Daily Papers

Reward models are essential for aligning Large Language Models (LLMs) with human values, yet their development is hampered by costly preference datasets and poor interpretability. While recent rubric-based approaches offer transparency, they often lack systematic quality control and optimization, creating a trade-off between scalability and reliability. We address these limitations with a novel, training-free framework built on a key assumption: evaluation rubrics underlying human preferences exhibit significant generalization ability across diverse queries, a property that enables remarkable data efficiency. Our two-stage approach first infers high-quality, query-specific rubrics using a validation-guided Propose-Evaluate-Revise pipeline. Second, it generalizes these granular rubrics into a compact, non-redundant core set by maximizing an information-theoretic coding rate. The final output is an interpretable, hierarchical "Theme-Tips" rubric set. Extensive experiments demonstrate the framework's exceptional data efficiency and performance. Critically, using just 70 preference pairs (1.5\% of the source data), our method also empowers smaller models like Qwen3-8B to outperform specialized, fully-trained counterparts. This work pioneers a scalable, interpretable, and data-efficient path for reward modeling.

To learn intrinsic low-dimensional structures from high-dimensional data that most discriminate between classes, we propose the principle of Maximal Coding Rate Reduction (MCR^2), an information-theoretic measure that maximizes the coding rate difference between the whole dataset and the sum of each individual class. We clarify its relationships with most existing frameworks such as cross-entropy, information bottleneck, information gain, contractive and contrastive learning, and provide theoretical guarantees for learning diverse and discriminative features. The coding rate can be accurately computed from finite samples of degenerate subspace-like distributions and can learn intrinsic representations in supervised, self-supervised, and unsupervised settings in a unified manner. Empirically, the representations learned using this principle alone are significantly more robust to label corruptions in classification than those using cross-entropy, and can lead to state-of-the-art results in clustering mixed data from self-learned invariant features.

The efficient coding hypothesis proposes that the response properties of sensory systems are adapted to the statistics of their inputs such that they capture maximal information about the environment, subject to biological constraints. While elegant, information theoretic properties are notoriously difficult to measure in practical settings or to employ as objective functions in optimization. This difficulty has necessitated that computational models designed to test the hypothesis employ several different information metrics ranging from approximations and lower bounds to proxy measures like reconstruction error. Recent theoretical advances have characterized a novel and ecologically relevant efficiency metric, the manifold capacity, which is the number of object categories that may be represented in a linearly separable fashion. However, calculating manifold capacity is a computationally intensive iterative procedure that until now has precluded its use as an objective. Here we outline the simplifying assumptions that allow manifold capacity to be optimized directly, yielding Maximum Manifold Capacity Representations (MMCR). The resulting method is closely related to and inspired by advances in the field of self supervised learning (SSL), and we demonstrate that MMCRs are competitive with state of the art results on standard SSL benchmarks. Empirical analyses reveal differences between MMCRs and representations learned by other SSL frameworks, and suggest a mechanism by which manifold compression gives rise to class separability. Finally we evaluate a set of SSL methods on a suite of neural predictivity benchmarks, and find MMCRs are higly competitive as models of the ventral stream.

This paper investigates a novel lossy compression framework operating under logarithmic loss, designed to handle situations where the reconstruction distribution diverges from the source distribution. This framework is especially relevant for applications that require joint compression and retrieval, and in scenarios involving distributional shifts due to processing. We show that the proposed formulation extends the classical minimum entropy coupling framework by integrating a bottleneck, allowing for a controlled degree of stochasticity in the coupling. We explore the decomposition of the Minimum Entropy Coupling with Bottleneck (MEC-B) into two distinct optimization problems: Entropy-Bounded Information Maximization (EBIM) for the encoder, and Minimum Entropy Coupling (MEC) for the decoder. Through extensive analysis, we provide a greedy algorithm for EBIM with guaranteed performance, and characterize the optimal solution near functional mappings, yielding significant theoretical insights into the structural complexity of this problem. Furthermore, we illustrate the practical application of MEC-B through experiments in Markov Coding Games (MCGs) under rate limits. These games simulate a communication scenario within a Markov Decision Process, where an agent must transmit a compressed message from a sender to a receiver through its actions. Our experiments highlight the trade-offs between MDP rewards and receiver accuracy across various compression rates, showcasing the efficacy of our method compared to conventional compression baseline.

Deep neural networks have demonstrated remarkable performance in supervised learning tasks but require large amounts of labeled data. Self-supervised learning offers an alternative paradigm, enabling the model to learn from data without explicit labels. Information theory has been instrumental in understanding and optimizing deep neural networks. Specifically, the information bottleneck principle has been applied to optimize the trade-off between compression and relevant information preservation in supervised settings. However, the optimal information objective in self-supervised learning remains unclear. In this paper, we review various approaches to self-supervised learning from an information-theoretic standpoint and present a unified framework that formalizes the self-supervised information-theoretic learning problem. We integrate existing research into a coherent framework, examine recent self-supervised methods, and identify research opportunities and challenges. Moreover, we discuss empirical measurement of information-theoretic quantities and their estimators. This paper offers a comprehensive review of the intersection between information theory, self-supervised learning, and deep neural networks.

Learning compact discrete representations of data is a key task on its own or for facilitating subsequent processing of data. In this paper we present a model that produces Discrete InfoMax Codes (DIMCO); we learn a probabilistic encoder that yields k-way d-dimensional codes associated with input data. Our model's learning objective is to maximize the mutual information between codes and labels with a regularization, which enforces entries of a codeword to be as independent as possible. We show that the infomax principle also justifies previous loss functions (e.g., cross-entropy) as its special cases. Our analysis also shows that using shorter codes, as DIMCO does, reduces overfitting in the context of few-shot classification. Through experiments in various domains, we observe this implicit meta-regularization effect of DIMCO. Furthermore, we show that the codes learned by DIMCO are efficient in terms of both memory and retrieval time compared to previous methods.

A range of recent works addresses the problem of compression of sequence of tokens into a shorter sequence of real-valued vectors to be used as inputs instead of token embeddings or key-value cache. These approaches allow to reduce the amount of compute in existing language models. Despite relying on powerful models as encoders, the maximum attainable lossless compression ratio is typically not higher than x10. This fact is highly intriguing because, in theory, the maximum information capacity of large real-valued vectors is far beyond the presented rates even for 16-bit precision and a modest vector size. In this work, we explore the limits of compression by replacing the encoder with a per-sample optimization procedure. We show that vectors with compression ratios up to x1500 exist, which highlights two orders of magnitude gap between existing and practically attainable solutions. Furthermore, we empirically show that the compression limits are determined not by the length of the input but by the amount of uncertainty to be reduced, namely, the cross-entropy loss on this sequence without any conditioning. The obtained limits highlight the substantial gap between the theoretical capacity of input embeddings and their practical utilization, suggesting significant room for optimization in model design.

Neural image compression methods have seen increasingly strong performance in recent years. However, they suffer orders of magnitude higher computational complexity compared to traditional codecs, which stands in the way of real-world deployment. This paper takes a step forward in closing this gap in decoding complexity by adopting shallow or even linear decoding transforms. To compensate for the resulting drop in compression performance, we exploit the often asymmetrical computation budget between encoding and decoding, by adopting more powerful encoder networks and iterative encoding. We theoretically formalize the intuition behind, and our experimental results establish a new frontier in the trade-off between rate-distortion and decoding complexity for neural image compression. Specifically, we achieve rate-distortion performance competitive with the established mean-scale hyperprior architecture of Minnen et al. (2018), while reducing the overall decoding complexity by 80 %, or over 90 % for the synthesis transform alone. Our code can be found at https://github.com/mandt-lab/shallow-ntc.

Conventional communication systems, including both separation-based coding and AI-driven joint source-channel coding (JSCC), are largely guided by Shannon's rate-distortion theory. However, relying on generic distortion metrics fails to capture complex human visual perception, often resulting in blurred or unrealistic reconstructions. In this paper, we propose Joint Source-Channel-Generation Coding (JSCGC), a novel paradigm that shifts the focus from deterministic reconstruction to probabilistic generation. JSCGC leverages a generative model at the receiver as a generator rather than a conventional decoder to parameterize the data distribution, enabling direct maximization of mutual information under channel constraints while controlling stochastic sampling to produce outputs residing on the authentic data manifold with high fidelity. We further derive a theoretical lower bound on the maximum semantic inconsistency with given transmitted mutual information, elucidating the fundamental limits of communication in controlling the generative process. Extensive experiments on image transmission demonstrate that JSCGC substantially improves perceptual quality and semantic fidelity, significantly outperforming conventional distortion-oriented JSCC methods.

Numerous deep learning algorithms have been inspired by and understood via the notion of information bottleneck, where unnecessary information is (often implicitly) minimized while task-relevant information is maximized. However, a rigorous argument for justifying why it is desirable to control information bottlenecks has been elusive. In this paper, we provide the first rigorous learning theory for justifying the benefit of information bottleneck in deep learning by mathematically relating information bottleneck to generalization errors. Our theory proves that controlling information bottleneck is one way to control generalization errors in deep learning, although it is not the only or necessary way. We investigate the merit of our new mathematical findings with experiments across a range of architectures and learning settings. In many cases, generalization errors are shown to correlate with the degree of information bottleneck: i.e., the amount of the unnecessary information at hidden layers. This paper provides a theoretical foundation for current and future methods through the lens of information bottleneck. Our new generalization bounds scale with the degree of information bottleneck, unlike the previous bounds that scale with the number of parameters, VC dimension, Rademacher complexity, stability or robustness. Our code is publicly available at: https://github.com/xu-ji/information-bottleneck

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.

