neural networks, making them highly efficient for deployment. However, effectively reducing these models to their low-bit counterparts without compromising the original accuracy remains a key challenge. In this paper, we propose an innovative PTQ algorithm termed COMQ, which sequentially conducts coordinate-wise minimization of the layer-wise reconstruction errors. We consider the widely used integer quantization, where every quantized weight can be decomposed into a shared floating-point scalar and an integer bit-code. Within a fixed layer, COMQ treats all the scaling factor(s) and bit-codes as the variables of the reconstruction error. Every iteration improves this error along a single coordinate while keeping all other variables constant. COMQ is easy to use and requires no hyper-parameter tuning. It instead involves only dot products and rounding operations. We update these variables in a carefully designed greedy order, significantly enhancing the accuracy. COMQ achieves remarkable results in quantizing 4-bit Vision Transformers, with a negligible loss of less than 1% in Top-1 accuracy. In 4-bit INT quantization of convolutional neural networks, COMQ maintains near-lossless accuracy with a minimal drop of merely 0.3% in Top-1 accuracy.

Post-training quantization is a key technique for reducing the memory and inference latency of large language models by quantizing weights and activations without requiring retraining. However, existing methods either (1) fail to account for the varying importance of hidden features to the end loss or, when incorporating end loss, (2) neglect the critical interactions between model weights. To address these limitations, we propose GuidedQuant, a novel quantization approach that integrates gradient information from the end loss into the quantization objective while preserving cross-weight dependencies within output channels. GuidedQuant consistently boosts the performance of state-of-the-art quantization methods across weight-only scalar, weight-only vector, and weight-and-activation quantization. Additionally, we introduce a novel non-uniform scalar quantization algorithm, which is guaranteed to monotonically decrease the quantization objective value, and outperforms existing methods in this category. We release the code at https://github.com/snu-mllab/GuidedQuant.

We compress KV cache entries by quantizing angles in the Fast Walsh-Hadamard domain, where a random diagonal rotation makes consecutive element pairs approximately uniformly distributed on the unit circle. We extend this angular quantizer with per-layer early-boost, which independently configures K and V codebook sizes at each layer, allocating higher precision to a model-specific subset of critical layers. Across seven models (1B to 7B parameters), per-layer early-boost achieves lossless compression on four models and near-lossless quality on six of seven, at 3.28 to 3.67 angle bits per element. Asymmetric norm quantization (8-bit for keys, 4-bit log-space for values) yields 6.56 total bits per element on Mistral-7B with perplexity degradation of +0.0014 and no calibration data. A layer-group sensitivity analysis reveals model-specific bottleneck patterns, including K-dominated versus V-dominated layers and negative-transfer layers where increased precision degrades quality.

Quantization is essential for deploying Large Language Models (LLMs) by enhancing memory efficiency and inference speed. Existing methods for activation quantization mainly address channel-wise outliers, often neglecting token-wise outliers, leading to reliance on costly per-token dynamic quantization. To address this, we introduce PrefixQuant, a novel technique that isolates outlier tokens offline without re-training. Specifically, PrefixQuant identifies high-frequency outlier tokens and prefixes them in the KV cache, preventing the generation of outlier tokens during inference and simplifying quantization. To our knowledge, PrefixQuant is the first to enable efficient per-tensor static quantization to outperform expensive per-token dynamic quantization. For instance, in W4A4KV4 (4- bit weight, 4-bit activation, and 4-bit KV cache) Llama-3-8B, PrefixQuant with per-tensor static quantization achieves a 7.43 WikiText2 perplexity and 71.08% average accuracy on 5 common-sense reasoning tasks, outperforming previous per-token dynamic quantization methods like QuaRot with 0.98 perplexity improvement and +5.98 points accuracy. Additionally, the inference speed of W4A4 quantized models using PrefixQuant is 1.60x to 2.81x faster than FP16 models and exceeds QuaRot models by 1.2x to 1.3x. Our code is available at https://github.com/ChenMnZ/PrefixQuant.

Quantizing model weights is critical for reducing the communication and inference costs of large models. However, quantizing models -- especially to low precisions like int4 or int2 -- requires a trade-off in model quality; int2, in particular, is known to severely degrade model quality. Consequently, practitioners are often forced to maintain multiple models with different quantization levels or serve a single model that best satisfies the quality-latency trade-off. On the other hand, integer data types, such as int8, inherently possess a nested (Matryoshka) structure where smaller bit-width integers, like int4 or int2, are nested within the most significant bits. This paper proposes Matryoshka Quantization (MatQuant), a novel multi-scale quantization technique that addresses the challenge of needing multiple quantized models. It allows training and maintaining just one model, which can then be served at different precision levels. Furthermore, due to the co-training and co-distillation regularization provided by MatQuant, the int2 precision models extracted by MatQuant can be up to 10% more accurate than standard int2 quantization (using techniques like QAT or OmniQuant). This represents significant progress in model quantization, demonstrated by the fact that, with the same recipe, an int2 FFN-quantized Gemma-2 9B model is more accurate than an int8 FFN-quantized Gemma-2 2B model.

Large language models (LLMs) deliver strong performance, but their high compute and memory costs make deployment difficult in resource-constrained scenarios. Weight-only post-training quantization (PTQ) is appealing, as it reduces memory usage and enables practical speedup without low-bit operators or specialized hardware. However, accuracy often degrades significantly in weight-only PTQ at sub-4-bit precision, and our analysis identifies two main causes: (1) down-projection matrices are a well-known quantization bottleneck, but maintaining their fidelity often requires extra bit-width; (2) weight quantization induces activation deviations, but effective correction strategies remain underexplored. To address these issues, we propose D^2Quant, a novel weight-only PTQ framework that improves quantization from both the weight and activation perspectives. On the weight side, we design a Dual-Scale Quantizer (DSQ) tailored to down-projection matrices, with an absorbable scaling factor that significantly improves accuracy without increasing the bit budget. On the activation side, we propose Deviation-Aware Correction (DAC), which incorporates a mean-shift correction within LayerNorm to mitigate quantization-induced activation distribution shifts. Extensive experiments across multiple LLM families and evaluation metrics show that D^2Quant delivers superior performance for weight-only PTQ at sub-4-bit precision. The code and models will be available at https://github.com/XIANGLONGYAN/D2Quant.

Recent advances in large language model (LLM) pretraining have led to high-quality LLMs with impressive abilities. By compressing such LLMs via quantization to 3-4 bits per parameter, they can fit into memory-limited devices such as laptops and mobile phones, enabling personalized use. However, quantization down to 3-4 bits per parameter usually leads to moderate-to-high accuracy losses, especially for smaller models in the 1-10B parameter range, which are well-suited for edge deployments. To address this accuracy issue, we introduce the Sparse-Quantized Representation (SpQR), a new compressed format and quantization technique which enables for the first time near-lossless compression of LLMs across model scales, while reaching similar compression levels to previous methods. SpQR works by identifying and isolating outlier weights, which cause particularly-large quantization errors, and storing them in higher precision, while compressing all other weights to 3-4 bits, and achieves relative accuracy losses of less than 1% in perplexity for highly-accurate LLaMA and Falcon LLMs. This makes it possible to run 33B parameter LLM on a single 24 GB consumer GPU without any performance degradation at 15% speedup thus making powerful LLMs available to consumer without any downsides. SpQR comes with efficient algorithms for both encoding weights into its format, as well as decoding them efficiently at runtime. Specifically, we provide an efficient GPU inference algorithm for SpQR which yields faster inference than 16-bit baselines at similar accuracy, while enabling memory compression gains of more than 4x.

We present PolarQuant, a post-training weight quantization method for large language models (LLMs) that exploits the distributional structure of neural network weights to achieve near-lossless compression. PolarQuant operates in three stages: (1) block-wise normalization to the unit hypersphere, (2) Walsh-Hadamard rotation to transform coordinates into approximately Gaussian random variables, and (3) quantization with centroids matched to the Gaussian distribution. Our ablation reveals that Hadamard rotation alone accounts for 98% of the quality improvement, reducing Qwen3.5-9B perplexity from 6.90 (absmax Q5) to 6.40 (Delta = +0.03 from FP16), making it practically lossless without any calibration data. Furthermore, PolarQuant functions as an effective preprocessing step for downstream INT4 quantizers: PolarQuant Q5 dequantized and re-quantized by torchao INT4 achieves perplexity 6.56 versus 6.68 for direct absmax INT4, while maintaining 43.1 tok/s throughput at 6.5 GB VRAM. Code and models are publicly available.

Microscaling floating-point (MXFP) formats have emerged as a promising standard for deploying Multi-modal Large Language Models (MLLMs) and Large Language Models (LLMs) on modern accelerator architectures. However, existing Post-Training Quantization (PTQ) methods, particularly rotation-based techniques designed for integer formats, suffer from severe performance collapse when applied to MXFP4. Recent studies attribute this failure to a fundamental format mismatch: global orthogonal rotations inadvertently transfer outlier energy across quantization blocks, inducing new outliers that disrupt local block-wise scaling, while often creating bimodal activation distributions that underutilize the limited quantization range. To address these issues, we propose BATQuant (Block-wise Affine Transformation), which restricts transformations to align with MXFP granularity to prevent cross-block outlier propagation, while relaxing orthogonality constraints to optimize distribution shaping. To ensure parameter efficiency, we introduce Global and Private Kronecker (GPK) decomposition to effectively reduces storage and runtime overhead and incorporate Block-wise Learnable Clipping to suppress residual outliers. Extensive experiments on both MLLMs and LLMs demonstrate that BATQuant establishes new state-of-the-art results under aggressive W4A4KV16 configurations, recovering up to 96.43% of full-precision performance on multimodal benchmarks and clearly outperforming existing methods across diverse tasks.

Post-training quantization has emerged as the most widely used strategy for deploying large language models at low precision. Still, current methods show perplexity degradation at bit-widths less than or equal to 4, partly because representing outliers causes precision issues in parameters that share the same scales as these outliers. This problem is especially pronounced for calibration-free, uniform quantization methods. We introduce SINQ to augment existing post-training quantizers with an additional second-axis scale factor and a fast Sinkhorn-Knopp-style algorithm that finds scales to normalize per-row and per-column variances, thereby minimizing a novel per-matrix proxy target for quantization: the matrix imbalance. Our method has no interactions between layers and can be trivially applied to new architectures to quantize any linear layers. We evaluate our method on the Qwen3 model family and DeepSeek-V2.5. SINQ improves WikiText2 and C4 perplexity significantly against uncalibrated uniform quantization baselines and can be further enhanced by combining it with calibration and non-uniform quantization levels. Code to reproduce the results of this work and to easily quantize models using SINQ is available at https://github.com/huawei-csl/SINQ.

With the rising popularity of Large Language Models (LLMs), there has been an increasing interest in compression techniques that enable their efficient deployment. This study focuses on the Post-Training Quantization (PTQ) of LLMs. Drawing from recent advances, our work introduces QuantEase, a layer-wise quantization framework where individual layers undergo separate quantization. The problem is framed as a discrete-structured non-convex optimization, prompting the development of algorithms rooted in Coordinate Descent (CD) techniques. These CD-based methods provide high-quality solutions to the complex non-convex layer-wise quantization problems. Notably, our CD-based approach features straightforward updates, relying solely on matrix and vector operations, circumventing the need for matrix inversion or decomposition. We also explore an outlier-aware variant of our approach, allowing for retaining significant weights (outliers) with complete precision. Our proposal attains state-of-the-art performance in terms of perplexity and zero-shot accuracy in empirical evaluations across various LLMs and datasets, with relative improvements up to 15% over methods such as GPTQ. Leveraging careful linear algebra optimizations, QuantEase can quantize models like Falcon-180B on a single NVIDIA A100 GPU in sim3 hours. Particularly noteworthy is our outlier-aware algorithm's capability to achieve near or sub-3-bit quantization of LLMs with an acceptable drop in accuracy, obviating the need for non-uniform quantization or grouping techniques, improving upon methods such as SpQR by up to two times in terms of perplexity.

We propose LLM-FP4 for quantizing both weights and activations in large language models (LLMs) down to 4-bit floating-point values, in a post-training manner. Existing post-training quantization (PTQ) solutions are primarily integer-based and struggle with bit widths below 8 bits. Compared to integer quantization, floating-point (FP) quantization is more flexible and can better handle long-tail or bell-shaped distributions, and it has emerged as a default choice in many hardware platforms. One characteristic of FP quantization is that its performance largely depends on the choice of exponent bits and clipping range. In this regard, we construct a strong FP-PTQ baseline by searching for the optimal quantization parameters. Furthermore, we observe a high inter-channel variance and low intra-channel variance pattern in activation distributions, which adds activation quantization difficulty. We recognize this pattern to be consistent across a spectrum of transformer models designed for diverse tasks, such as LLMs, BERT, and Vision Transformer models. To tackle this, we propose per-channel activation quantization and show that these additional scaling factors can be reparameterized as exponential biases of weights, incurring a negligible cost. Our method, for the first time, can quantize both weights and activations in the LLaMA-13B to only 4-bit and achieves an average score of 63.1 on the common sense zero-shot reasoning tasks, which is only 5.8 lower than the full-precision model, significantly outperforming the previous state-of-the-art by 12.7 points. Code is available at: https://github.com/nbasyl/LLM-FP4.

Quantization has become a crucial step for the efficient deployment of deep neural networks, where floating point operations are converted to simpler fixed point operations. In its most naive form, it simply consists in a combination of scaling and rounding transformations, leading to either a limited compression rate or a significant accuracy drop. Recently, Gradient-based post-training quantization (GPTQ) methods appears to be constitute a suitable trade-off between such simple methods and more powerful, yet expensive Quantization-Aware Training (QAT) approaches, particularly when attempting to quantize LLMs, where scalability of the quantization process is of paramount importance. GPTQ essentially consists in learning the rounding operation using a small calibration set. In this work, we challenge common choices in GPTQ methods. In particular, we show that the process is, to a certain extent, robust to a number of variables (weight selection, feature augmentation, choice of calibration set). More importantly, we derive a number of best practices for designing more efficient and scalable GPTQ methods, regarding the problem formulation (loss, degrees of freedom, use of non-uniform quantization schemes) or optimization process (choice of variable and optimizer). Lastly, we propose a novel importance-based mixed-precision technique. Those guidelines lead to significant performance improvements on all the tested state-of-the-art GPTQ methods and networks (e.g. +6.819 points on ViT for 4-bit quantization), paving the way for the design of scalable, yet effective quantization methods.

We present an overview of techniques for quantizing convolutional neural networks for inference with integer weights and activations. Per-channel quantization of weights and per-layer quantization of activations to 8-bits of precision post-training produces classification accuracies within 2% of floating point networks for a wide variety of CNN architectures. Model sizes can be reduced by a factor of 4 by quantizing weights to 8-bits, even when 8-bit arithmetic is not supported. This can be achieved with simple, post training quantization of weights.We benchmark latencies of quantized networks on CPUs and DSPs and observe a speedup of 2x-3x for quantized implementations compared to floating point on CPUs. Speedups of up to 10x are observed on specialized processors with fixed point SIMD capabilities, like the Qualcomm QDSPs with HVX. Quantization-aware training can provide further improvements, reducing the gap to floating point to 1% at 8-bit precision. Quantization-aware training also allows for reducing the precision of weights to four bits with accuracy losses ranging from 2% to 10%, with higher accuracy drop for smaller networks.We introduce tools in TensorFlow and TensorFlowLite for quantizing convolutional networks and review best practices for quantization-aware training to obtain high accuracy with quantized weights and activations. We recommend that per-channel quantization of weights and per-layer quantization of activations be the preferred quantization scheme for hardware acceleration and kernel optimization. We also propose that future processors and hardware accelerators for optimized inference support precisions of 4, 8 and 16 bits.

Large language model (LLM) inference is often bounded by memory footprint and memory bandwidth in resource-constrained deployments, making quantization a fundamental technique for efficient serving. While post-training quantization (PTQ) maintains high fidelity at 4-bit, it deteriorates at 2-3 bits. Fundamentally, existing methods enforce a shape-invariant quantization grid (e.g., the fixed uniform intervals of UINT2) for each group, severely restricting the feasible set for error minimization. To address this, we propose Bit-Plane Decomposition Quantization (BPDQ), which constructs a variable quantization grid via bit-planes and scalar coefficients, and iteratively refines them using approximate second-order information while progressively compensating quantization errors to minimize output discrepancy. In the 2-bit regime, BPDQ enables serving Qwen2.5-72B on a single RTX 3090 with 83.85% GSM8K accuracy (vs. 90.83% at 16-bit). Moreover, we provide theoretical analysis showing that the variable grid expands the feasible set, and that the quantization process consistently aligns with the optimization objective in Hessian-induced geometry. Code: github.com/KingdalfGoodman/BPDQ.