This paper presents a novel information-theoretic perspective on generalization in machine learning by framing the learning problem within the context of lossy compression and applying finite blocklength analysis. In our approach, the sampling of training data formally corresponds to an encoding process, and the model construction to a decoding process. By leveraging finite blocklength analysis, we derive lower bounds on sample complexity and generalization error for a fixed randomized learning algorithm and its associated optimal sampling strategy. Our bounds explicitly characterize the degree of overfitting of the learning algorithm and the mismatch between its inductive bias and the task as distinct terms. This separation provides a significant advantage over existing frameworks. Additionally, we decompose the overfitting term to show its theoretical connection to existing metrics found in information-theoretic bounds and stability theory, unifying these perspectives under our proposed framework.

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

Data used for analytics and machine learning often take the form of tables with categorical entries. We introduce a family of lossless compression algorithms for such data that proceed in four steps: (i) Estimate latent variables associated to rows and columns; (ii) Partition the table in blocks according to the row/column latents; (iii) Apply a sequential (e.g. Lempel-Ziv) coder to each of the blocks; (iv) Append a compressed encoding of the latents. We evaluate it on several benchmark datasets, and study optimal compression in a probabilistic model for that tabular data, whereby latent values are independent and table entries are conditionally independent given the latent values. We prove that the model has a well defined entropy rate and satisfies an asymptotic equipartition property. We also prove that classical compression schemes such as Lempel-Ziv and finite-state encoders do not achieve this rate. On the other hand, the latent estimation strategy outlined above achieves the optimal rate.

We carry out an information-theoretical analysis of a two-layer neural network trained from input-output pairs generated by a teacher network with matching architecture, in overparametrized regimes. Our results come in the form of bounds relating i) the mutual information between training data and network weights, or ii) the Bayes-optimal generalization error, to the same quantities but for a simpler (generalized) linear model for which explicit expressions are rigorously known. Our bounds, which are expressed in terms of the number of training samples, input dimension and number of hidden units, thus yield fundamental performance limits for any neural network (and actually any learning procedure) trained from limited data generated according to our two-layer teacher neural network model. The proof relies on rigorous tools from spin glasses and is guided by ``Gaussian equivalence principles'' lying at the core of numerous recent analyses of neural networks. With respect to the existing literature, which is either non-rigorous or restricted to the case of the learning of the readout weights only, our results are information-theoretic (i.e. are not specific to any learning algorithm) and, importantly, cover a setting where all the network parameters are trained.

The Information Bottleneck (IB) principle offers an information-theoretic framework for analyzing the training process of deep neural networks (DNNs). Its essence lies in tracking the dynamics of two mutual information (MI) values: one between the hidden layer and the class label, and the other between the hidden layer and the DNN input. According to the hypothesis put forth by Shwartz-Ziv and Tishby (2017), the training process consists of two distinct phases: fitting and compression. The latter phase is believed to account for the good generalization performance exhibited by DNNs. Due to the challenging nature of estimating MI between high-dimensional random vectors, this hypothesis has only been verified for toy NNs or specific types of NNs, such as quantized NNs and dropout NNs. In this paper, we introduce a comprehensive framework for conducting IB analysis of general NNs. Our approach leverages the stochastic NN method proposed by Goldfeld et al. (2019) and incorporates a compression step to overcome the obstacles associated with high dimensionality. In other words, we estimate the MI between the compressed representations of high-dimensional random vectors. The proposed method is supported by both theoretical and practical justifications. Notably, we demonstrate the accuracy of our estimator through synthetic experiments featuring predefined MI values. Finally, we perform IB analysis on a close-to-real-scale convolutional DNN, which reveals new features of the MI dynamics.

Does semantic communication require a semantic information theory parallel to Shannon's information theory, or can Shannon's work be generalized for semantic communication? This paper advocates for the latter and introduces a semantic generalization of Shannon's information theory (G theory for short). The core idea is to replace the distortion constraint with the semantic constraint, achieved by utilizing a set of truth functions as a semantic channel. These truth functions enable the expressions of semantic distortion, semantic information measures, and semantic information loss. Notably, the maximum semantic information criterion is equivalent to the maximum likelihood criterion and similar to the Regularized Least Squares criterion. This paper shows G theory's applications to daily and electronic semantic communication, machine learning, constraint control, Bayesian confirmation, portfolio theory, and information value. The improvements in machine learning methods involve multilabel learning and classification, maximum mutual information classification, mixture models, and solving latent variables. Furthermore, insights from statistical physics are discussed: Shannon information is similar to free energy; semantic information to free energy in local equilibrium systems; and information efficiency to the efficiency of free energy in performing work. The paper also proposes refining Friston's minimum free energy principle into the maximum information efficiency principle. Lastly, it compares G theory with other semantic information theories and discusses its limitation in representing the semantics of complex data.

Image codecs are typically optimized to trade-off bitrate \vs distortion metrics. At low bitrates, this leads to compression artefacts which are easily perceptible, even when training with perceptual or adversarial losses. To improve image quality and remove dependency on the bitrate, we propose to decode with iterative diffusion models. We condition the decoding process on a vector-quantized image representation, as well as a global image description to provide additional context. We dub our model PerCo for 'perceptual compression', and compare it to state-of-the-art codecs at rates from 0.1 down to 0.003 bits per pixel. The latter rate is more than an order of magnitude smaller than those considered in most prior work, compressing a 512x768 Kodak image with less than 153 bytes. Despite this ultra-low bitrate, our approach maintains the ability to reconstruct realistic images. We find that our model leads to reconstructions with state-of-the-art visual quality as measured by FID and KID. As predicted by rate-distortion-perception theory, visual quality is less dependent on the bitrate than previous methods.

Agentic language model (LM) systems power modern applications like "Deep Research" and "Claude Code," and leverage multi-LM architectures to overcome context limitations. Beneath their apparent diversity lies a recurring pattern: smaller "compressor" LMs (that can even run locally) distill raw context into compact text that is then consumed by larger "predictor" LMs. Despite their popularity, the design of compressor-predictor systems remains largely ad hoc, with little guidance on how compressor and predictor choices shape downstream performance. In practice, attributing gains to compression versus prediction requires costly, task-specific pairwise sweeps. We argue that these agentic system design questions are, at root, information-theoretic. Viewing the compressor LM as a noisy channel, we introduce a simple estimator of mutual information between the context and its compression to quantify compression quality in a task-independent way. We show that mutual information strongly predicts downstream performance, independent of any specific task. Through an information-theoretic framework, we perform a comprehensive empirical analysis across five datasets and three model families. Results reveal that larger compressors not only are more accurate, but also more token-efficient, conveying more bits of information per token. A 7B Qwen-2.5 compressor, for instance, is 1.6times more accurate, 4.6times more concise, and conveys 5.5times more bits of mutual information per token than its 1.5B sibling. Across datasets, scaling compressors is substantially more effective than scaling predictors, enabling larger on-device compressors to pair with smaller cloud predictors. Applied to a Deep Research system, these principles enable local compressors as small as 3B parameters to recover 99% of frontier-LM accuracy at 26% of API costs.

Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated without considering a downstream task? On these questions, Shannon information and Kolmogorov complexity come up nearly empty-handed, in part because they assume observers with unlimited computational capacity and fail to target the useful information content. In this work, we identify and exemplify three seeming paradoxes in information theory: (1) information cannot be increased by deterministic transformations; (2) information is independent of the order of data; (3) likelihood modeling is merely distribution matching. To shed light on the tension between these results and modern practice, and to quantify the value of data, we introduce epiplexity, a formalization of information capturing what computationally bounded observers can learn from data. Epiplexity captures the structural content in data while excluding time-bounded entropy, the random unpredictable content exemplified by pseudorandom number generators and chaotic dynamical systems. With these concepts, we demonstrate how information can be created with computation, how it depends on the ordering of the data, and how likelihood modeling can produce more complex programs than present in the data generating process itself. We also present practical procedures to estimate epiplexity which we show capture differences across data sources, track with downstream performance, and highlight dataset interventions that improve out-of-distribution generalization. In contrast to principles of model selection, epiplexity provides a theoretical foundation for data selection, guiding how to select, generate, or transform data for learning systems.

Semantic communications utilize the transceiver computing resources to alleviate scarce transmission resources, such as bandwidth and energy. Although the conventional deep learning (DL) based designs may achieve certain transmission efficiency, the uninterpretability issue of extracted features is the major challenge in the development of semantic communications. In this paper, we propose an explainable and robust semantic communication framework by incorporating the well-established bit-level communication system, which not only extracts and disentangles features into independent and semantically interpretable features, but also only selects task-relevant features for transmission, instead of all extracted features. Based on this framework, we derive the optimal input for rate-distortion-perception theory, and derive both lower and upper bounds on the semantic channel capacity. Furthermore, based on the β-variational autoencoder (β-VAE), we propose a practical explainable semantic communication system design, which simultaneously achieves semantic features selection and is robust against semantic channel noise. We further design a real-time wireless mobile semantic communication proof-of-concept prototype. Our simulations and experiments demonstrate that our proposed explainable semantic communications system can significantly improve transmission efficiency, and also verify the effectiveness of our proposed robust semantic transmission scheme.

In this paper, we contend that a natural objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a low-dimensional Gaussian mixture supported on incoherent subspaces. The goodness of such a representation can be evaluated by a principled measure, called sparse rate reduction, that simultaneously maximizes the intrinsic information gain and extrinsic sparsity of the learned representation. From this perspective, popular deep network architectures, including transformers, can be viewed as realizing iterative schemes to optimize this measure. Particularly, we derive a transformer block from alternating optimization on parts of this objective: the multi-head self-attention operator compresses the representation by implementing an approximate gradient descent step on the coding rate of the features, and the subsequent multi-layer perceptron sparsifies the features. This leads to a family of white-box transformer-like deep network architectures, named CRATE, which are mathematically fully interpretable. We show, by way of a novel connection between denoising and compression, that the inverse to the aforementioned compressive encoding can be realized by the same class of CRATE architectures. Thus, the so-derived white-box architectures are universal to both encoders and decoders. Experiments show that these networks, despite their simplicity, indeed learn to compress and sparsify representations of large-scale real-world image and text datasets, and achieve performance very close to highly engineered transformer-based models: ViT, MAE, DINO, BERT, and GPT2. We believe the proposed computational framework demonstrates great potential in bridging the gap between theory and practice of deep learning, from a unified perspective of data compression. Code is available at: https://ma-lab-berkeley.github.io/CRATE .

Credit risk modeling relies extensively on Weight of Evidence (WoE) and Information Value (IV) for feature engineering, and Population Stability Index (PSI) for drift monitoring, yet their theoretical foundations remain disconnected. We establish a unified information-theoretic framework revealing these industry-standard metrics as instances of classical information divergences. Specifically, we prove that IV exactly equals PSI (Jeffreys divergence) computed between good and bad credit outcomes over identical bins. Through the delta method applied to WoE transformations, we derive standard errors for IV and PSI, enabling formal hypothesis testing and probabilistic fairness constraints for the first time. We formalize credit modeling's inherent performance-fairness trade-off as maximizing IV for predictive power while minimizing IV for protected attributes. Using automated binning with depth-1 XGBoost stumps, we compare three encoding strategies: logistic regression with one-hot encoding, WoE transformation, and constrained XGBoost. All methods achieve comparable predictive performance (AUC 0.82-0.84), demonstrating that principled, information-theoretic binning outweighs encoding choice. Mixed-integer programming traces Pareto-efficient solutions along the performance-fairness frontier with uncertainty quantification. This framework bridges theory and practice, providing the first rigorous statistical foundation for widely-used credit risk metrics while offering principled tools for balancing accuracy and fairness in regulated environments.

A new information theoretic condition is presented for reconstructing a discrete random variable X based on the knowledge of a set of discrete functions of X. The reconstruction condition is derived from Shannon's 1953 lattice theory with two entropic metrics of Shannon and Rajski. Because such a theoretical material is relatively unknown and appears quite dispersed in different references, we first provide a synthetic description (with complete proofs) of its concepts, such as total, common and complementary informations. Definitions and properties of the two entropic metrics are also fully detailed and shown compatible with the lattice structure. A new geometric interpretation of such a lattice structure is then investigated that leads to a necessary (and sometimes sufficient) condition for reconstructing the discrete random variable X given a set { X_1,ldots,X_{n} } of elements in the lattice generated by X. Finally, this condition is illustrated in five specific examples of perfect reconstruction problems: reconstruction of a symmetric random variable from the knowledge of its sign and absolute value, reconstruction of a word from a set of linear combinations, reconstruction of an integer from its prime signature (fundamental theorem of arithmetic) and from its remainders modulo a set of coprime integers (Chinese remainder theorem), and reconstruction of the sorting permutation of a list from a minimal set of pairwise comparisons.

Humans organize knowledge into compact categories through semantic compression by mapping diverse instances to abstract representations while preserving meaning (e.g., robin and blue jay are both birds; most birds can fly). These concepts reflect a trade-off between expressive fidelity and representational simplicity. Large Language Models (LLMs) demonstrate remarkable linguistic abilities, yet whether their internal representations strike a human-like trade-off between compression and semantic fidelity is unclear. We introduce a novel information-theoretic framework, drawing from Rate-Distortion Theory and the Information Bottleneck principle, to quantitatively compare these strategies. Analyzing token embeddings from a diverse suite of LLMs against seminal human categorization benchmarks, we uncover key divergences. While LLMs form broad conceptual categories that align with human judgment, they struggle to capture the fine-grained semantic distinctions crucial for human understanding. More fundamentally, LLMs demonstrate a strong bias towards aggressive statistical compression, whereas human conceptual systems appear to prioritize adaptive nuance and contextual richness, even if this results in lower compressional efficiency by our measures. These findings illuminate critical differences between current AI and human cognitive architectures, guiding pathways toward LLMs with more human-aligned conceptual representations.

Recent years have witnessed the rapid advancements of large language models (LLMs) and their expanding applications, leading to soaring demands for computational resources. The widespread adoption of test-time scaling further aggravates the tension between model capability and resource consumption, highlighting the importance of inference efficiency. However, a unified metric that accurately reflects an LLM's efficiency across different model sizes and architectures remains absent. Motivated by the correlation between compression and intelligence, we introduce information capacity, a measure of model efficiency based on text compression performance relative to computational complexity. Larger models can predict the next token more accurately, achieving greater compression gains but at higher computational costs. Empirical evaluations on mainstream open-source models show that models of varying sizes within a series exhibit consistent information capacity. This metric enables a fair efficiency comparison across model series and accurate performance prediction within a model series. A distinctive feature of information capacity is that it incorporates tokenizer efficiency, which affects both input and output token counts but is often neglected in LLM evaluations. We assess the information capacity of 49 models on 5 heterogeneous datasets and observe consistent results on the influences of tokenizer efficiency, pretraining data, and the mixture-of-experts architecture.

Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and data processing inequalities. We show that several quantitative aspects of information theory can be captured by an enriched version of Markov categories, where the spaces of morphisms are equipped with a divergence or even a metric. As it is customary in information theory, mutual information can be defined as a measure of how far a joint source is from displaying independence of its components. More strikingly, Markov categories give a notion of determinism for sources and channels, and we can define entropy exactly by measuring how far a source or channel is from being deterministic. This recovers Shannon and R\'enyi entropies, as well as the Gini-Simpson index used in ecology to quantify diversity, and it can be used to give a conceptual definition of generalized entropy.

Large language models (LLMs) have demonstrated remarkable capabilities in numerous real-world applications. While the vast majority of research conducted from an experimental perspective is progressing rapidly, it demands substantial computational power, data, and other resources. Therefore, how to open the black-box of LLMs from a theoretical standpoint has become a critical challenge. This paper takes the theory of rate-distortion function, directed information, and Granger causality as its starting point to investigate the information-theoretic principles behind LLMs, leading to the development of semantic information theory for LLMs, where the fundamental unit is token, rather than bits that lacks any semantic meaning. By defining the probabilistic model of LLMs, we discuss structure-agnostic information-theoretic measures, such as the directed rate-distortion function in pre-training, the directed rate-reward function in post-training, and the semantic information flow in inference phase. This paper also delves deeply into the theory of token-level semantic embedding and the information-theoretically optimal vectorization method. Thereafter, we propose a general definition of autoregression LLM, where the Transformer architecture and its performance such as ELBO, generalization error bound, memory capacity, and semantic information measures can be derived theoretically. Other architectures, such as Mamba/Mamba2 and LLaDA, are also discussed in our framework. Consequently, this paper provides a theoretical framework for understanding LLMs from the perspective of semantic information theory, which also offers the necessary theoretical tools for further in-depth research.

We study the problem of optimally projecting the transition matrix of a finite ergodic multivariate Markov chain onto a lower-dimensional state space. Specifically, we seek to construct a projected Markov chain that optimizes various information-theoretic criteria under cardinality constraints. These criteria include entropy rate, information-theoretic distance to factorizability, independence, and stationarity. We formulate these tasks as best subset selection problems over multivariate Markov chains and leverage the submodular (or supermodular) structure of the objective functions to develop efficient greedy-based algorithms with theoretical guarantees. We extend our analysis to k-submodular settings and introduce a generalized version of the distorted greedy algorithm, which may be of independent interest. Finally, we illustrate the theory and algorithms through extensive numerical experiments with publicly available code on multivariate Markov chains associated with the Bernoulli-Laplace and Curie-Weiss model.

This paper explores the relationship between the condition number of a neural network's weight tensor and the extent of information encoded by the associated processing unit, viewed through the lens of information theory. It argues that a high condition number, though not sufficient for effective knowledge encoding, may indicate that the unit has learned to selectively amplify and compress information. This intuition is formalized for linear units with Gaussian inputs, linking the condition number and the transformation's log-volume scaling factor to the characteristics of the output entropy and the geometric properties of the learned transformation. The analysis demonstrates that for a fixed weight norm, a concentrated distribution of singular values (high condition number) corresponds to reduced overall information transfer, indicating a specialized and efficient encoding strategy. Furthermore, the linear stage entropy bound provides an upper limit on post-activation information for contractive, element-wise nonlinearities, supporting the condition number as a scale-invariant proxy for encoding capacity in practical neural networks. An empirical case study applies these principles to guide selective fine-tuning of Large Language Models for both a new task and a new input modality. The experiments show that the proposed method, named KappaTune, effectively mitigates catastrophic forgetting. Unlike many existing catastrophic forgetting mitigation methods that rely on access to pre-training statistics, which are often unavailable, this selective fine-tuning approach offers a way to bypass this common requirement.

High-performance learned image compression codecs require flexible probability models to fit latent representations. Gaussian Mixture Models (GMMs) were proposed to satisfy this demand, but suffer from a significant runtime performance bottleneck due to the large Cumulative Distribution Function (CDF) tables that must be built for rANS coding. This paper introduces a fast coding algorithm that entirely eliminates this bottleneck. By leveraging the CDF's monotonic property, our decoder performs a dynamic binary search to find the correct symbol, eliminating the need for costly table construction and lookup. Aided by SIMD optimizations and numerical approximations, our approach accelerates the GMM entropy coding process by up to approximately 90x without compromising rate-distortion performance, significantly improving the practicality of GMM-based codecs. The implementation will be made publicly available at https://github.com/tokkiwa/FlashGMM.