The KV cache in large language models is a dominant factor in memory usage, limiting their broader applicability. Quantizing the cache to lower bit widths is an effective way to reduce computational costs; however, previous methods struggle with quantizing key vectors due to outliers, resulting in excessive overhead. We propose a novel quantization approach called PolarQuant, which efficiently addresses the outlier challenge. We observe that outliers typically appear in only one of two dimensions, which are rotated together by a specific angle when rotary position embeddings are applied. When represented as two-dimensional vectors, these dimensions exhibit well-structured patterns, with radii and angles smoothly distributed in polar coordinates. This alleviates the challenge of outliers on per-channel quantization, making them well-suited for quantization. Thus, PolarQuant divides key vectors into groups of two-dimensional sub-vectors, encoding them as the corresponding quantized radius and the polar angle, rather than quantizing original key vectors directly. PolarQuant achieves the superior efficiency in KV cache quantization and accelerates the decoding process by turning the query-key inner product into a table lookup, all while maintaining the downstream performance of full-precision models.

The field of image generation is currently bifurcated into autoregressive (AR) models operating on discrete tokens and diffusion models utilizing continuous latents. This divide, rooted in the distinction between VQ-VAEs and VAEs, hinders unified modeling and fair benchmarking. Finite Scalar Quantization (FSQ) offers a theoretical bridge, yet vanilla FSQ suffers from a critical flaw: its equal-interval quantization can cause activation collapse. This mismatch forces a trade-off between reconstruction fidelity and information efficiency. In this work, we resolve this dilemma by simply replacing the activation function in original FSQ with a distribution-matching mapping to enforce a uniform prior. Termed iFSQ, this simple strategy requires just one line of code yet mathematically guarantees both optimal bin utilization and reconstruction precision. Leveraging iFSQ as a controlled benchmark, we uncover two key insights: (1) The optimal equilibrium between discrete and continuous representations lies at approximately 4 bits per dimension. (2) Under identical reconstruction constraints, AR models exhibit rapid initial convergence, whereas diffusion models achieve a superior performance ceiling, suggesting that strict sequential ordering may limit the upper bounds of generation quality. Finally, we extend our analysis by adapting Representation Alignment (REPA) to AR models, yielding LlamaGen-REPA. Codes is available at https://github.com/Tencent-Hunyuan/iFSQ

Serving large-scale machine learning (ML) models efficiently and with low latency has become challenging owing to increasing model size and complexity. Quantizing models can simultaneously reduce memory and compute requirements, facilitating their widespread access. However, for large models not all layers are equally amenable to the same numerical precision and aggressive quantization can lead to unacceptable loss in model accuracy. One approach to prevent this accuracy degradation is mixed-precision quantization, which allows different tensors to be quantized to varying levels of numerical precision, leveraging the capabilities of modern hardware. Such mixed-precision quantiztaion can more effectively allocate numerical precision to different tensors `as needed' to preserve model accuracy while reducing footprint and compute latency. In this paper, we propose a method to efficiently determine quantization configurations of different tensors in ML models using post-training mixed precision quantization. We analyze three sensitivity metrics and evaluate them for guiding configuration search of two algorithms. We evaluate our method for computer vision and natural language processing and demonstrate latency reductions of up to 27.59% and 34.31% compared to the baseline 16-bit floating point model while guaranteeing no more than 1% accuracy degradation.

Matryoshka Quantization (MatQuant) is a recent quantization approach showing that a single integer-quantized model can be served across multiple precisions, by slicing the most significant bits (MSB) at inference time. This enables a single checkpoint to cover a wide range of memory and latency budgets, but renders quantization much more challenging. In particular, the initial MatQuant relies on expensive quantization-aware training (QAT) variants, rather than fast one-shot post training quantization (PTQ), and lacks open-source and kernel support. We address all of these limitations by introducing Post-Training Matryoshka Quantization (MatGPTQ), a new PTQ pipeline that produces a single parent model jointly optimized for multiple target precisions in one-shot, based on a small calibration set. MatGPTQ casts Matryoshka quantization as a multi-precision objective with bit-slicing and cross-bit error compensation, resulting in an algorithm that produces a multi-bit-width, "sliceable" model in a single pass. We also incorporate a new budget-aware search for heterogeneous per-layer bit-witdhs and provide efficient kernels that implement slicing and mixed-precision execution. Across standard LLMs and benchmarks, MatGPTQ preserves high-bit accuracy while substantially improving performance at low-bit-witdh settings. Overall, we establish a new state of the art for Matryoshka-style post-training quantization and make single-checkpoint, multi-precision deployment open and practical. Code is available at https://github.com/IST-DASLab/MatGPTQ.

We propose to replace vector quantization (VQ) in the latent representation of VQ-VAEs with a simple scheme termed finite scalar quantization (FSQ), where we project the VAE representation down to a few dimensions (typically less than 10). Each dimension is quantized to a small set of fixed values, leading to an (implicit) codebook given by the product of these sets. By appropriately choosing the number of dimensions and values each dimension can take, we obtain the same codebook size as in VQ. On top of such discrete representations, we can train the same models that have been trained on VQ-VAE representations. For example, autoregressive and masked transformer models for image generation, multimodal generation, and dense prediction computer vision tasks. Concretely, we employ FSQ with MaskGIT for image generation, and with UViM for depth estimation, colorization, and panoptic segmentation. Despite the much simpler design of FSQ, we obtain competitive performance in all these tasks. We emphasize that FSQ does not suffer from codebook collapse and does not need the complex machinery employed in VQ (commitment losses, codebook reseeding, code splitting, entropy penalties, etc.) to learn expressive discrete representations.

Modern sensors generate rich, high-fidelity data, yet applications operating on wearable or remote sensing devices remain constrained by bandwidth and power budgets. Standardized codecs such as JPEG and MPEG achieve efficient trade-offs between bitrate and perceptual quality but are designed for human perception, limiting their applicability to machine-perception tasks and non-traditional modalities such as spatial audio arrays, hyperspectral images, and 3D medical images. General-purpose compression schemes based on scalar quantization or resolution reduction are broadly applicable but fail to exploit inherent signal redundancies, resulting in suboptimal rate-distortion performance. Recent generative neural codecs, or tokenizers, model complex signal dependencies but are often over-parameterized, data-hungry, and modality-specific, making them impractical for resource-constrained environments. We introduce a Lightweight, Versatile, and Asymmetric neural codec architecture (LiVeAction), that addresses these limitations through two key ideas. (1) To reduce the complexity of the encoder to meet the resource constraints of the execution environments, we impose an FFT-like structure and reduce the overall size and depth of the neural-network-based analysis transform. (2) To allow arbitrary signal modalities and simplify training, we replace adversarial and perceptual losses with a variance-based rate penalty. Our design produces codecs that deliver superior rate-distortion performance compared to state-of-the-art generative tokenizers, while remaining practical for deployment on low-power sensors. We release our code, experiments, and python library at https://github.com/UT-SysML/liveaction .

Post-training quantization (PTQ) of large language models (LLMs) holds the promise in reducing the prohibitive computational cost at inference time. Quantization of all weight, activation and key-value (KV) cache tensors to 4-bit without significantly degrading generalizability is challenging, due to the high quantization error caused by extreme outliers in activations. To tackle this problem, we propose ResQ, a PTQ method that pushes further the state-of-the-art. By means of principal component analysis (PCA), it identifies a low-rank subspace (in practice 1/8 of the hidden dimension) in which activation variances are highest, and keep the coefficients within this subspace in high precision, e.g. 8-bit, while quantizing the rest to 4-bit. Within each subspace, invariant random rotation is applied to further suppress outliers. We show that this is a provably optimal mixed precision quantization scheme that minimizes error. With the Llama and Qwen2.5 families of models, we demonstrate that ResQ outperforms recent uniform and mixed precision PTQ methods on a variety of benchmarks, achieving up to 33\% lower perplexity on Wikitext than the next best method SpinQuant, and upto 3\times speedup over 16-bit baseline. Code is available at https://github.com/utkarsh-dmx/project-resq.

We compare two strategies for compressing the KV cache in transformer inference: rank reduction (discard dimensions) and quantization (keep all dimensions, reduce precision). At matched storage budgets across five models (124M-14B, MHA and GQA), we find that quantization consistently outperforms rank reduction by 4-364 PPL depending on model and compression level. The gap persists even when rank reduction is combined with quantization in hybrid baselines, and it grows with GQA aggressiveness. On LAMBADA, INT4 matches FP16 accuracy (+0.23 PPL on Mistral 7B, +0.58 on GPT-2) while rank-32 at identical storage collapses to 0.4%. We trace this gap to a structural asymmetry: under softmax attention routing, removing a dimension can flip which token is attended (a discrete failure), while quantization noise is bounded and typically preserves score ordering. We formalize this via a perturbation result showing projection damage exceeds quantization damage by 3 x 2^(2b) per direction under the softmax Fisher metric. A basis ablation confirms the finding is basis-independent (spread <0.4 PPL), establishing that the advantage comes from preserving dimensions, not from a better coordinate system. Joint K+V INT4 quantization achieves 75% total KV reduction at only +0.18 PPL on Mistral 7B.

Recent works on compression of large language models (LLM) using quantization considered reparameterizing the architecture such that weights are distributed on the sphere. This demonstratively improves the ability to quantize by increasing the mathematical notion of coherence, resulting in fewer weight outliers without affecting the network output. In this work, we aim to further exploit this spherical geometry of the weights when performing quantization by considering Pyramid Vector Quantization (PVQ) for large language models. Arranging points evenly on the sphere is notoriously difficult, especially in high dimensions, and in case approximate solutions exists, representing points explicitly in a codebook is typically not feasible due to its additional memory cost. Instead, PVQ uses a fixed integer lattice on the sphere by projecting points onto the 1-sphere, which allows for efficient encoding and decoding without requiring an explicit codebook in memory. To obtain a practical algorithm, we propose to combine PVQ with scale quantization for which we derive theoretically optimal quantizations, under empirically verified assumptions. Further, we extend pyramid vector quantization to use Hessian information to minimize quantization error under expected feature activations, instead of only relying on weight magnitudes. Experimentally, we achieves state-of-the-art quantization performance with pareto-optimal trade-off between performance and bits per weight and bits per activation, compared to compared methods. On weight-only, we find that we can quantize a Llama-3 70B model to 3.25 bits per weight and retain 98\% accuracy on downstream tasks.

Post-training quantization (PTQ) has emerged as a widely adopted technique for compressing and accelerating Large Language Models (LLMs). The major challenge in LLM quantization is that uneven and heavy-tailed data distributions can expand the quantization range, thereby reducing bit precision for most values. Recent methods attempt to eliminate outliers and balance inter-channel differences by employing linear transformations; however, they remain heuristic and are often overlook optimizing the data distribution across the entire quantization space.In this paper, we introduce Quantization Space Utilization Rate (QSUR), a novel metric that effectively assesses the quantizability of transformed data by measuring the space utilization of the data in the quantization space. We complement QSUR with mathematical derivations that examine the effects and limitations of various transformations, guiding our development of Orthogonal and Scaling Transformation-based Quantization (OSTQuant). OSQuant employs a learnable equivalent transformation, consisting of an orthogonal transformation and a scaling transformation, to optimize the distributions of weights and activations across the entire quantization space. Futhermore, we propose the KL-Top loss function, designed to mitigate noise during optimization while retaining richer semantic information within the limited calibration data imposed by PTQ. OSTQuant outperforms existing work on various LLMs and benchmarks. In the W4-only setting, it retains 99.5\% of the floating-point accuracy. In the more challenging W4A4KV4 configuration, OSTQuant reduces the performance gap by 32\% on the LLaMA-3-8B model compared to state-of-the-art methods. https://github.com/BrotherHappy/OSTQuant{https://github.com/BrotherHappy/OSTQuant}.

Existing vector quantization (VQ) methods struggle with scalability, largely attributed to the instability of the codebook that undergoes partial updates during training. The codebook is prone to collapse as utilization decreases, due to the progressively widening distribution gap between non-activated codes and visual features. To solve the problem, we propose Index Backpropagation Quantization (IBQ), a new VQ method for the joint optimization of all codebook embeddings and the visual encoder. Applying a straight-through estimator on the one-hot categorical distribution between the encoded feature and codebook, all codes are differentiable and maintain a consistent latent space with the visual encoder. IBQ enables scalable training of visual tokenizers and, for the first time, achieves a large-scale codebook (2^{18}) with high dimension (256) and high utilization. Experiments on the standard ImageNet benchmark demonstrate the scalability and superiority of IBQ, achieving competitive results on both reconstruction (1.00 rFID) and autoregressive visual generation (2.05 gFID). The code and models are available at https://github.com/TencentARC/SEED-Voken.

Post-Training Quantization (PTQ) is a powerful technique for model compression, reducing the precision of neural networks without additional training overhead. Recent works have investigated adopting 8-bit floating-point quantization (FP8) in the context of PTQ for model inference. However, the exploration of floating-point formats smaller than 8 bits and their comparison with integer quantization remains relatively limited. In this work, we present minifloats, which are reduced-precision floating-point formats capable of further reducing the memory footprint, latency, and energy cost of a model while approaching full-precision model accuracy. Our work presents a novel PTQ design-space exploration, comparing minifloat and integer quantization schemes across a range of 3 to 8 bits for both weights and activations. We examine the applicability of various PTQ techniques to minifloats, including weight equalization, bias correction, SmoothQuant, gradient-based learned rounding, and the GPTQ method. Our experiments validate the effectiveness of low-precision minifloats when compared to their integer counterparts across a spectrum of accuracy-precision trade-offs on a set of reference deep learning vision workloads. Finally, we evaluate our results against an FPGA-based hardware cost model, showing that integer quantization often remains the Pareto-optimal option, given its relatively smaller hardware resource footprint.

Non-parametric quantization has received much attention due to its efficiency on parameters and scalability to a large codebook. In this paper, we present a unified formulation of different non-parametric quantization methods through the lens of lattice coding. The geometry of lattice codes explains the necessity of auxiliary loss terms when training auto-encoders with certain existing lookup-free quantization variants such as BSQ. As a step forward, we explore a few possible candidates, including random lattices, generalized Fibonacci lattices, and densest sphere packing lattices. Among all, we find the Leech lattice-based quantization method, which is dubbed as Spherical Leech Quantization (Λ_{24}-SQ), leads to both a simplified training recipe and an improved reconstruction-compression tradeoff thanks to its high symmetry and even distribution on the hypersphere. In image tokenization and compression tasks, this quantization approach achieves better reconstruction quality across all metrics than BSQ, the best prior art, while consuming slightly fewer bits. The improvement also extends to state-of-the-art auto-regressive image generation frameworks.

Model quantization reduces neural network parameter precision to achieve compression, but often compromises accuracy. Existing post-training quantization (PTQ) methods employ iterative parameter updates to preserve accuracy under high compression ratios, incurring significant computational complexity and resource overhead, which limits applicability in resource-constrained edge computing and real-time inference scenarios. This paper proposes an efficient PTQ method guided by parameter sensitivity analysis. The approach prioritizes quantization of high-sensitivity parameters, leveraging unquantized low-sensitivity parameters to compensate for quantization errors, thereby mitigating accuracy degradation. Furthermore, by exploiting column-wise clustering of parameter sensitivity, the method introduces a row-parallel quantization framework with a globally shared inverse Hessian matrix update mechanism, reducing computational complexity by an order of magnitude. Experimental results on ResNet-50 and YOLOv5s demonstrate a 20-200-fold quantization speedup over the Optimal Brain Quantization baseline, with mean accuracy loss below 0.3%, confirming the method's efficacy in balancing efficiency and accuracy.

Diffusion Transformers (DiTs) have recently gained substantial attention in both industrial and academic fields for their superior visual generation capabilities, outperforming traditional diffusion models that use U-Net. However,the enhanced performance of DiTs also comes with high parameter counts and implementation costs, seriously restricting their use on resource-limited devices such as mobile phones. To address these challenges, we introduce the Hybrid Floating-point Quantization for DiT(HQ-DiT), an efficient post-training quantization method that utilizes 4-bit floating-point (FP) precision on both weights and activations for DiT inference. Compared to fixed-point quantization (e.g., INT8), FP quantization, complemented by our proposed clipping range selection mechanism, naturally aligns with the data distribution within DiT, resulting in a minimal quantization error. Furthermore, HQ-DiT also implements a universal identity mathematical transform to mitigate the serious quantization error caused by the outliers. The experimental results demonstrate that DiT can achieve extremely low-precision quantization (i.e., 4 bits) with negligible impact on performance. Our approach marks the first instance where both weights and activations in DiTs are quantized to just 4 bits, with only a 0.12 increase in sFID on ImageNet.