Transfer entropy (TE) is an information theoretic measure that reveals the directional flow of information between processes, providing valuable insights for a wide range of real-world applications. This work proposes Transfer Entropy Estimation via Transformers (TREET), a novel attention-based approach for estimating TE for stationary processes. The proposed approach employs Donsker-Varadhan representation to TE and leverages the attention mechanism for the task of neural estimation. We propose a detailed theoretical and empirical study of the TREET, comparing it to existing methods on a dedicated estimation benchmark. To increase its applicability, we design an estimated TE optimization scheme that is motivated by the functional representation lemma, and use it to estimate the capacity of communication channels with memory, which is a canonical optimization problem in information theory. We further demonstrate how an optimized TREET can be used to estimate underlying densities, providing experimental results. Finally, we apply TREET to feature analysis of patients with Apnea, demonstrating its applicability to real-world physiological data. Our work, applied with state-of-the-art deep learning methods, opens a new door for communication problems which are yet to be solved.

Neural networks achieve remarkable performance through superposition: encoding multiple features as overlapping directions in activation space rather than dedicating individual neurons to each feature. This challenges interpretability, yet we lack principled methods to measure superposition. We present an information-theoretic framework measuring a neural representation's effective degrees of freedom. We apply Shannon entropy to sparse autoencoder activations to compute the number of effective features as the minimum neurons needed for interference-free encoding. Equivalently, this measures how many "virtual neurons" the network simulates through superposition. When networks encode more effective features than actual neurons, they must accept interference as the price of compression. Our metric strongly correlates with ground truth in toy models, detects minimal superposition in algorithmic tasks, and reveals systematic reduction under dropout. Layer-wise patterns mirror intrinsic dimensionality studies on Pythia-70M. The metric also captures developmental dynamics, detecting sharp feature consolidation during grokking. Surprisingly, adversarial training can increase effective features while improving robustness, contradicting the hypothesis that superposition causes vulnerability. Instead, the effect depends on task complexity and network capacity: simple tasks with ample capacity allow feature expansion (abundance regime), while complex tasks or limited capacity force reduction (scarcity regime). By defining superposition as lossy compression, this work enables principled measurement of how neural networks organize information under computational constraints, connecting superposition to adversarial robustness.

Despite extensive progress on image generation, common deep generative model architectures are not easily applied to lossless compression. For example, VAEs suffer from a compression cost overhead due to their latent variables. This overhead can only be partially eliminated with elaborate schemes such as bits-back coding, often resulting in poor single-sample compression rates. To overcome such problems, we establish a new class of tractable lossless compression models that permit efficient encoding and decoding: Probabilistic Circuits (PCs). These are a class of neural networks involving |p| computational units that support efficient marginalization over arbitrary subsets of the D feature dimensions, enabling efficient arithmetic coding. We derive efficient encoding and decoding schemes that both have time complexity O (log(D) cdot |p|), where a naive scheme would have linear costs in D and |p|, making the approach highly scalable. Empirically, our PC-based (de)compression algorithm runs 5-40 times faster than neural compression algorithms that achieve similar bitrates. By scaling up the traditional PC structure learning pipeline, we achieve state-of-the-art results on image datasets such as MNIST. Furthermore, PCs can be naturally integrated with existing neural compression algorithms to improve the performance of these base models on natural image datasets. Our results highlight the potential impact that non-standard learning architectures may have on neural data compression.

Autoregressive Predictive Coding (APC), as a self-supervised objective, has enjoyed success in learning representations from large amounts of unlabeled data, and the learned representations are rich for many downstream tasks. However, the connection between low self-supervised loss and strong performance in downstream tasks remains unclear. In this work, we propose Vector-Quantized Autoregressive Predictive Coding (VQ-APC), a novel model that produces quantized representations, allowing us to explicitly control the amount of information encoded in the representations. By studying a sequence of increasingly limited models, we reveal the constituents of the learned representations. In particular, we confirm the presence of information with probing tasks, while showing the absence of information with mutual information, uncovering the model's preference in preserving speech information as its capacity becomes constrained. We find that there exists a point where phonetic and speaker information are amplified to maximize a self-supervised objective. As a byproduct, the learned codes for a particular model capacity correspond well to English phones.

We provide new estimates of an asymptotic upper bound on the entropy of English using the large language model LLaMA-7B as a predictor for the next token given a window of past tokens. This estimate is significantly smaller than currently available estimates in cover1978convergent, lutati2023focus. A natural byproduct is an algorithm for lossless compression of English text which combines the prediction from the large language model with a lossless compression scheme. Preliminary results from limited experiments suggest that our scheme outperforms state-of-the-art text compression schemes such as BSC, ZPAQ, and paq8h.

Collaborative perception empowers each agent to improve its perceptual ability through the exchange of perceptual messages with other agents. It inherently results in a fundamental trade-off between perception ability and communication cost. To address this bottleneck issue, our core idea is to optimize the collaborative messages from two key aspects: representation and selection. The proposed codebook-based message representation enables the transmission of integer codes, rather than high-dimensional feature maps. The proposed information-filling-driven message selection optimizes local messages to collectively fill each agent's information demand, preventing information overflow among multiple agents. By integrating these two designs, we propose CodeFilling, a novel communication-efficient collaborative perception system, which significantly advances the perception-communication trade-off and is inclusive to both homogeneous and heterogeneous collaboration settings. We evaluate CodeFilling in both a real-world dataset, DAIR-V2X, and a new simulation dataset, OPV2VH+. Results show that CodeFilling outperforms previous SOTA Where2comm on DAIR-V2X/OPV2VH+ with 1,333/1,206 times lower communication volume. Our code is available at https://github.com/PhyllisH/CodeFilling.

Prior studies in learned image compression (LIC) consistently show that only a small subset of latent channels is critical for reconstruction, while many others carry limited information. Exploiting this imbalance could improve both coding and computational efficiency, yet existing approaches often rely on costly, dataset-specific ablation tests and typically analyze channels in isolation, ignoring their interdependencies. We propose a generalizable, dataset-agnostic method to identify and organize important channels in pretrained VAE-based LIC models. Instead of brute-force empirical evaluations, our approach leverages intrinsic parameter statistics-weight variances, bias magnitudes, and pairwise correlations-to estimate channel importance. This analysis reveals a consistent organizational structure, termed the Invariant Salient Channel Space (ISCS), where Salient-Core channels capture dominant structures and Salient-Auxiliary channels provide complementary details. Building on ISCS, we introduce a deterministic channel ordering and grouping strategy that enables slice-parallel decoding, reduces redundancy, and improves bitrate efficiency. Experiments across multiple LIC architectures demonstrate that our method effectively reduces bitrate and computation while maintaining reconstruction quality, providing a practical and modular enhancement to existing learned compression frameworks.

To improve how neural networks function it is crucial to understand their learning process. The information bottleneck theory of deep learning proposes that neural networks achieve good generalization by compressing their representations to disregard information that is not relevant to the task. However, empirical evidence for this theory is conflicting, as compression was only observed when networks used saturating activation functions. In contrast, networks with non-saturating activation functions achieved comparable levels of task performance but did not show compression. In this paper we developed more robust mutual information estimation techniques, that adapt to hidden activity of neural networks and produce more sensitive measurements of activations from all functions, especially unbounded functions. Using these adaptive estimation techniques, we explored compression in networks with a range of different activation functions. With two improved methods of estimation, firstly, we show that saturation of the activation function is not required for compression, and the amount of compression varies between different activation functions. We also find that there is a large amount of variation in compression between different network initializations. Secondary, we see that L2 regularization leads to significantly increased compression, while preventing overfitting. Finally, we show that only compression of the last layer is positively correlated with generalization.

Region-of-Interest (ROI)-based image compression allocates bits unevenly according to the semantic importance of different regions. Such differentiated coding typically induces a sharp-peaked and heavy-tailed distribution. This distribution characteristic mathematically necessitates a probability model with adaptable shape parameters for accurate description. However, existing methods commonly use a Gaussian model to fit this distribution, resulting in a loss of coding performance. To systematically analyze the impact of this distribution on ROI coding, we develop a unified rate-distortion optimization theoretical paradigm. Building on this paradigm, we propose a novel Generalized Gaussian Model (GGM) to achieve flexible modeling of the latent variables distribution. To support stable optimization of GGM, we introduce effective differentiable functions and further propose a dynamic lower bound to alleviate train-test mismatch. Moreover, finite differences are introduced to solve the gradient computation after GGM fits the distribution. Experiments on COCO2017 demonstrate that our method achieves state-of-the-art in both ROI reconstruction and downstream tasks (e.g., Segmentation, Object Detection). Furthermore, compared to classical probability models, our GGM provides a more precise fit to feature distributions and achieves superior coding performance. The project page is at https://github.com/hukai-tju/ROIGGM.

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.

Learning complex functions that involve multi-step reasoning poses a significant challenge for standard supervised learning from input-output examples. Chain-of-thought (CoT) supervision, which provides intermediate reasoning steps together with the final output, has emerged as a powerful empirical technique, underpinning much of the recent progress in the reasoning capabilities of large language models. This paper develops a statistical theory of learning under CoT supervision. A key characteristic of the CoT setting, in contrast to standard supervision, is the mismatch between the training objective (CoT risk) and the test objective (end-to-end risk). A central part of our analysis, distinguished from prior work, is explicitly linking those two types of risk to achieve sharper sample complexity bounds. This is achieved via the *CoT information measure* I_{D, h_star}^{CoT}(epsilon; calH), which quantifies the additional discriminative power gained from observing the reasoning process. The main theoretical results demonstrate how CoT supervision can yield significantly faster learning rates compared to standard E2E supervision. Specifically, it is shown that the sample complexity required to achieve a target E2E error epsilon scales as d/I_{D, h_star}^{CoT}(epsilon; calH), where d is a measure of hypothesis class complexity, which can be much faster than standard d/epsilon rates. Information-theoretic lower bounds in terms of the CoT information are also obtained. Together, these results suggest that CoT information is a fundamental measure of statistical complexity for learning under chain-of-thought supervision.

Diffusion Language Models (DLMs) have recently emerged as a strong alternative to autoregressive language models (LMs). DLMs offer comparable accuracy with faster inference speed via parallel decoding. However, standard DLM decoding strategies relying on high-confidence tokens encounter an inherent information-theoretic bottleneck that restricts decoding progress and ultimately slows generation. We demonstrate both theoretically and empirically that prioritizing high-confidence tokens is inherently inefficient. High-probability tokens carry negligible information and strictly relying on them limits the effective progress made in each decoding round. We prove that the number of decoding rounds must grow linearly with the sample's total information (negative log-likelihood) and inversely with the per-round information budget, establishing a bits-to-rounds principle. We also propose Explore-Then-Exploit (ETE), a training-free decoding strategy that maximizes information throughput and decoding efficiency. ETE combines cross-block decoding with targeted exploration of high-uncertainty tokens to reshape the conditional distribution and trigger cascades of confident predictions. Experiments verify our theoretical bounds and demonstrate that ETE consistently reduces the required number of decoding rounds compared to confidence-only baselines without compromising generation quality.

For a language model (LM) to faithfully model human language, it must compress vast, potentially infinite information into relatively few dimensions. We propose analyzing compression in (pre-trained) LMs from two points of view: geometric and information-theoretic. We demonstrate that the two views are highly correlated, such that the intrinsic geometric dimension of linguistic data predicts their coding length under the LM. We then show that, in turn, high compression of a linguistic dataset predicts rapid adaptation to that dataset, confirming that being able to compress linguistic information is an important part of successful LM performance. As a practical byproduct of our analysis, we evaluate a battery of intrinsic dimension estimators for the first time on linguistic data, showing that only some encapsulate the relationship between information-theoretic compression, geometric compression, and ease-of-adaptation.

The information bottleneck (IB) approach is popular to improve the generalization, robustness and explainability of deep neural networks. Essentially, it aims to find a minimum sufficient representation t by striking a trade-off between a compression term I(x;t) and a prediction term I(y;t), where I(cdot;cdot) refers to the mutual information (MI). MI is for the IB for the most part expressed in terms of the Kullback-Leibler (KL) divergence, which in the regression case corresponds to prediction based on mean squared error (MSE) loss with Gaussian assumption and compression approximated by variational inference. In this paper, we study the IB principle for the regression problem and develop a new way to parameterize the IB with deep neural networks by exploiting favorable properties of the Cauchy-Schwarz (CS) divergence. By doing so, we move away from MSE-based regression and ease estimation by avoiding variational approximations or distributional assumptions. We investigate the improved generalization ability of our proposed CS-IB and demonstrate strong adversarial robustness guarantees. We demonstrate its superior performance on six real-world regression tasks over other popular deep IB approaches. We additionally observe that the solutions discovered by CS-IB always achieve the best trade-off between prediction accuracy and compression ratio in the information plane. The code is available at https://github.com/SJYuCNEL/Cauchy-Schwarz-Information-Bottleneck.

We consider low-latency image transmission over a noisy wireless channel when correlated side information is present only at the receiver side (the Wyner-Ziv scenario). In particular, we are interested in developing practical schemes using a data-driven joint source-channel coding (JSCC) approach, which has been previously shown to outperform conventional separation-based approaches in the practical finite blocklength regimes, and to provide graceful degradation with channel quality. We propose a novel neural network architecture that incorporates the decoder-only side information at multiple stages at the receiver side. Our results demonstrate that the proposed method succeeds in integrating the side information, yielding improved performance at all channel noise levels in terms of the various distortion criteria considered here, especially at low channel signal-to-noise ratios (SNRs) and small bandwidth ratios (BRs). We also provide the source code of the proposed method to enable further research and reproducibility of the results.

Modeling latent variables with priors and hyperpriors is an essential problem in variational image compression. Formally, trade-off between rate and distortion is handled well if priors and hyperpriors precisely describe latent variables. Current practices only adopt univariate priors and process each variable individually. However, we find inter-correlations and intra-correlations exist when observing latent variables in a vectorized perspective. These findings reveal visual redundancies to improve rate-distortion performance and parallel processing ability to speed up compression. This encourages us to propose a novel vectorized prior. Specifically, a multivariate Gaussian mixture is proposed with means and covariances to be estimated. Then, a novel probabilistic vector quantization is utilized to effectively approximate means, and remaining covariances are further induced to a unified mixture and solved by cascaded estimation without context models involved. Furthermore, codebooks involved in quantization are extended to multi-codebooks for complexity reduction, which formulates an efficient compression procedure. Extensive experiments on benchmark datasets against state-of-the-art indicate our model has better rate-distortion performance and an impressive 3.18times compression speed up, giving us the ability to perform real-time, high-quality variational image compression in practice. Our source code is publicly available at https://github.com/xiaosu-zhu/McQuic.

With the rapid advancement of large language models (LLMs), discrete speech representations have become crucial for integrating speech into LLMs. Existing methods for speech representation discretization rely on a predefined codebook size and Euclidean distance-based quantization. However, 1) the size of codebook is a critical parameter that affects both codec performance and downstream task training efficiency. 2) The Euclidean distance-based quantization may lead to audio distortion when the size of the codebook is controlled within a reasonable range. In fact, in the field of information compression, structural information and entropy guidance are crucial, but previous methods have largely overlooked these factors. Therefore, we address the above issues from an information-theoretic perspective, we present SECodec, a novel speech representation codec based on structural entropy (SE) for building speech language models. Specifically, we first model speech as a graph, clustering the speech features nodes within the graph and extracting the corresponding codebook by hierarchically and disentangledly minimizing 2D SE. Then, to address the issue of audio distortion, we propose a new quantization method. This method still adheres to the 2D SE minimization principle, adaptively selecting the most suitable token corresponding to the cluster for each incoming original speech node. Furthermore, we develop a Structural Entropy-based Speech Language Model (SESLM) that leverages SECodec. Experimental results demonstrate that SECodec performs comparably to EnCodec in speech reconstruction, and SESLM surpasses VALL-E in zero-shot text-to-speech tasks. Code, demo speeches, speech feature graph, SE codebook, and models are available at https://github.com/wlq2019/SECodec.

Compression is at the heart of intelligence. A theoretically optimal way to compress any sequence of data is to find the shortest program that outputs that sequence and then halts. However, such 'Kolmogorov compression' is uncomputable, and code generating LLMs struggle to approximate this theoretical ideal, as it requires reasoning, planning and search capabilities beyond those of current models. In this work, we introduce the KoLMogorov-Test (KT), a compression-as-intelligence test for code generating LLMs. In KT a model is presented with a sequence of data at inference time, and asked to generate the shortest program that produces the sequence. We identify several benefits of KT for both evaluation and training: an essentially infinite number of problem instances of varying difficulty is readily available, strong baselines already exist, the evaluation metric (compression) cannot be gamed, and pretraining data contamination is highly unlikely. To evaluate current models, we use audio, text, and DNA data, as well as sequences produced by random synthetic programs. Current flagship models perform poorly - both GPT4-o and Llama-3.1-405B struggle on our natural and synthetic sequences. On our synthetic distribution, we are able to train code generation models with lower compression rates than previous approaches. Moreover, we show that gains on synthetic data generalize poorly to real data, suggesting that new innovations are necessary for additional gains on KT.

Although recent generative image compression methods have demonstrated impressive potential in optimizing the rate-distortion-perception trade-off, they still face the critical challenge of flexible rate adaption to diverse compression necessities and scenarios. To overcome this challenge, this paper proposes a Controllable Generative Image Compression framework, termed Control-GIC, the first capable of fine-grained bitrate adaption across a broad spectrum while ensuring high-fidelity and generality compression. Control-GIC is grounded in a VQGAN framework that encodes an image as a sequence of variable-length codes (i.e. VQ-indices), which can be losslessly compressed and exhibits a direct positive correlation with the bitrates. Drawing inspiration from the classical coding principle, we correlate the information density of local image patches with their granular representations. Hence, we can flexibly determine a proper allocation of granularity for the patches to achieve dynamic adjustment for VQ-indices, resulting in desirable compression rates. We further develop a probabilistic conditional decoder capable of retrieving historic encoded multi-granularity representations according to transmitted codes, and then reconstruct hierarchical granular features in the formalization of conditional probability, enabling more informative aggregation to improve reconstruction realism. Our experiments show that Control-GIC allows highly flexible and controllable bitrate adaption where the results demonstrate its superior performance over recent state-of-the-art methods. Code is available at https://github.com/lianqi1008/Control-GIC.