Searching for approximate nearest neighbors (ANN) in the high-dimensional Euclidean space is a pivotal problem. Recently, with the help of fast SIMD-based implementations, Product Quantization (PQ) and its variants can often efficiently and accurately estimate the distances between the vectors and have achieved great success in the in-memory ANN search. Despite their empirical success, we note that these methods do not have a theoretical error bound and are observed to fail disastrously on some real-world datasets. Motivated by this, we propose a new randomized quantization method named RaBitQ, which quantizes D-dimensional vectors into D-bit strings. RaBitQ guarantees a sharp theoretical error bound and provides good empirical accuracy at the same time. In addition, we introduce efficient implementations of RaBitQ, supporting to estimate the distances with bitwise operations or SIMD-based operations. Extensive experiments on real-world datasets confirm that (1) our method outperforms PQ and its variants in terms of accuracy-efficiency trade-off by a clear margin and (2) its empirical performance is well-aligned with our theoretical analysis.

Conventional model compression techniques for LLMs address high memory consumption and slow inference challenges but typically require computationally expensive retraining to preserve accuracy. In contrast, one-shot compression methods eliminate retraining cost, but struggle to achieve accuracy comparable to dense models. This paper presents SLIM, a new one-shot compression framework that holistically integrates hardware-friendly quantization, sparsity, and low-rank approximation into a unified process. First, we formulate the quantization process using a probabilistic approach (SLIM-Quant) that enables us to apply uniform quantization. Then, we use an existing one-shot pruning method to apply semi-structured sparsity on top of the quantized weights. Finally, to compensate for the introduced aggregated quantization and sparsity error, we use a novel saliency function with unique invertible and additive features that enables us to mathematically compute the value of low-rank adapters. SLIM improves model accuracy by up to 5.66% (LLaMA-2-7B) for 2:4 sparsity with 4-bit weight quantization, outperforming prior methods. Models compressed with SLIM achieve up to 4.3x and 3.8x on Nvidia RTX3060 and A100 GPUs, respectively. Additionally, they achieve up to 0.23x end-to-end memory reduction in comparison to their dense counterparts. We also propose an optional PEFT recipe that further improves accuracy by up to 1.66% (LLaMA-2-13B) compared to SLIM without fine-tuning.

Recent work on KV cache quantization, culminating in TurboQuant, has approached the Shannon entropy limit for per-vector compression of transformer key-value caches. We observe that this limit applies to a strictly weaker problem than the one that actually matters: compressing the KV cache as a sequence. The tokens stored in a KV cache are not arbitrary floating-point data -- they are samples from the exact formal language the model was trained on, and the model is by construction a near-optimal predictor of that language. We introduce sequential KV compression, a two-layer architecture that exploits this structure. The first layer, probabilistic prefix deduplication, identifies semantically equivalent shared prefixes across sessions using the trie metric d_T(s, s') = -log_2 P_M(s ^ s') from Probabilistic Language Tries (PLTs). The second layer, predictive delta coding, stores only the residual of each new KV vector from the model's own prediction of it, achieving a per-token entropy bound of H(KV_{i+1} | KV_{<=i}) <= H(token_{i+1} | token_{<=i}). We prove that at typical language model perplexity -- approximately 10-20 for fluent English text -- this bound is 3.3-4.3 bits on average per token position, compared to TurboQuant's 3 bits per vector component (with typical attention heads having 64-128 components). The theoretical compression ratio over TurboQuant is approximately 914,000x at the Shannon limit. Even at 1000x above the entropy floor -- a deliberately pessimistic worst-case overhead, two orders of magnitude above the 2-5x typical of practical source coders -- the ratio remains approximately 914x over TurboQuant, with compression improving rather than degrading as context length grows. The two layers are orthogonal and compose with existing per-vector quantization methods including TurboQuant.

The increasing computational demands of foundation models have spurred research into low-precision training, with 4-bit floating-point (FP4) formats emerging as a frontier for maximizing hardware throughput. While numerous techniques have been proposed to stabilize FP4 training, they often present isolated solutions with varying, and not always clear, computational overheads. This paper aims to provide a unified view of the design space of FP4 training. We introduce a comprehensive, quantisation gradient-based framework for microscaling quantization that allows for a theoretical analysis of the computational costs associated with different stabilization methods on both the forward and backward passes. Using a simulator built on this framework, we conduct an extensive empirical study across a wide range of machine learning tasks, including regression, image classification, diffusion models, and language models. By systematically evaluating thousands of combinations of techniques, such as novel gradient approximations, rounding strategies, and scaling methods, we identify which configurations offer the most favourable performance-to-overhead trade-off. We find that the techniques enabling the best trade-off involve carefully combining Hadamard transformations, tensor scaling and stochastic rounding. We further find that using UE5M3 as a scaling factor potentially offers a good compromise between range and precision with manageable computational overhead.

Quantization techniques can reduce the size of Deep Neural Networks and improve inference latency and throughput by taking advantage of high throughput integer instructions. In this paper we review the mathematical aspects of quantization parameters and evaluate their choices on a wide range of neural network models for different application domains, including vision, speech, and language. We focus on quantization techniques that are amenable to acceleration by processors with high-throughput integer math pipelines. We also present a workflow for 8-bit quantization that is able to maintain accuracy within 1% of the floating-point baseline on all networks studied, including models that are more difficult to quantize, such as MobileNets and BERT-large.

Quantizing the weights of a neural network has two steps: (1) Finding a good low bit-complexity representation for weights (which we call the quantization grid) and (2) Rounding the original weights to values in the quantization grid. In this paper, we study the problem of rounding optimally given any quantization grid. The simplest and most commonly used way to round is Round-to-Nearest (RTN). By rounding in a data-dependent way instead, one can improve the quality of the quantized model significantly. We study the rounding problem from the lens of discrepancy theory, which studies how well we can round a continuous solution to a discrete solution without affecting solution quality too much. We prove that given m=poly(1/ε) samples from the data distribution, we can round all but O(m) model weights such that the expected approximation error of the quantized model on the true data distribution is le ε as long as the space of gradients of the original model is approximately low rank (which we empirically validate). Our proof, which is algorithmic, inspired a simple and practical rounding algorithm called DiscQuant. In our experiments, we demonstrate that DiscQuant significantly improves over the prior state-of-the-art rounding method called GPTQ and the baseline RTN over a range of benchmarks on Phi3mini-3.8B and Llama3.1-8B. For example, rounding Phi3mini-3.8B to a fixed quantization grid with 3.25 bits per parameter using DiscQuant gets 64\% accuracy on the GSM8k dataset, whereas GPTQ achieves 54\% and RTN achieves 31\% (the original model achieves 84\%). We make our code available at https://github.com/jerry-chee/DiscQuant.

This paper presents a comprehensive analysis of quantization techniques for optimizing Large Language Models (LLMs), specifically focusing on Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT). Through empirical evaluation across models ranging from 10M to 1B parameters, we demonstrate that quantization can achieve up to 68% reduction in model size while maintaining performance within 6% of full-precision baselines when utilizing our proposed scaling factor {\gamma}. Our experiments show that INT8 quantization delivers a 40% reduction in computational cost and power consumption, while INT4 quantization further improves these metrics by 60%. We introduce a novel theoretical framework for mixed-precision quantization, deriving optimal bit allocation strategies based on layer sensitivity and weight variance. Hardware efficiency evaluations on edge devices reveal that our quantization approach enables up to 2.4x throughput improvement for INT8 and 3x for INT4, with 60% power reduction compared to full-precision models.

Large Language Models (LLMs) have revolutionized natural language processing tasks. However, their practical application is constrained by substantial memory and computational demands. Post-training quantization (PTQ) is considered an effective method to accelerate LLM inference. Despite its growing popularity in LLM model compression, PTQ deployment faces two major challenges. First, low-bit quantization leads to performance degradation. Second, restricted by the limited integer computing unit type on GPUs, quantized matrix operations with different precisions cannot be effectively accelerated. To address these issues, we introduce a novel arbitrary-bit quantization algorithm and inference framework, ABQ-LLM. It achieves superior performance across various quantization settings and enables efficient arbitrary-precision quantized inference on the GPU. ABQ-LLM introduces several key innovations: (1) a distribution correction method for transformer blocks to mitigate distribution differences caused by full quantization of weights and activations, improving performance at low bit-widths. (2) the bit balance strategy to counteract performance degradation from asymmetric distribution issues at very low bit-widths (e.g., 2-bit). (3) an innovative quantization acceleration framework that reconstructs the quantization matrix multiplication of arbitrary precision combinations based on BTC (Binary TensorCore) equivalents, gets rid of the limitations of INT4/INT8 computing units. ABQ-LLM can convert each component bit width gain into actual acceleration gain, maximizing performance under mixed precision(e.g., W6A6, W2A8). Based on W2*A8 quantization configuration on LLaMA-7B model, it achieved a WikiText2 perplexity of 7.59 (2.17downarrow vs 9.76 in AffineQuant). Compared to SmoothQuant, we realized 1.6times acceleration improvement and 2.7times memory compression gain.

As the size of large language models (LLMs) continues to grow, model compression without sacrificing accuracy has become a crucial challenge for deployment. While some quantization methods, such as GPTQ, have made progress in achieving acceptable 4-bit weight-only quantization, attempts at lower bit quantization often result in severe performance degradation. In this paper, we introduce a technique called norm tweaking, which can be used as a plugin in current PTQ methods to achieve high precision while being cost-efficient. Our approach is inspired by the observation that rectifying the quantized activation distribution to match its float counterpart can readily restore accuracy for LLMs. To achieve this, we carefully design a tweaking strategy that includes calibration data generation and channel-wise distance constraint to update the weights of normalization layers for better generalization. We conduct extensive experiments on various datasets using several open-sourced LLMs. Our method demonstrates significant improvements in both weight-only quantization and joint quantization of weights and activations, surpassing existing PTQ methods. On GLM-130B and OPT-66B, our method even achieves the same level of accuracy at 2-bit quantization as their float ones. Our simple and effective approach makes it more practical for real-world applications.

Large Language Models (LLMs) have recently demonstrated a remarkable success across various tasks. However, efficiently serving LLMs has been a challenge due to its large memory bottleneck, specifically in small batch inference settings (e.g. mobile devices). Weight-only quantization can be a promising approach, but sub-4 bit quantization remains a challenge due to large-magnitude activation outliers. To mitigate the undesirable outlier effect, we first propose per-IC quantization, a simple yet effective method that creates quantization groups within each input channel (IC) rather than the conventional per-output channel (OC). Our method is motivated by the observation that activation outliers affect the input dimension of the weight matrix, so similarly grouping the weights in the IC direction can isolate outliers to be within a group. We also find that activation outliers do not dictate quantization difficulty, and inherent weight sensitivities also exist. With per-IC quantization as a new outlier-friendly scheme, we then propose Adaptive Dimensions (AdaDim), a versatile quantization framework that can adapt to various weight sensitivity patterns. We demonstrate the effectiveness of AdaDim by augmenting prior methods such as Round-To-Nearest and GPTQ, showing significant improvements across various language modeling benchmarks for both base (up to +4.7% on MMLU) and instruction-tuned (up to +10% on HumanEval) LLMs.

Low-precision number formats are widely used in modern machine learning systems due to their efficiency. Accurate direction representation is key to the accuracy of vector operations. This work precisely explores the extent to which the direction of a vector can be represented by selecting its scalar elements from a common finite alphabet of a given size. This is standard practice in machine learning, where low-precision significands may be narrow-width floating-point or integer values. A geometric framework is introduced for analyzing the directional coverage of such product-structured codes. This work analytically quantifies the suboptimality gap between such product-structured codes and spherical codes for the vector as a whole, in both low and asymptotically high dimensions. Furthermore, within the product code class, it is proven that the standard formats of two's complement, fixed-point, and floating-point are suboptimal, again with quantified gap, pointing to the potential to develop new scalar number formats. Such scalar alphabets are numerically optimized across multiple block dimensions for directional coverage, including the dimension used in NVIDIA's NVFP4 format. Experimental results are presented comparing the performance of standard formats and the optimized alphabet. We find that for four bits, NVIDIA's choice of E2M1 closely approximates the optimized alphabet, providing a geometric explanation for its strong performance in low-precision machine learning workloads and an analytical understanding of the link between that superiority and block size. We provide open-source formal proofs in Lean for the theorems in this work, along with the experimental code and the optimized alphabets obtained.

The MXFP4 microscaling format, which partitions tensors into blocks of 32 elements sharing an E8M0 scaling factor, has emerged as a promising substrate for efficient LLM inference, backed by native hardware support on NVIDIA Blackwell Tensor Cores. However, activation outliers pose a unique challenge under this format: a single outlier inflates the shared block scale, compressing the effective dynamic range of the remaining elements and causing significant quantization error. Existing rotation-based remedies, including randomized Hadamard and learnable rotations, are data-agnostic and therefore unable to specifically target the channels where outliers concentrate. We propose DuQuant++, which adapts the outlier-aware fine-grained rotation of DuQuant to the MXFP4 format by aligning the rotation block size with the microscaling group size (B{=}32). Because each MXFP4 group possesses an independent scaling factor, the cross-block variance issue that necessitates dual rotations and a zigzag permutation in the original DuQuant becomes irrelevant, enabling DuQuant++ to replace the entire pipeline with a single outlier-aware rotation, which halves the online rotation cost while simultaneously smoothing the weight distribution. Extensive experiments on the LLaMA-3 family under MXFP4 W4A4 quantization show that DuQuant++ consistently achieves state-of-the-art performance. Our code is available at https://github.com/Hsu1023/DuQuant-v2.

Although quantization for linear layers has been widely used, its application to accelerate the attention process remains limited. SageAttention utilizes 8-bit matrix multiplication, 16-bit matrix multiplication with 16-bit accumulator, and precision-enhancing methods, implementing an accurate and 2x speedup kernel compared to FlashAttention2. To further enhance the efficiency of attention computation while maintaining precision, we propose SageAttention2, which utilizes significantly faster 4-bit matrix multiplication (Matmul) alongside additional precision-enhancing techniques. First, we propose to quantize matrixes (Q, K) to INT4 in a warp-level granularity and quantize matrixes (widetilde P, V) to FP8. Second, we propose a method to smooth Q and V, enhancing the accuracy of attention with INT4 QK and FP8 PV. Third, we analyze the quantization accuracy across timesteps and layers, then propose an adaptive quantization method to ensure the end-to-end metrics over various models. The operations per second (OPS) of SageAttention2 surpass FlashAttention2 and xformers by about 3x and 5x on RTX4090, respectively. Comprehensive experiments confirm that our approach incurs negligible end-to-end metrics loss across diverse models, including those for large language processing, image generation, and video generation. The codes are available at https://github.com/thu-ml/SageAttention.

The significant resource requirements associated with Large-scale Language Models (LLMs) have generated considerable interest in the development of techniques aimed at compressing and accelerating neural networks. Among these techniques, Post-Training Quantization (PTQ) has emerged as a subject of considerable interest due to its noteworthy compression efficiency and cost-effectiveness in the context of training. Existing PTQ methods for LLMs limit the optimization scope to scaling transformations between pre- and post-quantization weights. In this paper, we advocate for the direct optimization using equivalent Affine transformations in PTQ (AffineQuant). This approach extends the optimization scope and thus significantly minimizing quantization errors. Additionally, by employing the corresponding inverse matrix, we can ensure equivalence between the pre- and post-quantization outputs of PTQ, thereby maintaining its efficiency and generalization capabilities. To ensure the invertibility of the transformation during optimization, we further introduce a gradual mask optimization method. This method initially focuses on optimizing the diagonal elements and gradually extends to the other elements. Such an approach aligns with the Levy-Desplanques theorem, theoretically ensuring invertibility of the transformation. As a result, significant performance improvements are evident across different LLMs on diverse datasets. To illustrate, we attain a C4 perplexity of 15.76 (2.26 lower vs 18.02 in OmniQuant) on the LLaMA2-7B model of W4A4 quantization without overhead. On zero-shot tasks, AffineQuant achieves an average of 58.61 accuracy (1.98 lower vs 56.63 in OmniQuant) when using 4/4-bit quantization for LLaMA-30B, which setting a new state-of-the-art benchmark for PTQ in LLMs.