Predictive coding networks are neuroscience-inspired models with roots in both Bayesian statistics and neuroscience. Training such models, however, is quite inefficient and unstable. In this work, we show how by simply changing the temporal scheduling of the update rule for the synaptic weights leads to an algorithm that is much more efficient and stable than the original one, and has theoretical guarantees in terms of convergence. The proposed algorithm, that we call incremental predictive coding (iPC) is also more biologically plausible than the original one, as it it fully automatic. In an extensive set of experiments, we show that iPC constantly performs better than the original formulation on a large number of benchmarks for image classification, as well as for the training of both conditional and masked language models, in terms of test accuracy, efficiency, and convergence with respect to a large set of hyperparameters.

We consider the image transmission problem over a noisy wireless channel via deep learning-based joint source-channel coding (DeepJSCC) along with a denoising diffusion probabilistic model (DDPM) at the receiver. Specifically, we are interested in the perception-distortion trade-off in the practical finite block length regime, in which separate source and channel coding can be highly suboptimal. We introduce a novel scheme that utilizes the range-null space decomposition of the target image. We transmit the range-space of the image after encoding and employ DDPM to progressively refine its null space contents. Through extensive experiments, we demonstrate significant improvements in distortion and perceptual quality of reconstructed images compared to standard DeepJSCC and the state-of-the-art generative learning-based method. We will publicly share our source code to facilitate further research and reproducibility.

Model compression aims to reduce the redundancy of deep networks to obtain compact models. Recently, channel pruning has become one of the predominant compression methods to deploy deep models on resource-constrained devices. Most channel pruning methods often use a fixed compression rate for all the layers of the model, which, however, may not be optimal. To address this issue, given a target compression rate for the whole model, one can search for the optimal compression rate for each layer. Nevertheless, these methods perform channel pruning for a specific target compression rate. When we consider multiple compression rates, they have to repeat the channel pruning process multiple times, which is very inefficient yet unnecessary. To address this issue, we propose a Conditional Automated Channel Pruning(CACP) method to obtain the compressed models with different compression rates through single channel pruning process. To this end, we develop a conditional model that takes an arbitrary compression rate as input and outputs the corresponding compressed model. In the experiments, the resultant models with different compression rates consistently outperform the models compressed by existing methods with a channel pruning process for each target compression rate.

The deployment of Large Language Models (LLMs) in long-context scenarios is hindered by computational inefficiency and significant information redundancy. Although recent advancements have widely adopted context compression to address these challenges, existing research only focus on model-side improvements, the impact of the data distribution itself on context compression remains largely unexplored. To bridge this gap, we are the first to adopt a data-centric perspective to systematically investigate how data distribution impacts compression quality, including two dimensions: input data and intrinsic data (i.e., the model's internal pretrained knowledge). We evaluate the semantic integrity of compressed representations using an autoencoder-based framework to systematically investigate it. Our experimental results reveal that: (1) encoder-measured input entropy negatively correlates with compression quality, while decoder-measured entropy shows no significant relationship under a frozen-decoder setting; and (2) the gap between intrinsic data of the encoder and decoder significantly diminishes compression gains, which is hard to mitigate. Based on these findings, we further present practical guidelines to optimize compression gains.

Exploiting partial first-order information in a cyclic way is arguably the most natural strategy to obtain scalable first-order methods. However, despite their wide use in practice, cyclic schemes are far less understood from a theoretical perspective than their randomized counterparts. Motivated by a recent success in analyzing an extrapolated cyclic scheme for generalized variational inequalities, we propose an Accelerated Cyclic Coordinate Dual Averaging with Extrapolation (A-CODER) method for composite convex optimization, where the objective function can be expressed as the sum of a smooth convex function accessible via a gradient oracle and a convex, possibly nonsmooth, function accessible via a proximal oracle. We show that A-CODER attains the optimal convergence rate with improved dependence on the number of blocks compared to prior work. Furthermore, for the setting where the smooth component of the objective function is expressible in a finite sum form, we introduce a variance-reduced variant of A-CODER, VR-A-CODER, with state-of-the-art complexity guarantees. Finally, we demonstrate the effectiveness of our algorithms through numerical experiments.

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

We introduce PerCoV2, a novel and open ultra-low bit-rate perceptual image compression system designed for bandwidth- and storage-constrained applications. Building upon prior work by Careil et al., PerCoV2 extends the original formulation to the Stable Diffusion 3 ecosystem and enhances entropy coding efficiency by explicitly modeling the discrete hyper-latent image distribution. To this end, we conduct a comprehensive comparison of recent autoregressive methods (VAR and MaskGIT) for entropy modeling and evaluate our approach on the large-scale MSCOCO-30k benchmark. Compared to previous work, PerCoV2 (i) achieves higher image fidelity at even lower bit-rates while maintaining competitive perceptual quality, (ii) features a hybrid generation mode for further bit-rate savings, and (iii) is built solely on public components. Code and trained models will be released at https://github.com/Nikolai10/PerCoV2.

We propose a joint source and channel coding (JSCC) technique for wireless image transmission that does not rely on explicit codes for either compression or error correction; instead, it directly maps the image pixel values to the complex-valued channel input symbols. We parameterize the encoder and decoder functions by two convolutional neural networks (CNNs), which are trained jointly, and can be considered as an autoencoder with a non-trainable layer in the middle that represents the noisy communication channel. Our results show that the proposed deep JSCC scheme outperforms digital transmission concatenating JPEG or JPEG2000 compression with a capacity achieving channel code at low signal-to-noise ratio (SNR) and channel bandwidth values in the presence of additive white Gaussian noise (AWGN). More strikingly, deep JSCC does not suffer from the ``cliff effect'', and it provides a graceful performance degradation as the channel SNR varies with respect to the SNR value assumed during training. In the case of a slow Rayleigh fading channel, deep JSCC learns noise resilient coded representations and significantly outperforms separation-based digital communication at all SNR and channel bandwidth values.

We study neural image compression based on the Sparse Visual Representation (SVR), where images are embedded into a discrete latent space spanned by learned visual codebooks. By sharing codebooks with the decoder, the encoder transfers integer codeword indices that are efficient and cross-platform robust, and the decoder retrieves the embedded latent feature using the indices for reconstruction. Previous SVR-based compression lacks effective mechanism for rate-distortion tradeoffs, where one can only pursue either high reconstruction quality or low transmission bitrate. We propose a Masked Adaptive Codebook learning (M-AdaCode) method that applies masks to the latent feature subspace to balance bitrate and reconstruction quality. A set of semantic-class-dependent basis codebooks are learned, which are weighted combined to generate a rich latent feature for high-quality reconstruction. The combining weights are adaptively derived from each input image, providing fidelity information with additional transmission costs. By masking out unimportant weights in the encoder and recovering them in the decoder, we can trade off reconstruction quality for transmission bits, and the masking rate controls the balance between bitrate and distortion. Experiments over the standard JPEG-AI dataset demonstrate the effectiveness of our M-AdaCode approach.

Understanding neural networks is challenging in part because of the dense, continuous nature of their hidden states. We explore whether we can train neural networks to have hidden states that are sparse, discrete, and more interpretable by quantizing their continuous features into what we call codebook features. Codebook features are produced by finetuning neural networks with vector quantization bottlenecks at each layer, producing a network whose hidden features are the sum of a small number of discrete vector codes chosen from a larger codebook. Surprisingly, we find that neural networks can operate under this extreme bottleneck with only modest degradation in performance. This sparse, discrete bottleneck also provides an intuitive way of controlling neural network behavior: first, find codes that activate when the desired behavior is present, then activate those same codes during generation to elicit that behavior. We validate our approach by training codebook Transformers on several different datasets. First, we explore a finite state machine dataset with far more hidden states than neurons. In this setting, our approach overcomes the superposition problem by assigning states to distinct codes, and we find that we can make the neural network behave as if it is in a different state by activating the code for that state. Second, we train Transformer language models with up to 410M parameters on two natural language datasets. We identify codes in these models representing diverse, disentangled concepts (ranging from negative emotions to months of the year) and find that we can guide the model to generate different topics by activating the appropriate codes during inference. Overall, codebook features appear to be a promising unit of analysis and control for neural networks and interpretability. Our codebase and models are open-sourced at https://github.com/taufeeque9/codebook-features.

We introduce the Information-Estimation Metric (IEM), a novel form of distance function derived from an underlying continuous probability density over a domain of signals. The IEM is rooted in a fundamental relationship between information theory and estimation theory, which links the log-probability of a signal with the errors of an optimal denoiser, applied to noisy observations of the signal. In particular, the IEM between a pair of signals is obtained by comparing their denoising error vectors over a range of noise amplitudes. Geometrically, this amounts to comparing the score vector fields of the blurred density around the signals over a range of blur levels. We prove that the IEM is a valid global distance metric and derive a closed-form expression for its local second-order approximation, which yields a Riemannian metric. For Gaussian-distributed signals, the IEM coincides with the Mahalanobis distance. But for more complex distributions, it adapts, both locally and globally, to the geometry of the distribution. In practice, the IEM can be computed using a learned denoiser (analogous to generative diffusion models) and solving a one-dimensional integral. To demonstrate the value of our framework, we learn an IEM on the ImageNet database. Experiments show that this IEM is competitive with or outperforms state-of-the-art supervised image quality metrics in predicting human perceptual judgments.

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.

We establish a fundamental connection between score-based diffusion models and non-equilibrium thermodynamics by deriving performance limits based on entropy rates. Our main theoretical contribution is a lower bound on the negative log-likelihood of the data that relates model performance to entropy rates of diffusion processes. We numerically validate this bound on a synthetic dataset and investigate its tightness. By building a bridge to entropy rates - system, intrinsic, and exchange entropy - we provide new insights into the thermodynamic operation of these models, drawing parallels to Maxwell's demon and implications for thermodynamic computing hardware. Our framework connects generative modeling performance to fundamental physical principles through stochastic thermodynamics.

Auto-regressive language models factorize sequence probabilities and are trained by minimizing the negative log-likelihood (NLL) objective. While empirically powerful, a deep theoretical understanding of why this simple objective yields such versatile representations remains elusive. This work introduces a unifying analytical framework using Markov Categories (MCs) to deconstruct the AR generation process and the NLL objective. We model the single-step generation map as a composition of Markov kernels in the category Stoch. This compositional view, when enriched with statistical divergences, allows us to dissect information flow and learned geometry. Our framework makes three main contributions. First, we provide a formal, information-theoretic rationale for the success of modern speculative decoding methods like EAGLE, quantifying the information surplus in hidden states that these methods exploit. Second, we formalize how NLL minimization forces the model to learn not just the next token, but the data's intrinsic conditional stochasticity, a process we analyze using categorical entropy. Third, and most centrally, we prove that NLL training acts as an implicit form of spectral contrastive learning. By analyzing the information geometry of the model's prediction head, we show that NLL implicitly forces the learned representation space to align with the eigenspectrum of a predictive similarity operator, thereby learning a geometrically structured space without explicit contrastive pairs. This compositional and information-geometric perspective reveals the deep structural principles underlying the effectiveness of modern LMs. Project Page: https://github.com/asiresearch/lm-theory

The analysis of scientific data and complex multivariate systems requires information quantities that capture relationships among multiple random variables. Recently, new information-theoretic measures have been developed to overcome the shortcomings of classical ones, such as mutual information, that are restricted to considering pairwise interactions. Among them, the concept of information synergy and redundancy is crucial for understanding the high-order dependencies between variables. One of the most prominent and versatile measures based on this concept is O-information, which provides a clear and scalable way to quantify the synergy-redundancy balance in multivariate systems. However, its practical application is limited to simplified cases. In this work, we introduce SOmegaI, which allows for the first time to compute O-information without restrictive assumptions about the system. Our experiments validate our approach on synthetic data, and demonstrate the effectiveness of SOmegaI in the context of a real-world use case.

Recent advancements in Large Language Model (LLM) compression, such as BitNet and BitNet b1.58, have marked significant strides in reducing the computational demands of LLMs through innovative one-bit quantization techniques. We extend this frontier by looking at Large Inference Models (LIMs) that have become indispensable across various applications. However, their scale and complexity often come at a significant computational cost. We introduce a novel approach that leverages one-bit algorithm unrolling, effectively integrating information from the physical world in the model architecture. Our method achieves a bit-per-link rate significantly lower than the 1.58 bits reported in prior work, thanks to the natural sparsity that emerges in our network architectures. We numerically demonstrate that the proposed one-bit algorithm unrolling scheme can improve both training and test outcomes by effortlessly increasing the number of layers while substantially compressing the network. Additionally, we provide theoretical results on the generalization gap, convergence rate, stability, and sensitivity of our proposed one-bit algorithm unrolling.

Accurate and efficient discrete video tokenization is essential for long video sequences processing. Yet, the inherent complexity and variable information density of videos present a significant bottleneck for current tokenizers, which rigidly compress all content at a fixed rate, leading to redundancy or information loss. Drawing inspiration from Shannon's information theory, this paper introduces InfoTok, a principled framework for adaptive video tokenization. We rigorously prove that existing data-agnostic training methods are suboptimal in representation length, and present a novel evidence lower bound (ELBO)-based algorithm that approaches theoretical optimality. Leveraging this framework, we develop a transformer-based adaptive compressor that enables adaptive tokenization. Empirical results demonstrate state-of-the-art compression performance, saving 20% tokens without influence on performance, and achieving 2.3x compression rates while still outperforming prior heuristic adaptive approaches. By allocating tokens according to informational richness, InfoTok enables a more compressed yet accurate tokenization for video representation, offering valuable insights for future research.

The design of codes for feedback-enabled communications has been a long-standing open problem. Recent research on non-linear, deep learning-based coding schemes have demonstrated significant improvements in communication reliability over linear codes, but are still vulnerable to the presence of forward and feedback noise over the channel. In this paper, we develop a new family of non-linear feedback codes that greatly enhance robustness to channel noise. Our autoencoder-based architecture is designed to learn codes based on consecutive blocks of bits, which obtains de-noising advantages over bit-by-bit processing to help overcome the physical separation between the encoder and decoder over a noisy channel. Moreover, we develop a power control layer at the encoder to explicitly incorporate hardware constraints into the learning optimization, and prove that the resulting average power constraint is satisfied asymptotically. Numerical experiments demonstrate that our scheme outperforms state-of-the-art feedback codes by wide margins over practical forward and feedback noise regimes, and provide information-theoretic insights on the behavior of our non-linear codes. Moreover, we observe that, in a long blocklength regime, canonical error correction codes are still preferable to feedback codes when the feedback noise becomes high.

Hierarchical classification offers an approach to incorporate the concept of mistake severity by leveraging a structured, labeled hierarchy. However, decoding in such settings frequently relies on heuristic decision rules, which may not align with task-specific evaluation metrics. In this work, we propose a framework for the optimal decoding of an output probability distribution with respect to a target metric. We derive optimal decision rules for increasingly complex prediction settings, providing universal algorithms when candidates are limited to the set of nodes. In the most general case of predicting a subset of nodes, we focus on rules dedicated to the hierarchical hF_{beta} scores, tailored to hierarchical settings. To demonstrate the practical utility of our approach, we conduct extensive empirical evaluations, showcasing the superiority of our proposed optimal strategies, particularly in underdetermined scenarios. These results highlight the potential of our methods to enhance the performance and reliability of hierarchical classifiers in real-world applications. The code is available at https://github.com/RomanPlaud/hierarchical_decision_rules

Key-value (KV) caching has become the de-facto to accelerate generation speed for large language models (LLMs) inference. However, the growing cache demand with increasing sequence length has transformed LLM inference to be a memory bound problem, significantly constraining the system throughput. Existing methods rely on dropping unimportant tokens or quantizing all entries uniformly. Such methods, however, often incur high approximation errors to represent the compressed matrices. The autoregressive decoding process further compounds the error of each step, resulting in critical deviation in model generation and deterioration of performance. To tackle this challenge, we propose GEAR, an efficient KV cache compression framework that achieves near-lossless high-ratio compression. GEAR first applies quantization to majority of entries of similar magnitudes to ultra-low precision. It then employs a low rank matrix to approximate the quantization error, and a sparse matrix to remedy individual errors from outlier entries. By adeptly integrating three techniques, GEAR is able to fully exploit their synergistic potentials. Our experiments demonstrate that compared to alternatives, GEAR achieves near-lossless 4-bit KV cache compression with up to 2.38x throughput improvement, while reducing peak-memory size up to 2.29x. Our code is publicly available at https://github.com/HaoKang-Timmy/GEAR.

Diffusion-based image compression has demonstrated impressive perceptual performance. However, it suffers from two critical drawbacks: (1) excessive decoding latency due to multi-step sampling, and (2) poor fidelity resulting from over-reliance on generative priors. To address these issues, we propose SODEC, a novel single-step diffusion image compression model. We argue that in image compression, a sufficiently informative latent renders multi-step refinement unnecessary. Based on this insight, we leverage a pre-trained VAE-based model to produce latents with rich information, and replace the iterative denoising process with a single-step decoding. Meanwhile, to improve fidelity, we introduce the fidelity guidance module, encouraging output that is faithful to the original image. Furthermore, we design the rate annealing training strategy to enable effective training under extremely low bitrates. Extensive experiments show that SODEC significantly outperforms existing methods, achieving superior rate-distortion-perception performance. Moreover, compared to previous diffusion-based compression models, SODEC improves decoding speed by more than 20times. Code is released at: https://github.com/zhengchen1999/SODEC.

Large models have achieved remarkable performance across various tasks, yet they incur significant computational costs and privacy concerns during both training and inference. Distributed deployment has emerged as a potential solution, but it necessitates the exchange of intermediate information between model segments, with feature representations serving as crucial information carriers. To optimize information exchange, feature coding methods are applied to reduce transmission and storage overhead. Despite its importance, feature coding for large models remains an under-explored area. In this paper, we draw attention to large model feature coding and make three contributions to this field. First, we introduce a comprehensive dataset encompassing diverse features generated by three representative types of large models. Second, we establish unified test conditions, enabling standardized evaluation pipelines and fair comparisons across future feature coding studies. Third, we introduce two baseline methods derived from widely used image coding techniques and benchmark their performance on the proposed dataset. These contributions aim to advance the field of feature coding, facilitating more efficient large model deployment. All source code and the dataset are now available at https://github.com/chansongoal/FCM-LM/tree/master{https://github.com/chansongoal/FCM-LM/tree/master}.

Reliable image transmission over wireless channels is particularly challenging at extremely low transmission rates, where conventional compression and channel coding schemes fail to preserve adequate visual quality. To address this issue, we propose a generative communication framework based on diffusion models, which integrates joint source channel coding (JSCC) with semantic-guided reconstruction leveraging a pre-trained generative model. Unlike conventional architectures that aim to recover exact pixel values of the original image, the proposed method focuses on preserving and reconstructing semantically meaningful visual content under severely constrained rates, ensuring perceptual plausibility and faithfulness to the scene intent. Specifically, the transmitter encodes the source image via JSCC and jointly transmits it with a textual prompt over the wireless channel. At the receiver, the corrupted low-rate representation is fused with the prompt and reconstructed through a Stable Diffusion model with ControlNet, enabling high-quality visual recovery. Leveraging both generative priors and semantic guidance, the proposed framework produces perceptually convincing images even under extreme bandwidth limitations. Experimental results demonstrate that the proposed method consistently outperforms conventional coding-based schemes and deep learning baselines, achieving superior perceptual quality and robustness across various channel conditions.