Quantizing large language models has become a standard way to reduce their memory and computational costs. Typically, existing methods focus on breaking down the problem into individual layer-wise sub-problems, and minimizing per-layer error, measured via various metrics. Yet, this approach currently lacks theoretical justification and the metrics employed may be sub-optimal. In this paper, we present a "linearity theorem" establishing a direct relationship between the layer-wise ell_2 reconstruction error and the model perplexity increase due to quantization. This insight enables two novel applications: (1) a simple data-free LLM quantization method using Hadamard rotations and MSE-optimal grids, dubbed HIGGS, which outperforms all prior data-free approaches such as the extremely popular NF4 quantized format, and (2) an optimal solution to the problem of finding non-uniform per-layer quantization levels which match a given compression constraint in the medium-bitwidth regime, obtained by reduction to dynamic programming. On the practical side, we demonstrate improved accuracy-compression trade-offs on Llama-3.1 and 3.2-family models, as well as on Qwen-family models. Further, we show that our method can be efficiently supported in terms of GPU kernels at various batch sizes, advancing both data-free and non-uniform quantization for LLMs.

The rapid advancement toward long-context reasoning and multi-modal intelligence has made the memory footprint of the Key-Value (KV) cache a dominant memory bottleneck for efficient deployment. While the established per-channel quantization effectively accommodates intrinsic channel-wise outliers in Key tensors, its efficacy diminishes under extreme compression. In this work, we revisit the inherent limitations of the per-channel quantization paradigm from both empirical and theoretical perspectives. Our analysis identifies Token Norm Imbalance (TNI) as the primary bottleneck to quantization fidelity. We demonstrate that TNI systematically amplifies errors when shared quantization parameters are required to span token groups exhibiting substantial norm disparities. Instead of relying on intricate quantization pipelines (e.g., TurboQuant), we propose OScaR (Omni-Scaled Canalized Rotation), an accurate and lightweight KV cache compression framework for X-LLMs (i.e., text-only, multi-modal, and omni-modal LLMs). Advancing the per-channel paradigm, OScaR employs Canalized Rotation followed by Omni-Token Scaling to mitigate TNI-induced sequence-dimensional variance both effectively and efficiently, further supported by our optimized system design and CUDA kernels. Extensive evaluations across X-LLMs show that OScaR consistently outperforms existing methods and achieves near-lossless performance under INT2 quantization, establishing it as a robust, low-complexity, and universal framework that defines a new Pareto front. Compared with the BF16 FlashDecoding-v2 baseline, our OScaR implementation achieves a notable up to 3.0x speedup in decoding, reduces memory footprint by 5.3x, and increases throughput by 4.1x. The code for OScaR is publicly available at https://github.com/ZunhaiSu/OScaR-KV-Quant.

Quantized neural network training optimizes a discrete, non-differentiable objective. The straight-through estimator (STE) enables backpropagation through surrogate gradients and is widely used. While previous studies have primarily focused on the properties of surrogate gradients and their convergence, the influence of quantization hyperparameters, such as bit width and quantization range, on learning dynamics remains largely unexplored. We theoretically show that in the high-dimensional limit, STE dynamics converge to a deterministic ordinary differential equation. This reveals that STE training exhibits a plateau followed by a sharp drop in generalization error, with plateau length depending on the quantization range. A fixed-point analysis quantifies the asymptotic deviation from the unquantized linear model. We also extend analytical techniques for stochastic gradient descent to nonlinear transformations of weights and inputs.

Deep neural network (DNN) deployment has been confined to larger hardware devices due to their expensive computational requirements. This challenge has recently reached another scale with the emergence of large language models (LLMs). In order to reduce both their memory footprint and latency, a promising technique is quantization. It consists in converting floating point representations to low bit-width fixed point representations, usually by assuming a uniform mapping onto a regular grid. This process, referred to in the literature as uniform quantization, may however be ill-suited as most DNN weights and activations follow a bell-shaped distribution. This is even worse on LLMs whose weight distributions are known to exhibit large, high impact, outlier values. In this work, we propose an improvement over the most commonly adopted way to tackle this limitation in deep learning models quantization, namely, non-uniform quantization. NUPES leverages automorphisms to preserve the scalar multiplications. Such transformations are derived from power functions. However, the optimization of the exponent parameter and weight values remains a challenging and novel problem which could not be solved with previous post training optimization techniques which only learn to round up or down weight values in order to preserve the predictive function. We circumvent this limitation with a new paradigm: learning new quantized weights over the entire quantized space. Similarly, we enable the optimization of the power exponent, i.e. the optimization of the quantization operator itself during training by alleviating all the numerical instabilities. The resulting predictive function is compatible with integer-only low-bit inference. We show the ability of the method to achieve state-of-the-art compression rates in both, data-free and data-driven configurations.

Recent advancements in machine learning achieved by Deep Neural Networks (DNNs) have been significant. While demonstrating high accuracy, DNNs are associated with a huge number of parameters and computations, which leads to high memory usage and energy consumption. As a result, deploying DNNs on devices with constrained hardware resources poses significant challenges. To overcome this, various compression techniques have been widely employed to optimize DNN accelerators. A promising approach is quantization, in which the full-precision values are stored in low bit-width precision. Quantization not only reduces memory requirements but also replaces high-cost operations with low-cost ones. DNN quantization offers flexibility and efficiency in hardware design, making it a widely adopted technique in various methods. Since quantization has been extensively utilized in previous works, there is a need for an integrated report that provides an understanding, analysis, and comparison of different quantization approaches. Consequently, we present a comprehensive survey of quantization concepts and methods, with a focus on image classification. We describe clustering-based quantization methods and explore the use of a scale factor parameter for approximating full-precision values. Moreover, we thoroughly review the training of a quantized DNN, including the use of a straight-through estimator and quantization regularization. We explain the replacement of floating-point operations with low-cost bitwise operations in a quantized DNN and the sensitivity of different layers in quantization. Furthermore, we highlight the evaluation metrics for quantization methods and important benchmarks in the image classification task. We also present the accuracy of the state-of-the-art methods on CIFAR-10 and ImageNet.

We study weight-only post-training quantization (PTQ), which quantizes the weights of a large language model (LLM) without retraining, using little or no calibration data. Weight-only PTQ is crucial for reducing the memory footprint and latency of LLM inference, especially in memory-bound, small-batch inference scenarios, such as personalized inference on edge devices. Despite its importance, irregular weight distributions with heavy-tailed outliers in LLMs complicate quantization, recently motivating rotation-based methods that transform weights into near-Gaussian distributions, which are more regular with fewer outliers, thereby reducing quantization error. In this work, we first derive the information-theoretically optimal bit allocation for Gaussianized weights under given bit budgets, revealing that fine-grained fractional-bit quantizers approaching the Gaussian distortion-rate bound are essential to achieve near-optimal quantization performance. To bridge this theoretical insight and practical implementation, we introduce Q-Palette, a versatile collection of fractional-bit quantizers that range from trellis-coded quantizers offering near-optimal distortion to simpler vector and scalar quantizers optimized for faster inference, all efficiently implemented with optimized CUDA kernels across various bitwidths. Furthermore, leveraging Q-Palette as a foundational component, we propose a novel mixed-scheme quantization framework, jointly optimizing quantizer choices and layer fusion decisions given resource constraints. The code is available at https://github.com/snu-mllab/Q-Palette.

As the size of large language models grows exponentially, GPU memory has become a bottleneck for adapting these models to downstream tasks. In this paper, we aim to push the limits of memory-efficient training by minimizing memory usage on model weights, gradients, and optimizer states, within a unified framework. Our idea is to eliminate both gradients and optimizer states using zeroth-order optimization, which approximates gradients by perturbing weights during forward passes to identify gradient directions. To minimize memory usage on weights, we employ model quantization, e.g., converting from bfloat16 to int4. However, directly applying zeroth-order optimization to quantized weights is infeasible due to the precision gap between discrete weights and continuous gradients, which would otherwise require de-quantization and re-quantization. To overcome this challenge, we propose Quantized Zeroth-order Optimization (QZO), a novel approach that perturbs the continuous quantization scale for gradient estimation and uses a directional derivative clipping method to stabilize training. QZO is orthogonal to both scalar-based and codebook-based post-training quantization methods. Compared to full-parameter fine-tuning in bfloat16, QZO can reduce the total memory cost by more than 18times for 4-bit LLMs, and enables fine-tuning Llama-2-13B and Stable Diffusion 3.5 Large within a single 24GB GPU.

While neural networks have been remarkably successful in a wide array of applications, implementing them in resource-constrained hardware remains an area of intense research. By replacing the weights of a neural network with quantized (e.g., 4-bit, or binary) counterparts, massive savings in computation cost, memory, and power consumption are attained. To that end, we generalize a post-training neural-network quantization method, GPFQ, that is based on a greedy path-following mechanism. Among other things, we propose modifications to promote sparsity of the weights, and rigorously analyze the associated error. Additionally, our error analysis expands the results of previous work on GPFQ to handle general quantization alphabets, showing that for quantizing a single-layer network, the relative square error essentially decays linearly in the number of weights -- i.e., level of over-parametrization. Our result holds across a range of input distributions and for both fully-connected and convolutional architectures thereby also extending previous results. To empirically evaluate the method, we quantize several common architectures with few bits per weight, and test them on ImageNet, showing only minor loss of accuracy compared to unquantized models. We also demonstrate that standard modifications, such as bias correction and mixed precision quantization, further improve accuracy.

Deep convolutional neural networks (DCNNs) have shown dominant performance in the task of super-resolution (SR). However, their heavy memory cost and computation overhead significantly restrict their practical deployments on resource-limited devices, which mainly arise from the floating-point storage and operations between weights and activations. Although previous endeavors mainly resort to fixed-point operations, quantizing both weights and activations with fixed coding lengths may cause significant performance drop, especially on low bits. Specifically, most state-of-the-art SR models without batch normalization have a large dynamic quantization range, which also serves as another cause of performance drop. To address these two issues, we propose a new quantization scheme termed PArameterized Max Scale (PAMS), which applies the trainable truncated parameter to explore the upper bound of the quantization range adaptively. Finally, a structured knowledge transfer (SKT) loss is introduced to fine-tune the quantized network. Extensive experiments demonstrate that the proposed PAMS scheme can well compress and accelerate the existing SR models such as EDSR and RDN. Notably, 8-bit PAMS-EDSR improves PSNR on Set5 benchmark from 32.095dB to 32.124dB with 2.42times compression ratio, which achieves a new state-of-the-art.

Large language models (LLMs) show great performance in various tasks, but face deployment challenges from limited memory capacity and bandwidth. Low-bit weight quantization can save memory and accelerate inference. Although floating-point (FP) formats show good performance in LLM quantization, they tend to perform poorly with small group sizes or sub-4 bits. We find the reason is that the absence of asymmetry in previous FP quantization makes it unsuitable for handling asymmetric value distribution of LLM weight tensors. In this work, we propose asymmetric FP quantization (AFPQ), which sets separate scales for positive and negative values. Our method leads to large accuracy improvements and can be easily plugged into other quantization methods, including GPTQ and AWQ, for better performance. Besides, no additional storage is needed compared with asymmetric integer (INT) quantization. The code is available at https://github.com/zhangsichengsjtu/AFPQ.

Large transformer models have demonstrated remarkable success. Post-training quantization (PTQ), which requires only a small dataset for calibration and avoids end-to-end retraining, is a promising solution for compressing these large models. Regrettably, existing PTQ methods typically exhibit non-trivial performance loss. We find that the performance bottleneck stems from over-consideration of hardware compatibility in the quantization process, compelling them to reluctantly employ simple quantizers, albeit at the expense of accuracy. With the above insights, we propose RepQuant, a novel PTQ framework with quantization-inference decoupling paradigm to address the above issues. RepQuant employs complex quantizers in the quantization process and simplified quantizers in the inference process, and performs mathematically equivalent transformations between the two through quantization scale reparameterization, thus ensuring both accurate quantization and efficient inference. More specifically, we focus on two components with extreme distributions: LayerNorm activations and Softmax activations. Initially, we apply channel-wise quantization and log2 quantization, respectively, which are tailored to their distributions. In particular, for the former, we introduce a learnable per-channel dual clipping scheme, which is designed to efficiently identify outliers in the unbalanced activations with fine granularity. Then, we reparameterize the scales to hardware-friendly layer-wise quantization and log2 quantization for inference. Moreover, quantized weight reconstruction is seamlessly integrated into the above procedure to further push the performance limits. Extensive experiments are performed on different large-scale transformer variants on multiple tasks, including vision, language, and multi-modal transformers, and RepQuant encouragingly demonstrates significant performance advantages.

Serving LLMs requires substantial memory due to the storage requirements of Key-Value (KV) embeddings in the KV cache, which grows with sequence length. An effective approach to compress KV cache is quantization. However, traditional quantization methods face significant memory overhead due to the need to store quantization constants (at least a zero point and a scale) in full precision per data block. Depending on the block size, this overhead can add 1 or 2 bits per quantized number. We introduce QJL, a new quantization approach that consists of a Johnson-Lindenstrauss (JL) transform followed by sign-bit quantization. In contrast to existing methods, QJL eliminates memory overheads by removing the need for storing quantization constants. We propose an asymmetric estimator for the inner product of two vectors and demonstrate that applying QJL to one vector and a standard JL transform without quantization to the other provides an unbiased estimator with minimal distortion. We have developed an efficient implementation of the QJL sketch and its corresponding inner product estimator, incorporating a lightweight CUDA kernel for optimized computation. When applied across various LLMs and NLP tasks to quantize the KV cache to only 3 bits, QJL demonstrates a more than fivefold reduction in KV cache memory usage without compromising accuracy, all while achieving faster runtime. Codes are available at https://github.com/amirzandieh/QJL.

The rapid scaling of language models (LMs) has resulted in unprecedented computational, memory, and energy requirements, making their training and deployment increasingly unsustainable. Quantization has emerged as an essential compression technique to reduce model size, alleviate memory bottlenecks, and accelerate inference. However, while uniform low-bit quantization (e.g., INT8, INT4) provides significant efficiency gains, it can degrade accuracy in sensitive components of transformer-based LMs. Mixed-precision quantization offers a promising alternative by selectively allocating precision across layers or within tensors to balance efficiency and accuracy. This survey provides a comprehensive overview of Mixed-Precision quantization frameworks for LMs (MXPLMs). We first review quantization fundamentals, including uniform and non-uniform quantizers, quantization granularity, and methods widely used in post-training quantization. We then categorize and compare recent MXPLM frameworks according to their bit allocation strategies and precision configurations across weights, activations, and key-value caches. A comparative analysis highlights differences in perplexity, zero-shot task performance, and deployment trade-offs. Furthermore, we contrast MXPLMs with earlier mixed-precision quantization methods for deep neural networks, identifying strategies that transfer and those that face challenges in the LM setting. Finally, we summarize open issues and future directions, including hardware-aware design, activation quantization, and scalable optimization methods for billion-parameter models. By consolidating recent advances, this work serves as a reference for understanding the current landscape and research prospects of mixed-precision quantization for large-scale language models.

The demand for inference on extremely large scale LLMs has seen enormous growth in the recent months. It made evident the colossal shortage of dedicated hardware capable of efficient and fast processing of the involved compute and memory movement. The problem is aggravated by the exploding raise in the lengths of the sequences being processed, since those require efficient on-chip storage of the KV-cache of size proportional to the sequence length. To make the required compute feasible and fit the involved data into available memory, numerous quantization techniques have been proposed that allow accurate quantization for both weights and activations. One of the main recent breakthroughs in this direction was introduction of the family of Block Floating Point (BFP) formats characterized by a block of mantissas with a shared scale factor. These enable memory- power-, and compute- efficient hardware support of the tensor operations and provide extremely good quantization accuracy. The main issues preventing widespread application of block formats is caused by the presence of outliers in weights and activations since those affect the accuracy of the other values in the same block. In this paper, we focus on the most critical problem of limited KV-cache storage. We propose a novel approach enabling usage of low precision BFP formats without compromising the resulting model accuracy. We exploit the common channel-wise patterns exhibited by the outliers to rearrange them in such a way, that their quantization quality is significantly improved. The methodology yields 2x savings in the memory footprint without significant degradation of the model's accuracy. Importantly, the rearrangement of channels happens at the compile time and thus has no impact on the inference latency.

Quantization has been widely used to compress and accelerate inference of large language models (LLMs). Existing methods focus on exploring the per-token dynamic calibration to ensure both inference acceleration and model accuracy under 4-bit quantization. However, in autoregressive generation inference of long sequences, the overhead of repeated dynamic quantization and dequantization steps becomes considerably expensive. In this work, we propose MergeQuant, an accurate and efficient per-channel static quantization framework. MergeQuant integrates the per-channel quantization steps with the corresponding scalings and linear mappings through a Quantization Step Migration (QSM) method, thereby eliminating the quantization overheads before and after matrix multiplication. Furthermore, in view of the significant differences between the different channel ranges, we propose dimensional reconstruction and adaptive clipping to address the non-uniformity of quantization scale factors and redistribute the channel variations to the subsequent modules to balance the parameter distribution under QSM. Within the static quantization setting of W4A4, MergeQuant reduces the accuracy gap on zero-shot tasks compared to FP16 baseline to 1.3 points on Llama-2-70B model. On Llama-2-7B model, MergeQuant achieves up to 1.77x speedup in decoding, and up to 2.06x speedup in end-to-end compared to FP16 baseline.

In this paper, we present a simple optimization-based preprocessing technique called Weight Magnitude Reduction (MagR) to improve the performance of post-training quantization. For each linear layer, we adjust the pre-trained floating-point weights by solving an ell_infty-regularized optimization problem. This process greatly diminishes the maximum magnitude of the weights and smooths out outliers, while preserving the layer's output. The preprocessed weights are centered more towards zero, which facilitates the subsequent quantization process. To implement MagR, we address the ell_infty-regularization by employing an efficient proximal gradient descent algorithm. Unlike existing preprocessing methods that involve linear transformations and subsequent post-processing steps, which can introduce significant overhead at inference time, MagR functions as a non-linear transformation, eliminating the need for any additional post-processing. This ensures that MagR introduces no overhead whatsoever during inference. Our experiments demonstrate that MagR achieves state-of-the-art performance on the Llama family of models. For example, we achieve a Wikitext2 perplexity of 5.95 on the LLaMA2-70B model for per-channel INT2 weight quantization without incurring any inference overhead.

The Muon optimizer has emerged as a compelling alternative to Adam for training large language models, achieving remarkable computational savings through gradient orthogonalization. However, Muon's optimizer state is more sensitive to quantization errors: because the orthogonalization discards the magnitudes of singular values and retains only directional information, even small quantization errors in singular vector directions are amplified in the update. In this work, we propose MuonQ, a low-bit Muon training framework built on the principle of directional fidelity optimization. First, we apply a pre-quantization normalization so that each step introduces quantization errors of the same magnitude, preventing the accumulated error from developing a preferred direction. Second, we introduce a structural decomposition that separately quantizes the dominant singular components via power iteration, ensuring that quantization errors perturb only singular value magnitudes rather than rotating singular vector directions. Third, we adopt μ-law companding quantization to allocate higher resolution to densely packed momentum values, shifting the quantization objective from outlier preservation to dense-region distinguishability. Together, these techniques enable stable 4-bit quantization of Muon's optimizer states. Pre-training experiments on GPT-style and LLaMA-style models demonstrate that MuonQ at 4-bit precision closely matches full-precision Muon in both training loss and downstream task accuracy, while reducing optimizer state memory by up to 7.3 times. Our code is available at https://github.com/YupengSu/MuonQ.

In this study, we propose a simple and efficient Non-Autoregressive (NAR) text-to-speech (TTS) system based on diffusion, named SimpleSpeech. Its simpleness shows in three aspects: (1) It can be trained on the speech-only dataset, without any alignment information; (2) It directly takes plain text as input and generates speech through an NAR way; (3) It tries to model speech in a finite and compact latent space, which alleviates the modeling difficulty of diffusion. More specifically, we propose a novel speech codec model (SQ-Codec) with scalar quantization, SQ-Codec effectively maps the complex speech signal into a finite and compact latent space, named scalar latent space. Benefits from SQ-Codec, we apply a novel transformer diffusion model in the scalar latent space of SQ-Codec. We train SimpleSpeech on 4k hours of a speech-only dataset, it shows natural prosody and voice cloning ability. Compared with previous large-scale TTS models, it presents significant speech quality and generation speed improvement. Demos are released.

Recently, quantization has been widely used for the compression and acceleration of large language models~(LLMs). Due to the outliers in LLMs, it is crucial to flatten weights and activations to minimize quantization error with the equally spaced quantization points. Prior research explores various pre-quantization transformations to suppress outliers, such as per-channel scaling and Hadamard transformation. However, we observe that these transformed weights and activations can still remain steep and outspread. In this paper, we propose FlatQuant (Fast and Learnable Affine Transformation), a new post-training quantization approach to enhance flatness of weights and activations. Our approach identifies optimal affine transformations tailored to each linear layer, calibrated in hours via a lightweight objective. To reduce runtime overhead, we apply Kronecker decomposition to the transformation matrices, and fuse all operations in FlatQuant into a single kernel. Extensive experiments show that FlatQuant sets up a new state-of-the-art quantization benchmark. For instance, it achieves less than 1% accuracy drop for W4A4 quantization on the LLaMA-3-70B model, surpassing SpinQuant by 7.5%. For inference latency, FlatQuant reduces the slowdown induced by pre-quantization transformation from 0.26x of QuaRot to merely 0.07x, bringing up to 2.3x speedup for prefill and 1.7x speedup for decoding, respectively. Code is available at: https://github.com/ruikangliu/FlatQuant.

Data clipping is crucial in reducing noise in quantization operations and improving the achievable accuracy of quantization-aware training (QAT). Current practices rely on heuristics to set clipping threshold scalars and cannot be shown to be optimal. We propose Optimally Clipped Tensors And Vectors (OCTAV), a recursive algorithm to determine MSE-optimal clipping scalars. Derived from the fast Newton-Raphson method, OCTAV finds optimal clipping scalars on the fly, for every tensor, at every iteration of the QAT routine. Thus, the QAT algorithm is formulated with provably minimum quantization noise at each step. In addition, we reveal limitations in common gradient estimation techniques in QAT and propose magnitude-aware differentiation as a remedy to further improve accuracy. Experimentally, OCTAV-enabled QAT achieves state-of-the-art accuracy on multiple tasks. These include training-from-scratch and retraining ResNets and MobileNets on ImageNet, and Squad fine-tuning using BERT models, where OCTAV-enabled QAT consistently preserves accuracy at low precision (4-to-6-bits). Our results require no modifications to the baseline training recipe, except for the insertion of quantization operations where appropriate.

Transformer-based large language models (LLMs) have achieved remarkable success as model sizes continue to grow, yet their deployment remains challenging due to significant computational and memory demands. Quantization has emerged as a promising solution, and state-of-the-art quantization algorithms for LLMs introduce the need for mixed-precision matrix multiplication (mpGEMM), where lower-precision weights are multiplied with higher-precision activations. Despite its benefits, current hardware accelerators such as GPUs and TPUs lack native support for efficient mpGEMM, leading to inefficient dequantization operations in the main sequential loop. To address this limitation, we introduce MixPE, a specialized mixed-precision processing element designed for efficient low-bit quantization in LLM inference. MixPE leverages two key innovations to minimize dequantization overhead and unlock the full potential of low-bit quantization. First, recognizing that scale and zero point are shared within each quantization group, we propose performing dequantization after per-group mpGEMM, significantly reducing dequantization overhead. Second, instead of relying on conventional multipliers, MixPE utilizes efficient shift\&add operations for multiplication, optimizing both computation and energy efficiency. Our experimental results demonstrate that MixPE surpasses the state-of-the-art quantization accelerators by 2.6times speedup and 1.4times energy reduction.

Learning-based 3D reconstruction models, represented by Visual Geometry Grounded Transformers (VGGTs), have made remarkable progress with the use of large-scale transformers. Their prohibitive computational and memory costs severely hinder real-world deployment. Post-Training Quantization (PTQ) has become a common practice for compressing and accelerating models. However, we empirically observe that PTQ faces unique obstacles when compressing billion-scale VGGTs: the data-independent special tokens induce heavy-tailed activation distributions, while the multi-view nature of 3D data makes calibration sample selection highly unstable. This paper proposes the first Quantization framework for VGGTs, namely QuantVGGT. This mainly relies on two technical contributions: First, we introduce Dual-Smoothed Fine-Grained Quantization, which integrates pre-global Hadamard rotation and post-local channel smoothing to mitigate heavy-tailed distributions and inter-channel variance robustly. Second, we design Noise-Filtered Diverse Sampling, which filters outliers via deep-layer statistics and constructs frame-aware diverse calibration clusters to ensure stable quantization ranges. Comprehensive experiments demonstrate that QuantVGGT achieves the state-of-the-art results across different benchmarks and bit-width, surpassing the previous state-of-the-art generic quantization method with a great margin. We highlight that our 4-bit QuantVGGT can deliver a 3.7times memory reduction and 2.5times acceleration in real-hardware inference, while maintaining reconstruction accuracy above 98\% of its full-precision counterpart. This demonstrates the vast advantages and practicality of QuantVGGT in resource-constrained scenarios. Our code is released in https://github.com/wlfeng0509/QuantVGGT.

Neural Audio Codecs (NACs) have become increasingly adopted in speech processing tasks due to their excellent rate-distortion performance and compatibility with Large Language Models (LLMs) as discrete feature representations for audio generation. While most existing codecs rely on Residual Vector Quantization (RVQ), Finite Scalar Quantization (FSQ) has recently emerged as a compelling alternative that simplifies training and natively supports single codebooks. We introduce NeuCodec, an FSQ-based NAC, and show that FSQ encodes baked-in redundancy which produces an encoding which is robust when transmitted through noisy channels. First, through an encoder distillation experiment, we show that two different encoders can learn to encode identical audio into vastly different code sequences whilst maintaining comparable reconstruction quality with the same quantizer and decoder. Second, we demonstrate that FSQ has vastly superior bit-level perturbation robustness by comparing the performance of RVQ and FSQ codecs when simulating the transmission of code sequences through a noisy channel.

Prevailing quantization techniques in Learned Image Compression (LIC) typically employ a static, uniform bit-width across all layers, failing to adapt to the highly diverse data distributions and sensitivity characteristics inherent in LIC models. This leads to a suboptimal trade-off between performance and efficiency. In this paper, we introduce DynaQuant, a novel framework for dynamic mixed-precision quantization that operates on two complementary levels. First, we propose content-aware quantization, where learnable scaling and offset parameters dynamically adapt to the statistical variations of latent features. This fine-grained adaptation is trained end-to-end using a novel Distance-aware Gradient Modulator (DGM), which provides a more informative learning signal than the standard Straight-Through Estimator. Second, we introduce a data-driven, dynamic bit-width selector that learns to assign an optimal bit precision to each layer, dynamically reconfiguring the network's precision profile based on the input data. Our fully dynamic approach offers substantial flexibility in balancing rate-distortion (R-D) performance and computational cost. Experiments demonstrate that DynaQuant achieves rd performance comparable to full-precision models while significantly reducing computational and storage requirements, thereby enabling the practical deployment of advanced LIC on diverse hardware platforms.

Second-order optimizers, maintaining a matrix termed a preconditioner, are superior to first-order optimizers in both theory and practice. The states forming the preconditioner and its inverse root restrict the maximum size of models trained by second-order optimizers. To address this, compressing 32-bit optimizer states to lower bitwidths has shown promise in reducing memory usage. However, current approaches only pertain to first-order optimizers. In this paper, we propose the first 4-bit second-order optimizers, exemplified by 4-bit Shampoo, maintaining performance similar to that of 32-bit ones. We show that quantizing the eigenvector matrix of the preconditioner in 4-bit Shampoo is remarkably better than quantizing the preconditioner itself both theoretically and experimentally. By rectifying the orthogonality of the quantized eigenvector matrix, we enhance the approximation of the preconditioner's eigenvector matrix, which also benefits the computation of its inverse 4-th root. Besides, we find that linear square quantization slightly outperforms dynamic tree quantization when quantizing second-order optimizer states. Evaluation on various networks for image classification demonstrates that our 4-bit Shampoo achieves comparable test accuracy to its 32-bit counterpart while being more memory-efficient. The source code will be made available.

As new optimizers gain traction and model quantization becomes standard for efficient deployment, a key question arises: how does the choice of optimizer affect model performance in the presence of quantization? Despite progress in both areas, systematic evidence on optimizer-quantization interactions remains limited. To fill this gap, we study the impact of optimizer choice on model robustness under quantization, considering both post-training quantization (PTQ), and quantization-aware training (QAT). We first train full-precision models, ranging from 50M to 1.5B parameters, with six optimizers, to explore the hyperparameter landscape, and establish well-tuned baselines. We then apply PTQ to evaluate how model performance degrades when trained with different optimizers. We find that outlier-related metrics, such as the max-to-mean ratio (MMR) and Kurtosis, fail to predict the PTQ performance across different optimizers. We show analytically that this is due to the MMR capturing only isolated layer errors, while ignoring how quantization errors accumulate and propagate through the network. To study the QAT degradation, we train quantized models from scratch and compare them to our original-precision baselines. We find that optimizers performing well in the original pretraining setup may not remain optimal under QAT, and that models trained with Shampoo show the lowest accuracy degradation. Finally, we derive scaling laws for quantization-aware training under different optimizers, showing that Shampoo achieves the highest parameter efficiency of all tested optimizers.

The key-value (KV) cache accelerates LLMs decoding by storing KV tensors from previously generated tokens. It reduces redundant computation at the cost of increased memory usage. To mitigate this overhead, existing approaches compress KV tensors into lower-bit representations; however, quantization errors can accumulate as more tokens are generated, potentially resulting in undesired outputs. In this paper, we introduce SQuat (Subspace-orthogonal KV cache quantization). It first constructs a subspace spanned by query tensors to capture the most critical task-related information. During key tensor quantization, it enforces that the difference between the (de)quantized and original keys remains orthogonal to this subspace, minimizing the impact of quantization errors on the attention mechanism's outputs. SQuat requires no model fine-tuning, no additional calibration dataset for offline learning, and is grounded in a theoretical framework we develop. Through numerical experiments, we show that our method reduces peak memory by 2.17 to 2.82, improves throughput by 2.45 to 3.60, and achieves more favorable benchmark scores than existing KV cache quantization algorithms.

Optimizer states are a major source of memory consumption for training neural networks, limiting the maximum trainable model within given memory budget. Compressing the optimizer states from 32-bit floating points to lower bitwidth is promising to reduce the training memory footprint, while the current lowest achievable bitwidth is 8-bit. In this work, we push optimizer states bitwidth down to 4-bit through a detailed empirical analysis of first and second moments. Specifically, we find that moments have complicated outlier patterns, that current block-wise quantization cannot accurately approximate. We use a smaller block size and propose to utilize both row-wise and column-wise information for better quantization. We further identify a zero point problem of quantizing the second moment, and solve this problem with a linear quantizer that excludes the zero point. Our 4-bit optimizers are evaluated on a wide variety of benchmarks including natural language understanding, machine translation, image classification, and instruction tuning. On all the tasks our optimizers can achieve comparable accuracy with their full-precision counterparts, while enjoying better memory efficiency.

Quantization has become one of the most effective methodologies to compress LLMs into smaller size. However, the existing quantization solutions still show limitations of either non-negligible accuracy drop or system inefficiency. In this paper, we make a comprehensive analysis of the general quantization principles on their effect to the triangle of accuracy, memory consumption and system efficiency. We propose MixLLM that explores the new optimization space of mixed-precision quantization between output features based on the insight that different output features matter differently in the model. MixLLM identifies the output features with high salience in the global view rather than within each single layer, effectively assigning the larger bit-width to output features that need it most to achieve good accuracy with low memory consumption. We present the sweet spot of quantization configuration of algorithm-system co-design that leads to high accuracy and system efficiency. To address the system challenge, we design the two-step dequantization to make use of the int8 Tensor Core easily and fast data type conversion to reduce dequantization overhead significantly, and present the software pipeline to overlap the memory access, dequantization and the MatMul to the best. Extensive experiments show that with only 10% more bits, the PPL increasement can be reduced from about 0.5 in SOTA to within 0.2 for Llama 3.1 70B, while on average MMLU-Pro improves by 0.93 over the SOTA of three popular models. In addition to its superior accuracy, MixLLM also achieves state-of-the-art system efficiency.

Transformer-based large language models (LLMs) have achieved great success with the growing model size. LLMs' size grows by 240times every two years, which outpaces the hardware progress and makes model inference increasingly costly. Model quantization is a promising approach to mitigate the widening gap between LLM size and hardware capacity. However, the existence of outliers, values with significant magnitudes, in LLMs makes existing quantization methods less effective. Prior outlier-aware quantization schemes adopt sparsity encoding techniques to separate outliers from normal values where the process requires global coordination (e.g., a global sparsity coordination list). This incurs complex encoding/decoding hardware logics and an extra orchestration controller for the computation between outlier and normal values. As such, it is not hardware-efficient and hence only achieves sub-optimal quantization benefits. We propose OliVe, an algorithm/architecture co-designed solution that adopts an outlier-victim pair (OVP) quantization and handles outlier values locally with low hardware overheads and high performance gains. The key insight of OliVe is that outliers are important while the normal values next to them are not. Thus those normal values (called victims) can be sacrificed to accommodate outliers. This enables a memory-aligned OVP encoding scheme, which can be efficiently integrated to the existing hardware accelerators like systolic array and tensor core. As a result, OliVe-based accelerator surpasses the existing outlier-aware accelerator, GOBO, by 4.5times speedup and 4.0times energy reduction, respectively, with a superior model accuracy.

Large language models (LLMs) have numerous applications across various domains, but their high computational and memory demands pose significant deployment challenges. Weight quantization is an effective technique for reducing the decoding latency and memory requirements of LLMs. Existing approaches primarily aim to maintain the quality of quantized models by preserving outliers in input features, but they still suffer significant quality loss at lower bit widths. Our approach builds on Optimal Brain Quantization (OBQ), an iterative weight-update-based quantization framework. We identify a key limitation of OBQ, specifically that its uniform quantization grid is suboptimal for maintaining model quality, as it introduces large errors to the task loss. To address this, we propose LeanQuant, which learns a loss-error-aware quantization grid by leveraging the inverse diagonal Hessian. Extensive empirical evaluations demonstrate that LeanQuant is both efficient and accurate; it can quantize a 70-billion-parameter model in 6 hours using a single 32GB GPU and performs favorably compared to competitive baselines in the 4-bit, 3-bit, and 2-bit regions.

The rapid scaling of Large Language Models (LLMs) elevates inference costs and compounds substantial deployment barriers. While quantization to 8 or 4 bits mitigates this, sub-3-bit methods face severe accuracy, scalability, and efficiency degradation. We propose Convolutional Code Quantization (CCQ), an inference-optimized quantization approach compressing LLMs to 2.0-2.75 bits with minimal accuracy loss. Departing from error-prone scalar quantization or slow vector quantization, CCQ integrates a hardware-aware bit-shift encoding and decoding solution with Convolutional Code, Hybrid Encoding, and Code Cluster, jointly overcoming accuracy-speed bottlenecks. We construct a lookup-free encoding space, enabling a linear mapping between the codebook and weight vectors, thereby optimizing inference performance. Meanwhile, by drawing on the concept of data mapping from vector quantization, we minimize the performance degradation of the model under extremely low-bit conditions. Experiments demonstrate that CCQ achieves outstanding performance on LLMs across various benchmarks. We compress DeepSeek-V3 (671B total parameters) to 184GB and ERNIE-4.5-300B-A47B to 89GB, enabling single-GPU deployment of ERNIE 4.5 and eliminating inter-card communication. The 2-bit ERNIE-4.5-300B-A47B model and inference engine have been open-sourced.

Quantization to low bitwidth is a standard approach for deploying large language models, however, a few extreme weights and activations stretch the dynamic range and reduce the effective resolution of the quantizer. A common mitigation approach is to apply some fixed orthogonal transforms, such as Hadamard matrices, before quantization, which typically reduces the dynamic range. Yet, these transforms ignore the statistics of the data, and their optimality is currently not understood. In this work, we derive, for the first time, closed-form optimal linear blockwise transforms for joint weight-activation quantization using standard data-free quantizers for common numerical formats. Specifically, we provide derivations of the optimal adaptive (data-aware) transforms for round-to-nearest (RTN), AbsMax-scaled block quantizers for both integer and floating-point formats. The resulting construction, which we call WUSH, combines a Hadamard backbone with a data-dependent component based on second-order moments, yielding a non-orthogonal transform that is provably optimal under mild assumptions and remains structured for efficient implementation. Preliminary experimental results show that our approach consistently improves upon the Hadamard transform for common formats.

There has been significant interest in "extreme" compression of large language models (LLMs), i.e., to 1-2 bits per parameter, which allows such models to be executed efficiently on resource-constrained devices. Existing work focused on improved one-shot quantization techniques and weight representations; yet, purely post-training approaches are reaching diminishing returns in terms of the accuracy-vs-bit-width trade-off. State-of-the-art quantization methods such as QuIP# and AQLM include fine-tuning (part of) the compressed parameters over a limited amount of calibration data; however, such fine-tuning techniques over compressed weights often make exclusive use of straight-through estimators (STE), whose performance is not well-understood in this setting. In this work, we question the use of STE for extreme LLM compression, showing that it can be sub-optimal, and perform a systematic study of quantization-aware fine-tuning strategies for LLMs. We propose PV-Tuning - a representation-agnostic framework that generalizes and improves upon existing fine-tuning strategies, and provides convergence guarantees in restricted cases. On the practical side, when used for 1-2 bit vector quantization, PV-Tuning outperforms prior techniques for highly-performant models such as Llama and Mistral. Using PV-Tuning, we achieve the first Pareto-optimal quantization for Llama 2 family models at 2 bits per parameter.

In recent years, huge progress has been made on learning neural implicit representations from multi-view images for 3D reconstruction. As an additional input complementing coordinates, using sinusoidal functions as positional encodings plays a key role in revealing high frequency details with coordinate-based neural networks. However, high frequency positional encodings make the optimization unstable, which results in noisy reconstructions and artifacts in empty space. To resolve this issue in a general sense, we introduce to learn neural implicit representations with quantized coordinates, which reduces the uncertainty and ambiguity in the field during optimization. Instead of continuous coordinates, we discretize continuous coordinates into discrete coordinates using nearest interpolation among quantized coordinates which are obtained by discretizing the field in an extremely high resolution. We use discrete coordinates and their positional encodings to learn implicit functions through volume rendering. This significantly reduces the variations in the sample space, and triggers more multi-view consistency constraints on intersections of rays from different views, which enables to infer implicit function in a more effective way. Our quantized coordinates do not bring any computational burden, and can seamlessly work upon the latest methods. Our evaluations under the widely used benchmarks show our superiority over the state-of-the-art. Our code is available at https://github.com/MachinePerceptionLab/CQ-NIR.

Model compression has emerged as a mainstream solution to reduce memory usage and computational overhead. This paper presents Group Quantization and Sparse Acceleration (GQSA), a novel compression technique tailored for LLMs. Traditional methods typically focus exclusively on either quantization or sparsification, but relying on a single strategy often results in significant performance loss at high compression rates. In contrast, GQSA integrates quantization and sparsification in a tightly coupled manner, leveraging GPU-friendly structured group sparsity and quantization for efficient acceleration. Building upon system-algorithm co-design principles, we propose a two-stage sparse optimization strategy that ensures the performance superiority of the compressed model. On the engine side, we introduce a "task-centric" parallel strategy, which, to the best of our knowledge, is the first application in the domain of sparse computing. Compared to the traditional 2:4 sparse method, the GQSA offers a more flexible and adjustable sparsity rate, as well as a higher weight compression rate, and is efficiently compatible with weight-only quantization methods. Experimental results demonstrate that, under the GQSA W4S50% compression setting, the model's accuracy surpasses that of both 2:4 pruning and W2 quantization. Furthermore, at the inference level, GQSA outperforms W2 by 1.26times and 2:4 pruning by 2.35times in terms of speed.

Straight-through estimator (STE), which enables the gradient flow over the non-differentiable function via approximation, has been favored in studies related to quantization-aware training (QAT). However, STE incurs unstable convergence during QAT, resulting in notable quality degradation in low precision. Recently, pseudoquantization training has been proposed as an alternative approach to updating the learnable parameters using the pseudo-quantization noise instead of STE. In this study, we propose a novel noise proxy-based integrated pseudoquantization (NIPQ) that enables unified support of pseudoquantization for both activation and weight by integrating the idea of truncation on the pseudo-quantization framework. NIPQ updates all of the quantization parameters (e.g., bit-width and truncation boundary) as well as the network parameters via gradient descent without STE instability. According to our extensive experiments, NIPQ outperforms existing quantization algorithms in various vision and language applications by a large margin.

This paper introduces an information-aware quantization framework that adaptively compresses the key-value (KV) cache in large language models (LLMs). Although prior work has underscored the distinct roles of key and value cache during inference, our systematic analysis -- examining singular value distributions, spectral norms, and Frobenius norms -- reveals, for the first time, that key matrices consistently exhibit higher norm values and are more sensitive to quantization than value matrices. Furthermore, our theoretical analysis shows that matrices with higher spectral norms amplify quantization errors more significantly. Motivated by these insights, we propose a mixed-precision quantization strategy, KV-AdaQuant, which allocates more bit-width for keys and fewer for values since key matrices have higher norm values. With the same total KV bit budget, this approach effectively mitigates error propagation across transformer layers while achieving significant memory savings. Our extensive experiments on multiple LLMs (1B--70B) demonstrate that our mixed-precision quantization scheme maintains high model accuracy even under aggressive compression. For instance, using 4-bit for Key and 2-bit for Value achieves an accuracy of 75.2%, whereas reversing the assignment (2-bit for Key and 4-bit for Value) yields only 54.7% accuracy. The code is available at https://tinyurl.com/kv-adaquant

In disentangled representation learning, a model is asked to tease apart a dataset's underlying sources of variation and represent them independently of one another. Since the model is provided with no ground truth information about these sources, inductive biases take a paramount role in enabling disentanglement. In this work, we construct an inductive bias towards encoding to and decoding from an organized latent space. Concretely, we do this by (i) quantizing the latent space into discrete code vectors with a separate learnable scalar codebook per dimension and (ii) applying strong model regularization via an unusually high weight decay. Intuitively, the latent space design forces the encoder to combinatorially construct codes from a small number of distinct scalar values, which in turn enables the decoder to assign a consistent meaning to each value. Regularization then serves to drive the model towards this parsimonious strategy. We demonstrate the broad applicability of this approach by adding it to both basic data-reconstructing (vanilla autoencoder) and latent-reconstructing (InfoGAN) generative models. For reliable evaluation, we also propose InfoMEC, a new set of metrics for disentanglement that is cohesively grounded in information theory and fixes well-established shortcomings in previous metrics. Together with regularization, latent quantization dramatically improves the modularity and explicitness of learned representations on a representative suite of benchmark datasets. In particular, our quantized-latent autoencoder (QLAE) consistently outperforms strong methods from prior work in these key disentanglement properties without compromising data reconstruction.

Post-training quantization (PTQ) is crucial for deploying efficient object detection models, like YOLO, on resource-constrained devices. However, the impact of reduced precision on model robustness to real-world input degradations such as noise, blur, and compression artifacts is a significant concern. This paper presents a comprehensive empirical study evaluating the robustness of YOLO models (nano to extra-large scales) across multiple precision formats: FP32, FP16 (TensorRT), Dynamic UINT8 (ONNX), and Static INT8 (TensorRT). We introduce and evaluate a degradation-aware calibration strategy for Static INT8 PTQ, where the TensorRT calibration process is exposed to a mix of clean and synthetically degraded images. Models were benchmarked on the COCO dataset under seven distinct degradation conditions (including various types and levels of noise, blur, low contrast, and JPEG compression) and a mixed-degradation scenario. Results indicate that while Static INT8 TensorRT engines offer substantial speedups (~1.5-3.3x) with a moderate accuracy drop (~3-7% mAP50-95) on clean data, the proposed degradation-aware calibration did not yield consistent, broad improvements in robustness over standard clean-data calibration across most models and degradations. A notable exception was observed for larger model scales under specific noise conditions, suggesting model capacity may influence the efficacy of this calibration approach. These findings highlight the challenges in enhancing PTQ robustness and provide insights for deploying quantized detectors in uncontrolled environments. All code and evaluation tables are available at https://github.com/AllanK24/QRID.

Post-training quantization (PTQ) has driven attention to producing efficient large language models (LLMs) with ultra-low costs. Since hand-craft quantization parameters lead to low performance in low-bit quantization, recent methods optimize the quantization parameters through block-wise reconstruction between the floating-point and quantized models. However, these methods suffer from two challenges: accumulated errors from independent one-by-one block quantization and reconstruction difficulties from extreme weight and activation outliers. To address these two challenges, we propose CBQ, a cross-block reconstruction-based PTQ method for LLMs. To reduce error accumulation, we introduce a cross-block dependency with the aid of a homologous reconstruction scheme to build the long-range dependency between adjacent multi-blocks with overlapping. To reduce reconstruction difficulty, we design a coarse-to-fine pre-processing (CFP) to truncate weight outliers and dynamically scale activation outliers before optimization, and an adaptive rounding scheme, called LoRA-Rounding, with two low-rank learnable matrixes to further rectify weight quantization errors. Extensive experiments demonstrate that: (1) CBQ pushes both activation and weight quantization to low-bit settings W4A4, W4A8, and W2A16. (2) CBQ achieves better performance than the existing state-of-the-art methods on various LLMs and benchmark datasets.

Large language models (LLMs) are increasingly utilized for complex tasks requiring longer context lengths, with some models supporting up to 128K or 1M tokens. This trend, however, presents significant challenges in inference speed and memory management. Quantization emerges as a promising approach to address the widening gap between LLM size and memory capacity. However, traditional quantization schemes often yield suboptimal compression results for KV caches due to two key factors: i) On-the-fly quantization and de-quantization, causing significant performance overhead; ii) Prevalence of outliers in KV values, challenging low-bitwidth uniform quantization. To this end, we propose MILLION, a novel quantization framework achieving low-bitwidth KV cache through product quantization. First, we conduct a thorough analysis of KV cache distribution, revealing the limitations of existing quantization schemes. Second, we introduce a non-uniform quantization algorithm based on product quantization, which efficiently compresses data while preserving accuracy. Third, we develop a high-performance GPU inference framework with efficient attention kernel and pipeline design for MILLION that leverages sparse computation and asynchronous quantization, significantly enhancing inference speed. Comprehensive evaluation results demonstrate that MILLION can achieve 4 bits quantization with trivial perplexity and accuracy loss, and achieve 2.09x end-to-end performance gains at 32K context length. Code is released at https://github.com/ZongwuWang/MILLION.

Efficiently serving neural network models with low latency is becoming more challenging due to increasing model complexity and parameter count. Model quantization offers a solution which simultaneously reduces memory footprint and compute requirements. However, aggressive quantization may lead to an unacceptable loss in model accuracy owing to differences in sensitivity to numerical imperfection across different layers in the model. To address this challenge, we propose a mixed-precision post training quantization (PTQ) approach that assigns different numerical precisions to tensors in a network based on their specific needs, for a reduced memory footprint and improved latency while preserving model accuracy. Previous works rely on layer-wise Hessian information to determine numerical precision, but as we demonstrate, Hessian estimation is typically insufficient in determining an effective ordering of layer sensitivities. We address this by augmenting the estimated Hessian with additional information to capture inter-layer dependencies. We demonstrate that this consistently improves PTQ performance along the accuracy-latency Pareto frontier across multiple models. Our method combines second-order information and inter-layer dependencies to guide a bisection search, finding quantization configurations within a user-configurable model accuracy degradation range. We evaluate the effectiveness of our method on the ResNet50, MobileNetV2, and BERT models. Our experiments demonstrate latency reductions compared to a 16-bit baseline of 25.48%, 21.69%, and 33.28% respectively, while maintaining model accuracy to within 99.99% of the baseline model.

Multimodal Large Language Models (MLLMs) have achieved remarkable success across various applications, yet their computational overhead during deployment remains a critical challenge. While Key-Value (KV) caching improves inference efficiency by trading memory for computation, the growing memory footprint from storing extensive KV caches reduces throughput and limits long-term execution on devices with constrained GPU memory. Existing approaches primarily focus on dropping unimportant tokens to reduce the KV cache size, mitigating memory constraints at the cost of potential information loss. In contrast, we propose a simple yet effective visual quantization strategy that preserves all visual tokens while significantly reducing memory consumption. To achieve an extreme quantization ratio, i.e., 1-bit quantization, we propose group-specific quantization and quantile-based quantization approaches, motivated by the inherent patterns of the KV cache. Our method is plug-and-play, enabling seamless integration into various MLLMs to improve memory efficiency without architectural modifications. Extensive experiments demonstrate that our approach effectively reduces memory overhead while maintaining computational efficiency and preserving multimodal performance.

Text-to-image diffusion models have emerged as a powerful framework for high-quality image generation given textual prompts. Their success has driven the rapid development of production-grade diffusion models that consistently increase in size and already contain billions of parameters. As a result, state-of-the-art text-to-image models are becoming less accessible in practice, especially in resource-limited environments. Post-training quantization (PTQ) tackles this issue by compressing the pretrained model weights into lower-bit representations. Recent diffusion quantization techniques primarily rely on uniform scalar quantization, providing decent performance for the models compressed to 4 bits. This work demonstrates that more versatile vector quantization (VQ) may achieve higher compression rates for large-scale text-to-image diffusion models. Specifically, we tailor vector-based PTQ methods to recent billion-scale text-to-image models (SDXL and SDXL-Turbo), and show that the diffusion models of 2B+ parameters compressed to around 3 bits using VQ exhibit the similar image quality and textual alignment as previous 4-bit compression techniques.

Mixed-Precision Quantization~(MQ) can achieve a competitive accuracy-complexity trade-off for models. Conventional training-based search methods require time-consuming candidate training to search optimized per-layer bit-width configurations in MQ. Recently, some training-free approaches have presented various MQ proxies and significantly improve search efficiency. However, the correlation between these proxies and quantization accuracy is poorly understood. To address the gap, we first build the MQ-Bench-101, which involves different bit configurations and quantization results. Then, we observe that the existing training-free proxies perform weak correlations on the MQ-Bench-101. To efficiently seek superior proxies, we develop an automatic search of proxies framework for MQ via evolving algorithms. In particular, we devise an elaborate search space involving the existing proxies and perform an evolution search to discover the best correlated MQ proxy. We proposed a diversity-prompting selection strategy and compatibility screening protocol to avoid premature convergence and improve search efficiency. In this way, our Evolving proxies for Mixed-precision Quantization~(EMQ) framework allows the auto-generation of proxies without heavy tuning and expert knowledge. Extensive experiments on ImageNet with various ResNet and MobileNet families demonstrate that our EMQ obtains superior performance than state-of-the-art mixed-precision methods at a significantly reduced cost. The code will be released.

Retrieval-Augmented Generation enhances language models by retrieving relevant information from external knowledge bases, relying on high-dimensional vector embeddings typically stored in float32 precision. However, storing these embeddings at scale presents significant memory challenges. To address this issue, we systematically investigate on MTEB benchmark two complementary optimization strategies: quantization, evaluating standard formats (float16, int8, binary) and low-bit floating-point types (float8), and dimensionality reduction, assessing methods like PCA, Kernel PCA, UMAP, Random Projections and Autoencoders. Our results show that float8 quantization achieves a 4x storage reduction with minimal performance degradation (<0.3%), significantly outperforming int8 quantization at the same compression level, being simpler to implement. PCA emerges as the most effective dimensionality reduction technique. Crucially, combining moderate PCA (e.g., retaining 50% dimensions) with float8 quantization offers an excellent trade-off, achieving 8x total compression with less performance impact than using int8 alone (which provides only 4x compression). To facilitate practical application, we propose a methodology based on visualizing the performance-storage trade-off space to identify the optimal configuration that maximizes performance within their specific memory constraints.

Post-training quantization (PTQ) is widely regarded as one of the most efficient compression methods practically, benefitting from its data privacy and low computation costs. We argue that an overlooked problem of oscillation is in the PTQ methods. In this paper, we take the initiative to explore and present a theoretical proof to explain why such a problem is essential in PTQ. And then, we try to solve this problem by introducing a principled and generalized framework theoretically. In particular, we first formulate the oscillation in PTQ and prove the problem is caused by the difference in module capacity. To this end, we define the module capacity (ModCap) under data-dependent and data-free scenarios, where the differentials between adjacent modules are used to measure the degree of oscillation. The problem is then solved by selecting top-k differentials, in which the corresponding modules are jointly optimized and quantized. Extensive experiments demonstrate that our method successfully reduces the performance drop and is generalized to different neural networks and PTQ methods. For example, with 2/4 bit ResNet-50 quantization, our method surpasses the previous state-of-the-art method by 1.9%. It becomes more significant on small model quantization, e.g. surpasses BRECQ method by 6.61% on MobileNetV2*0.5.

Large Language Models (LLMs) have demonstrated remarkable capabilities but typically require extensive computational resources and memory for inference. Post-training quantization (PTQ) can effectively reduce these demands by storing weights in lower bit-width formats. However, standard uniform quantization often leads to notable performance degradation, particularly in low-bit scenarios. In this work, we introduce a Grouped Lattice Vector Quantization (GLVQ) framework that assigns each group of weights a customized lattice codebook, defined by a learnable generation matrix. To address the non-differentiability of the quantization process, we adopt Babai rounding to approximate nearest-lattice-point search during training, which enables stable optimization of the generation matrices. Once trained, decoding reduces to a simple matrix-vector multiplication, yielding an efficient and practical quantization pipeline. Experiments on multiple benchmarks show that our approach achieves a better trade-off between model size and accuracy compared to existing post-training quantization baselines, highlighting its effectiveness in deploying large models under stringent resource constraints. Our source code is available on GitHub repository: https://github.com/xzhang9308/GLVQ.

Diffusion Models (DM) have revolutionized the text-to-image visual generation process. However, the large computational cost and model footprint of DMs hinders practical deployment, especially on edge devices. Post-training quantization (PTQ) is a lightweight method to alleviate these burdens without the need for training or fine-tuning. While recent DM PTQ methods achieve W4A8 on integer-based PTQ, two key limitations remain: First, while most existing DM PTQ methods evaluate on classical DMs like Stable Diffusion XL, 1.5 or earlier, which use convolutional U-Nets, newer Diffusion Transformer (DiT) models like the PixArt series, Hunyuan and others adopt fundamentally different transformer backbones to achieve superior image synthesis. Second, integer (INT) quantization is prevailing in DM PTQ but doesn't align well with the network weight and activation distribution, while Floating-Point Quantization (FPQ) is still under-investigated, yet it holds the potential to better align the weight and activation distributions in low-bit settings for DiT. In response, we introduce FP4DiT, a PTQ method that leverages FPQ to achieve W4A6 quantization. Specifically, we extend and generalize the Adaptive Rounding PTQ technique to adequately calibrate weight quantization for FPQ and demonstrate that DiT activations depend on input patch data, necessitating robust online activation quantization techniques. Experimental results demonstrate that FP4DiT outperforms integer-based PTQ at W4A6 and W4A8 precision and generates convincing visual content on PixArt-alpha, PixArt-Sigma and Hunyuan in terms of several T2I metrics such as HPSv2 and CLIP.

Quantization addresses the high resource demand for large language models (LLMs) by alleviating memory pressure and bandwidth congestion and providing significantly scaled compute power with a tolerable impact on accuracy. Four-bit floating point (FP4), the lowest-precision format that preserves essential numerical properties such as exponent and sign, has begun to be adopted in cutting-edge architectures, including Blackwell and AMD CDNA, to support LLM quantization and reduce deployment costs. Although aggressive quantization can yield efficiency gains, the quantization sensitivity of within-transformer layers and whether these sensitivities generalize across existing FP4 formats and model scales remain underexplored. To elucidate quantization sensitivity, this study conducts a systematic analysis of two FP4 formats, MXFP4 and NVFP4, across three Qwen2.5 model scales (0.5B, 7B, and 14B), using controlled component-wise and block-wise isolation methodologies. We observe that MLP up- and down-projection layers consistently dominate in terms of sensitivity, while gate and attention projections are moderately and substantially less sensitive to FP4 quantization, respectively. We further find that sensitivity does not universally localize to the final blocks, but early blocks can be highly sensitive, particularly under MXFP4. Our results provide a diagnostic characterization of the inference behavior of FP4 across components, depths, and FP4 formats.

Vision tokenizers have gained a lot of attraction due to their scalability and compactness; previous works depend on old-school GAN-based hyperparameters, biased comparisons, and a lack of comprehensive analysis of the scaling behaviours. To tackle those issues, we introduce Grouped Spherical Quantization (GSQ), featuring spherical codebook initialization and lookup regularization to constrain codebook latent to a spherical surface. Our empirical analysis of image tokenizer training strategies demonstrates that GSQ-GAN achieves superior reconstruction quality over state-of-the-art methods with fewer training iterations, providing a solid foundation for scaling studies. Building on this, we systematically examine the scaling behaviours of GSQ, specifically in latent dimensionality, codebook size, and compression ratios, and their impact on model performance. Our findings reveal distinct behaviours at high and low spatial compression levels, underscoring challenges in representing high-dimensional latent spaces. We show that GSQ can restructure high-dimensional latent into compact, low-dimensional spaces, thus enabling efficient scaling with improved quality. As a result, GSQ-GAN achieves a 16x down-sampling with a reconstruction FID (rFID) of 0.50.

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model compression techniques, notably quantization and sparsification, which have emerged to mitigate the steep computational demands associated with large-scale training and inference. This paper investigates the interplay between scaling laws and compression formats, exploring whether a unified scaling framework can accurately predict model performance when training occurs over various compressed representations, such as sparse, scalar-quantized, sparse-quantized or even vector-quantized formats. Our key contributions include validating a general scaling law formulation and showing that it is applicable both individually but also composably across compression types. Based on this, our main finding is demonstrating both theoretically and empirically that there exists a simple "capacity" metric -- based on the representation's ability to fit random Gaussian data -- which can robustly predict parameter efficiency across multiple compressed representations. On the practical side, we extend our formulation to directly compare the accuracy potential of different compressed formats, and to derive better algorithms for training over sparse-quantized formats.

The complicated architecture and high training cost of vision transformers urge the exploration of post-training quantization. However, the heavy-tailed distribution of vision transformer activations hinders the effectiveness of previous post-training quantization methods, even with advanced quantizer designs. Instead of tuning the quantizer to better fit the complicated activation distribution, this paper proposes NoisyQuant, a quantizer-agnostic enhancement for the post-training activation quantization performance of vision transformers. We make a surprising theoretical discovery that for a given quantizer, adding a fixed Uniform noisy bias to the values being quantized can significantly reduce the quantization error under provable conditions. Building on the theoretical insight, NoisyQuant achieves the first success on actively altering the heavy-tailed activation distribution with additive noisy bias to fit a given quantizer. Extensive experiments show NoisyQuant largely improves the post-training quantization performance of vision transformer with minimal computation overhead. For instance, on linear uniform 6-bit activation quantization, NoisyQuant improves SOTA top-1 accuracy on ImageNet by up to 1.7%, 1.1% and 0.5% for ViT, DeiT, and Swin Transformer respectively, achieving on-par or even higher performance than previous nonlinear, mixed-precision quantization.

Diffusion models have demonstrated remarkable capabilities in image synthesis and related generative tasks. Nevertheless, their practicality for low-latency real-world applications is constrained by substantial computational costs and latency issues. Quantization is a dominant way to compress and accelerate diffusion models, where post-training quantization (PTQ) and quantization-aware training (QAT) are two main approaches, each bearing its own properties. While PTQ exhibits efficiency in terms of both time and data usage, it may lead to diminished performance in low bit-width. On the other hand, QAT can alleviate performance degradation but comes with substantial demands on computational and data resources. To capitalize on the advantages while avoiding their respective drawbacks, we introduce a data-free and parameter-efficient fine-tuning framework for low-bit diffusion models, dubbed EfficientDM, to achieve QAT-level performance with PTQ-like efficiency. Specifically, we propose a quantization-aware variant of the low-rank adapter (QALoRA) that can be merged with model weights and jointly quantized to low bit-width. The fine-tuning process distills the denoising capabilities of the full-precision model into its quantized counterpart, eliminating the requirement for training data. We also introduce scale-aware optimization and employ temporal learned step-size quantization to further enhance performance. Extensive experimental results demonstrate that our method significantly outperforms previous PTQ-based diffusion models while maintaining similar time and data efficiency. Specifically, there is only a marginal 0.05 sFID increase when quantizing both weights and activations of LDM-4 to 4-bit on ImageNet 256x256. Compared to QAT-based methods, our EfficientDM also boasts a 16.2x faster quantization speed with comparable generation quality.

Quantization is a crucial technique for deploying deep learning models on resource-constrained devices, such as embedded FPGAs. Prior efforts mostly focus on quantizing matrix multiplications, leaving other layers like BatchNorm or shortcuts in floating-point form, even though fixed-point arithmetic is more efficient on FPGAs. A common practice is to fine-tune a pre-trained model to fixed-point for FPGA deployment, but potentially degrading accuracy. This work presents QFX, a novel trainable fixed-point quantization approach that automatically learns the binary-point position during model training. Additionally, we introduce a multiplier-free quantization strategy within QFX to minimize DSP usage. QFX is implemented as a PyTorch-based library that efficiently emulates fixed-point arithmetic, supported by FPGA HLS, in a differentiable manner during backpropagation. With minimal effort, models trained with QFX can readily be deployed through HLS, producing the same numerical results as their software counterparts. Our evaluation shows that compared to post-training quantization, QFX can quantize models trained with element-wise layers quantized to fewer bits and achieve higher accuracy on both CIFAR-10 and ImageNet datasets. We further demonstrate the efficacy of multiplier-free quantization using a state-of-the-art binarized neural network accelerator designed for an embedded FPGA (AMD Xilinx Ultra96 v2). We plan to release QFX in open-source format.

A lot of recent progress has been made in ultra low-bit quantization, promising significant improvements in latency, memory footprint and energy consumption on edge devices. Quantization methods such as Learned Step Size Quantization can achieve model accuracy that is comparable to full-precision floating-point baselines even with sub-byte quantization. However, it is extremely challenging to deploy these ultra low-bit quantized models on mainstream CPU devices because commodity SIMD (Single Instruction, Multiple Data) hardware typically supports no less than 8-bit precision. To overcome this limitation, we propose DeepGEMM, a lookup table based approach for the execution of ultra low-precision convolutional neural networks on SIMD hardware. The proposed method precomputes all possible products of weights and activations, stores them in a lookup table, and efficiently accesses them at inference time to avoid costly multiply-accumulate operations. Our 2-bit implementation outperforms corresponding 8-bit integer kernels in the QNNPACK framework by up to 1.74x on x86 platforms.

Recent years have witnessed an increasing interest in deploying LLMs on resource-constrained devices, among which quantization has emerged as a promising lightweight technique that converts full-precision model weights and activations into lower-bit formats. Existing weight quantization approaches can be roughly divided into three categories: Post-Training Quantization (PTQ) that calibrates quantized parameters on a small dataset without retraining but suffers from severe performance degradation below 4-bit, Quantization-Aware Training (QAT) that searches low-bit parameters using surrogate gradients but demands substantial computational resources, and Quantization-Aware Distillation that integrates QAT with knowledge transfer from a full-precision teacher but manually selects features to distill and relies heavily on teacher-specific data. In this paper, we propose EdgeRazor, a lightweight framework for LLMs with mixed-precision and extremely low-bit weight quantization. The EdgeRazor framework contains three modules: Mixed-Precision Quantization-Aware Distillation for the fine-grained control of precision, Adaptive Feature Distillation that derives an n-bit student from its 16-bit teacher, and Entropy-Aware KL Divergence on both human-annotated and distilled datasets, whose forward-reverse balance is determined solely by the teacher's output distribution. Empirical investigations of EdgeRazor are conducted on base, instruction-tuned, and multimodal LLMs. Notably, EdgeRazor with 1.88-bit surpasses all contenders with the 3-bit precision, especially outperforms the leading 2-bit PTQ methods by 11.3 points, within a 4-10times lower training budget than the leading QAT approach. EdgeRazor delivers higher compression ratios at all bit width; the 1.58-bit Qwen3-0.6B reduces storage from 1.41 GB to 0.28 GB while accelerating decoding by 15.1times relative to the 16-bit baseline.

Diffusion models are emerging models that generate images by iteratively denoising random Gaussian noise using deep neural networks. These models typically exhibit high computational and memory demands, necessitating effective post-training quantization for high-performance inference. Recent works propose low-bitwidth (e.g., 8-bit or 4-bit) quantization for diffusion models, however 4-bit integer quantization typically results in low-quality images. We observe that on several widely used hardware platforms, there is little or no difference in compute capability between floating-point and integer arithmetic operations of the same bitwidth (e.g., 8-bit or 4-bit). Therefore, we propose an effective floating-point quantization method for diffusion models that provides better image quality compared to integer quantization methods. We employ a floating-point quantization method that was effective for other processing tasks, specifically computer vision and natural language tasks, and tailor it for diffusion models by integrating weight rounding learning during the mapping of the full-precision values to the quantized values in the quantization process. We comprehensively study integer and floating-point quantization methods in state-of-the-art diffusion models. Our floating-point quantization method not only generates higher-quality images than that of integer quantization methods, but also shows no noticeable degradation compared to full-precision models (32-bit floating-point), when both weights and activations are quantized to 8-bit floating-point values, while has minimal degradation with 4-bit weights and 8-bit activations.

There is a constant need for high-performing and computationally efficient neural network models for image super-resolution: computationally efficient models can be used via low-capacity devices and reduce carbon footprints. One way to obtain such models is to compress models, e.g. quantization. Another way is a neural architecture search that automatically discovers new, more efficient solutions. We propose a novel quantization-aware procedure, the QuantNAS that combines pros of these two approaches. To make QuantNAS work, the procedure looks for quantization-friendly super-resolution models. The approach utilizes entropy regularization, quantization noise, and Adaptive Deviation for Quantization (ADQ) module to enhance the search procedure. The entropy regularization technique prioritizes a single operation within each block of the search space. Adding quantization noise to parameters and activations approximates model degradation after quantization, resulting in a more quantization-friendly architectures. ADQ helps to alleviate problems caused by Batch Norm blocks in super-resolution models. Our experimental results show that the proposed approximations are better for search procedure than direct model quantization. QuantNAS discovers architectures with better PSNR/BitOps trade-off than uniform or mixed precision quantization of fixed architectures. We showcase the effectiveness of our method through its application to two search spaces inspired by the state-of-the-art SR models and RFDN. Thus, anyone can design a proper search space based on an existing architecture and apply our method to obtain better quality and efficiency. The proposed procedure is 30\% faster than direct weight quantization and is more stable.

Current model quantization methods have shown their promising capability in reducing storage space and computation complexity. However, due to the diversity of quantization forms supported by different hardware, one limitation of existing solutions is that usually require repeated optimization for different scenarios. How to construct a model with flexible quantization forms has been less studied. In this paper, we explore a one-shot network quantization regime, named Elastic Quantization Neural Networks (EQ-Net), which aims to train a robust weight-sharing quantization supernet. First of all, we propose an elastic quantization space (including elastic bit-width, granularity, and symmetry) to adapt to various mainstream quantitative forms. Secondly, we propose the Weight Distribution Regularization Loss (WDR-Loss) and Group Progressive Guidance Loss (GPG-Loss) to bridge the inconsistency of the distribution for weights and output logits in the elastic quantization space gap. Lastly, we incorporate genetic algorithms and the proposed Conditional Quantization-Aware Accuracy Predictor (CQAP) as an estimator to quickly search mixed-precision quantized neural networks in supernet. Extensive experiments demonstrate that our EQ-Net is close to or even better than its static counterparts as well as state-of-the-art robust bit-width methods. Code can be available at https://github.com/xuke225/EQ-Net.git{https://github.com/xuke225/EQ-Net}.

Diffusion models have been proven highly effective at generating high-quality images. However, as these models grow larger, they require significantly more memory and suffer from higher latency, posing substantial challenges for deployment. In this work, we aim to accelerate diffusion models by quantizing their weights and activations to 4 bits. At such an aggressive level, both weights and activations are highly sensitive, where conventional post-training quantization methods for large language models like smoothing become insufficient. To overcome this limitation, we propose SVDQuant, a new 4-bit quantization paradigm. Different from smoothing which redistributes outliers between weights and activations, our approach absorbs these outliers using a low-rank branch. We first consolidate the outliers by shifting them from activations to weights, then employ a high-precision low-rank branch to take in the weight outliers with Singular Value Decomposition (SVD). This process eases the quantization on both sides. However, na\"{\i}vely running the low-rank branch independently incurs significant overhead due to extra data movement of activations, negating the quantization speedup. To address this, we co-design an inference engine Nunchaku that fuses the kernels of the low-rank branch into those of the low-bit branch to cut off redundant memory access. It can also seamlessly support off-the-shelf low-rank adapters (LoRAs) without the need for re-quantization. Extensive experiments on SDXL, PixArt-Sigma, and FLUX.1 validate the effectiveness of SVDQuant in preserving image quality. We reduce the memory usage for the 12B FLUX.1 models by 3.5times, achieving 3.0times speedup over the 4-bit weight-only quantized baseline on the 16GB laptop 4090 GPU, paving the way for more interactive applications on PCs. Our quantization library and inference engine are open-sourced.

Consistency learning with feature perturbation is a widely used strategy in semi-supervised medical image segmentation. However, many existing perturbation methods rely on dropout, and thus require a careful manual tuning of the dropout rate, which is a sensitive hyperparameter and often difficult to optimize and may lead to suboptimal regularization. To overcome this limitation, we propose VQ-Seg, the first approach to employ vector quantization (VQ) to discretize the feature space and introduce a novel and controllable Quantized Perturbation Module (QPM) that replaces dropout. Our QPM perturbs discrete representations by shuffling the spatial locations of codebook indices, enabling effective and controllable regularization. To mitigate potential information loss caused by quantization, we design a dual-branch architecture where the post-quantization feature space is shared by both image reconstruction and segmentation tasks. Moreover, we introduce a Post-VQ Feature Adapter (PFA) to incorporate guidance from a foundation model (FM), supplementing the high-level semantic information lost during quantization. Furthermore, we collect a large-scale Lung Cancer (LC) dataset comprising 828 CT scans annotated for central-type lung carcinoma. Extensive experiments on the LC dataset and other public benchmarks demonstrate the effectiveness of our method, which outperforms state-of-the-art approaches. Code available at: https://github.com/script-Yang/VQ-Seg.

Mixed-precision quantization has been widely applied on deep neural networks (DNNs) as it leads to significantly better efficiency-accuracy tradeoffs compared to uniform quantization. Meanwhile, determining the exact precision of each layer remains challenging. Previous attempts on bit-level regularization and pruning-based dynamic precision adjustment during training suffer from noisy gradients and unstable convergence. In this work, we propose Continuous Sparsification Quantization (CSQ), a bit-level training method to search for mixed-precision quantization schemes with improved stability. CSQ stabilizes the bit-level mixed-precision training process with a bi-level gradual continuous sparsification on both the bit values of the quantized weights and the bit selection in determining the quantization precision of each layer. The continuous sparsification scheme enables fully-differentiable training without gradient approximation while achieving an exact quantized model in the end.A budget-aware regularization of total model size enables the dynamic growth and pruning of each layer's precision towards a mixed-precision quantization scheme of the desired size. Extensive experiments show CSQ achieves better efficiency-accuracy tradeoff than previous methods on multiple models and datasets.

Due to highly constrained computing power and memory, deploying 3D lidar-based detectors on edge devices equipped in autonomous vehicles and robots poses a crucial challenge. Being a convenient and straightforward model compression approach, Post-Training Quantization (PTQ) has been widely adopted in 2D vision tasks. However, applying it directly to 3D lidar-based tasks inevitably leads to performance degradation. As a remedy, we propose an effective PTQ method called LiDAR-PTQ, which is particularly curated for 3D lidar detection (both SPConv-based and SPConv-free). Our LiDAR-PTQ features three main components, (1) a sparsity-based calibration method to determine the initialization of quantization parameters, (2) a Task-guided Global Positive Loss (TGPL) to reduce the disparity between the final predictions before and after quantization, (3) an adaptive rounding-to-nearest operation to minimize the layerwise reconstruction error. Extensive experiments demonstrate that our LiDAR-PTQ can achieve state-of-the-art quantization performance when applied to CenterPoint (both Pillar-based and Voxel-based). To our knowledge, for the very first time in lidar-based 3D detection tasks, the PTQ INT8 model's accuracy is almost the same as the FP32 model while enjoying 3times inference speedup. Moreover, our LiDAR-PTQ is cost-effective being 30times faster than the quantization-aware training method. Code will be released at https://github.com/StiphyJay/LiDAR-PTQ.

Quantization for deep neural networks (DNNs) is the process of mapping the parameter values of DNNs from original data types to other data types of lower precision to reduce model sizes and make inference faster. Quantization often maps different original values to a single quantized value because the range of the original values is larger than the range of the quantized values. This leads to the degradation of the accuracy of the quantized DNNs. Outliers are a main cause of the degradation of quantization resolution because they enlarge the range of original values. To solve the problem, the percentile method is often used to clip outliers. However, clipping the outliers has another problem of removing the important and strong signals in the DNNs. This paper proposes SplitQuant to keep the outliers and improve the quantization resolution at the same time. SplitQuant narrows down the range of the original values and mitigates the effect of outliers by splitting each quantizable layer into three mathematically equivalent layers and applies different scaling factors. Especially, weights and biases are clustered into lower, middle and upper clusters for optimized split. By preprocessing DNNs with SplitQuant, quantization algorithms can achieve better results. SplitQuant was applied on two BERT-Tiny models and improved the accuracy of INT2 quantization by 3.3%p and 2.1%p, achieving accuracies comparable to those of the original FP32 models.

Vector Quantized Variational Autoencoders (VQ-VAEs) are fundamental to modern generative modeling, yet they often suffer from training instability and "codebook collapse" due to the inherent coupling of representation learning and discrete codebook optimization. In this paper, we propose VP-VAE (Vector Perturbation VAE), a novel paradigm that decouples representation learning from discretization by eliminating the need for an explicit codebook during training. Our key insight is that, from the neural network's viewpoint, performing quantization primarily manifests as injecting a structured perturbation in latent space. Accordingly, VP-VAE replaces the non-differentiable quantizer with distribution-consistent and scale-adaptive latent perturbations generated via Metropolis--Hastings sampling. This design enables stable training without a codebook while making the model robust to inference-time quantization error. Moreover, under the assumption of approximately uniform latent variables, we derive FSP (Finite Scalar Perturbation), a lightweight variant of VP-VAE that provides a unified theoretical explanation and a practical improvement for FSQ-style fixed quantizers. Extensive experiments on image and audio benchmarks demonstrate that VP-VAE and FSP improve reconstruction fidelity and achieve substantially more balanced token usage, while avoiding the instability inherent to coupled codebook training.

Neural audio codecs have recently gained traction for their ability to compress high-fidelity audio and generate discrete tokens that can be utilized in downstream generative modeling tasks. However, leading approaches often rely on resource-intensive models and multi-quantizer architectures, resulting in considerable computational overhead and constrained real-world applicability. In this paper, we present SQCodec, a lightweight neural audio codec that leverages a single quantizer to address these limitations. SQCodec explores streamlined convolutional networks and local Transformer modules, alongside TConv, a novel mechanism designed to capture acoustic variations across multiple temporal scales, thereby enhancing reconstruction fidelity while reducing model complexity. Extensive experiments across diverse datasets show that SQCodec achieves audio quality comparable to multi-quantizer baselines, while its single-quantizer design offers enhanced adaptability and its lightweight architecture reduces resource consumption by an order of magnitude. The source code is publicly available at https://github.com/zhai-lw/SQCodec.

Quantization scale and bit-width are the most important parameters when considering how to quantize a neural network. Prior work focuses on optimizing quantization scales in a global manner through gradient methods (gradient descent \& Hessian analysis). Yet, when applying perturbations to quantization scales, we observe a very jagged, highly non-smooth test loss landscape. In fact, small perturbations in quantization scale can greatly affect accuracy, yielding a 0.5-0.8% accuracy boost in 4-bit quantized vision transformers (ViTs). In this regime, gradient methods break down, since they cannot reliably reach local minima. In our work, dubbed Evol-Q, we use evolutionary search to effectively traverse the non-smooth landscape. Additionally, we propose using an infoNCE loss, which not only helps combat overfitting on the small calibration dataset (1,000 images) but also makes traversing such a highly non-smooth surface easier. Evol-Q improves the top-1 accuracy of a fully quantized ViT-Base by 10.30%, 0.78%, and 0.15% for 3-bit, 4-bit, and 8-bit weight quantization levels. Extensive experiments on a variety of CNN and ViT architectures further demonstrate its robustness in extreme quantization scenarios. Our code is available at https://github.com/enyac-group/evol-q

Large language models (LLMs) have demonstrated state-of-the-art performance across various tasks. However, the latency of inference and the large GPU memory consumption of LLMs restrict their deployment performance. Recently, there have been some efficient attempts to quantize LLMs, yet inference with large batch size or long sequence still has the issue of being compute-bound. Fine-grained quantization methods have showcased their proficiency in achieving low-bit quantization for LLMs, while requiring FP16 data type for linear layer computations, which is time-consuming when dealing with large batch size or long sequence. In this paper, we introduce a method called FlattenQuant, which significantly reduces the maximum value of the tensor by flattening the large channels in the tensor, to achieve low bit per-tensor quantization with minimal accuracy loss. Our experiments show that FlattenQuant can directly use 4 bits to achieve 48.29% of the linear layer calculation in LLMs, with the remaining layers using 8 bits. The 4-bit matrix multiplication introduced in the FlattenQuant method can effectively address the compute-bound caused by large matrix calculation. Our work achieves up to 2times speedup and 2.3times memory reduction for LLMs with negligible loss in accuracy.

Quantization is a widely-used compression technology to reduce the overhead of serving large language models (LLMs) on terminal devices and in cloud data centers. However, prevalent quantization methods, such as 8-bit weight-activation or 4-bit weight-only quantization, achieve limited performance improvements due to poor support for low-precision (e.g., 4-bit) activation. This work, for the first time, realizes practical W4A4KV4 serving for LLMs, fully utilizing the INT4 tensor cores on modern GPUs and reducing the memory bottleneck caused by the KV cache. Specifically, we propose a novel fine-grained mixed-precision quantization algorithm (FMPQ) that compresses most activations into 4-bit with negligible accuracy loss. To support mixed-precision matrix multiplication for W4A4 and W4A8, we develop a highly optimized W4Ax kernel. Our approach introduces a novel mixed-precision data layout to facilitate access and fast dequantization for activation and weight tensors, utilizing the GPU's software pipeline to hide the overhead of data loading and conversion. Additionally, we propose fine-grained streaming multiprocessor (SM) scheduling to achieve load balance across different SMs. We integrate the optimized W4Ax kernel into our inference framework, COMET, and provide efficient management to support popular LLMs such as LLaMA-3-70B. Extensive evaluations demonstrate that, when running LLaMA family models on a single A100-80G-SMX4, COMET achieves a kernel-level speedup of 2.88times over cuBLAS and a 2.02 times throughput improvement compared to TensorRT-LLM from an end-to-end framework perspective.

Quantizing the weights of large language models (LLMs) from 16-bit to lower bitwidth is the de facto approach to deploy massive transformers onto more affordable accelerators. GPTQ emerged as one of the standard methods for one-shot post-training quantization at LLM scale. Yet, its inner workings are described as a sequence of ad-hoc algebraic updates that obscure any geometric meaning or worst-case guarantees. In this work, we show that, when executed back-to-front (from the last to first dimension) for a linear layer, GPTQ is mathematically identical to Babai's nearest plane algorithm for the classical closest vector problem (CVP) on a lattice defined by the Hessian matrix of the layer's inputs. This equivalence is based on a sophisticated mathematical argument, and has two analytical consequences: (i) the GPTQ error propagation step gains an intuitive geometric interpretation; (ii) GPTQ inherits the error upper bound of Babai's algorithm under the no-clipping condition. Taken together, these results place GPTQ on firm theoretical footing and open the door to importing decades of progress in lattice algorithms towards the design of future quantization algorithms for billion-parameter models.

Model quantization is widely applied for compressing and accelerating deep neural networks (DNNs). However, conventional Quantization-Aware Training (QAT) focuses on training DNNs with uniform bit-width. The bit-width settings vary across different hardware and transmission demands, which induces considerable training and storage costs. Hence, the scheme of one-shot joint training multiple precisions is proposed to address this issue. Previous works either store a larger FP32 model to switch between different precision models for higher accuracy or store a smaller INT8 model but compromise accuracy due to using shared quantization parameters. In this paper, we introduce the Double Rounding quantization method, which fully utilizes the quantized representation range to accomplish nearly lossless bit-switching while reducing storage by using the highest integer precision instead of full precision. Furthermore, we observe a competitive interference among different precisions during one-shot joint training, primarily due to inconsistent gradients of quantization scales during backward propagation. To tackle this problem, we propose an Adaptive Learning Rate Scaling (ALRS) technique that dynamically adapts learning rates for various precisions to optimize the training process. Additionally, we extend our Double Rounding to one-shot mixed precision training and develop a Hessian-Aware Stochastic Bit-switching (HASB) strategy. Experimental results on the ImageNet-1K classification demonstrate that our methods have enough advantages to state-of-the-art one-shot joint QAT in both multi-precision and mixed-precision. We also validate the feasibility of our method on detection and segmentation tasks, as well as on LLMs task. Our codes are available at https://github.com/haiduo/Double-Rounding.