Modern video generation frameworks based on Latent Diffusion Models suffer from inefficiencies in tokenization due to the Frame-Proportional Information Assumption. Existing tokenizers provide fixed temporal compression rates, causing the computational cost of the diffusion model to scale linearly with the frame rate. The paper proposes the Duration-Proportional Information Assumption: the upper bound on the information capacity of a video is proportional to the duration rather than the number of frames. Based on this insight, the paper introduces VFRTok, a Transformer-based video tokenizer, that enables variable frame rate encoding and decoding through asymmetric frame rate training between the encoder and decoder. Furthermore, the paper proposes Partial Rotary Position Embeddings (RoPE) to decouple position and content modeling, which groups correlated patches into unified tokens. The Partial RoPE effectively improves content-awareness, enhancing the video generation capability. Benefiting from the compact and continuous spatio-temporal representation, VFRTok achieves competitive reconstruction quality and state-of-the-art generation fidelity while using only 1/8 tokens compared to existing tokenizers.

According to Algorithmic Information Theory (AIT) -- Intelligent representations compress data into the shortest possible program that can reconstruct its content, exhibiting low Kolmogorov Complexity (KC). In contrast, most visual representation learning systems use fixed-length representations for all inputs, ignoring variations in complexity or familiarity. Recent adaptive tokenization methods address this by allocating variable-length representations but typically require test-time search over multiple encodings to find the most predictive one. Inspired by Kolmogorov Complexity principles, we propose a single-pass adaptive tokenizer, KARL, which predicts the appropriate number of tokens for an image in a single forward pass, halting once its approximate KC is reached. The token count serves as a proxy for the minimum description length. KARL's training procedure closely resembles the Upside-Down Reinforcement Learning paradigm, as it learns to conditionally predict token halting based on a desired reconstruction quality. KARL matches the performance of recent adaptive tokenizers while operating in a single pass. We present scaling laws for KARL, analyzing the role of encoder/decoder size, continuous vs. discrete tokenization and more. Additionally, we offer a conceptual study drawing an analogy between Adaptive Image Tokenization and Algorithmic Information Theory, examining the predicted image complexity (KC) across axes such as structure vs. noise and in- vs. out-of-distribution familiarity -- revealing alignment with human intuition.

The Fisher information is a fundamental concept for characterizing the sensitivity of parameters in neural networks. However, leveraging the full observed Fisher information is too expensive for large models, so most methods rely on simple diagonal approximations. While efficient, this approach ignores parameter correlations, often resulting in reduced performance on downstream tasks. In this work, we mitigate these limitations and propose Generalized Fisher-Weighted SVD (GFWSVD), a post-training LLM compression technique that accounts for both diagonal and off-diagonal elements of the Fisher information matrix, providing a more accurate reflection of parameter importance. To make the method tractable, we introduce a scalable adaptation of the Kronecker-factored approximation algorithm for the observed Fisher information. We demonstrate the effectiveness of our method on LLM compression, showing improvements over existing compression baselines. For example, at a 20 compression rate on the MMLU benchmark, our method outperforms FWSVD, which is based on a diagonal approximation of the Fisher information, by 5 percent, SVD-LLM by 3 percent, and ASVD by 6 percent compression rate.

Semantic maps are increasingly utilized in areas such as robotics, autonomous systems, and extended reality, motivating the investigation of efficient compression methods that preserve structured semantic information. This paper studies lossless compression of semantic maps through a novel chain-coding-based framework that explicitly exploits contour topology and shared boundaries between adjacent semantic regions. We propose an extended chain code (ECC) to represent long-range contour transitions more compactly, while retaining a legacy three-orthogonal chain code (3OT) as a fallback mode for further efficiency. To efficiently encode sequences of ECC symbols, a context-adaptive entropy coding scheme based on Markov modeling is employed. Furthermore, a skip-coding mechanism is introduced to eliminate redundant representations of shared contours between adjacent semantic regions, supporting both complete and partial skips via run-length signaling. Experimental results demonstrate that the proposed method achieves an average bitrate reduction of 18\% compared with a state-of-the-art benchmark on semantic map datasets. In addition, the proposed encoder and decoder achieve up to 98\% and 50\% runtime reduction, respectively, relative to a modern generic lossless codec. Extended evaluations on occupancy maps further confirm consistent compression gains across the majority of tested scenarios.

While most autoregressive LLMs are constrained to one-by-one decoding, diffusion LLMs (dLLMs) have attracted growing interest for their potential to dramatically accelerate inference through parallel decoding. Despite this promise, the conditional independence assumption in dLLMs causes parallel decoding to ignore token dependencies, inevitably degrading generation quality when these dependencies are strong. However, existing works largely overlook these inherent challenges, and evaluations on standard benchmarks (e.g., math and coding) are not sufficient to capture the quality degradation caused by parallel decoding. To address this gap, we first provide an information-theoretic analysis of parallel decoding. We then conduct case studies on analytically tractable synthetic list operations from both data distribution and decoding strategy perspectives, offering quantitative insights that highlight the fundamental limitations of parallel decoding. Building on these insights, we propose ParallelBench, the first benchmark specifically designed for dLLMs, featuring realistic tasks that are trivial for humans and autoregressive LLMs yet exceptionally challenging for dLLMs under parallel decoding. Using ParallelBench, we systematically analyze both dLLMs and autoregressive LLMs, revealing that: (i) dLLMs under parallel decoding can suffer dramatic quality degradation in real-world scenarios, and (ii) current parallel decoding strategies struggle to adapt their degree of parallelism based on task difficulty, thus failing to achieve meaningful speedup without compromising quality. Our findings underscore the pressing need for innovative decoding methods that can overcome the current speed-quality trade-off. We release our benchmark to help accelerate the development of truly efficient dLLMs.

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models Phi and the downstream task is specified by a class of prediction functions Psi. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of mathcal{O}(mathcal{C_Phi/m} + mathcal{C_Psi/n}) for downstream tasks, where C_Phi, C_Psi are complexity measures of function classes Phi, Psi, and m, n are the number of unlabeled and labeled data respectively. Comparing to the baseline of mathcal{O}(mathcal{C_{Phi circ Psi}/n}) achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when m gg n and C_{Phicirc Psi} > C_Psi. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

In this paper, we present a new technique to obtain upper bounds on undirected unicast network information capacity. Using this technique, we characterize an upper bound, called partition bound, on the symmetric rate of information flow in undirected unicast networks and give an algorithm to compute it. Two classes of networks are presented for which the bound is tight and the capacity is achievable by routing thus confirming the undirected unicast conjecture for these classes of networks. We also show that the bound can be loose in general and present an approach to tighten it.

Distributed representations of words encode lexical semantic information, but what type of information is encoded and how? Focusing on the skip-gram with negative-sampling method, we found that the squared norm of static word embedding encodes the information gain conveyed by the word; the information gain is defined by the Kullback-Leibler divergence of the co-occurrence distribution of the word to the unigram distribution. Our findings are explained by the theoretical framework of the exponential family of probability distributions and confirmed through precise experiments that remove spurious correlations arising from word frequency. This theory also extends to contextualized word embeddings in language models or any neural networks with the softmax output layer. We also demonstrate that both the KL divergence and the squared norm of embedding provide a useful metric of the informativeness of a word in tasks such as keyword extraction, proper-noun discrimination, and hypernym discrimination.

We study distributed contextual linear bandits with stochastic contexts, where N agents act cooperatively to solve a linear bandit-optimization problem with d-dimensional features over the course of T rounds. For this problem, we derive the first ever information-theoretic lower bound Omega(dN) on the communication cost of any algorithm that performs optimally in a regret minimization setup. We then propose a distributed batch elimination version of the LinUCB algorithm, DisBE-LUCB, where the agents share information among each other through a central server. We prove that the communication cost of DisBE-LUCB matches our lower bound up to logarithmic factors. In particular, for scenarios with known context distribution, the communication cost of DisBE-LUCB is only mathcal{O}(dN) and its regret is {mathcal{O}}(dNT), which is of the same order as that incurred by an optimal single-agent algorithm for NT rounds. We also provide similar bounds for practical settings where the context distribution can only be estimated. Therefore, our proposed algorithm is nearly minimax optimal in terms of both regret and communication cost. Finally, we propose DecBE-LUCB, a fully decentralized version of DisBE-LUCB, which operates without a central server, where agents share information with their immediate neighbors through a carefully designed consensus procedure.

Most frame-based learned video codecs can be interpreted as recurrent neural networks (RNNs) propagating reference information along the temporal dimension. This work revisits the limitations of the current approaches from an RNN perspective. The output-recurrence methods, which propagate decoded frames, are intuitive but impose dual constraints on the output decoded frames, leading to suboptimal rate-distortion performance. In contrast, the hidden-to-hidden connection approaches, which propagate latent features within the RNN, offer greater flexibility but require large buffer sizes. To address these issues, we propose HyTIP, a learned video coding framework that combines both mechanisms. Our hybrid buffering strategy uses explicit decoded frames and a small number of implicit latent features to achieve competitive coding performance. Experimental results show that our HyTIP outperforms the sole use of either output-recurrence or hidden-to-hidden approaches. Furthermore, it achieves comparable performance to state-of-the-art methods but with a much smaller buffer size, and outperforms VTM 17.0 (Low-delay B) in terms of PSNR-RGB and MS-SSIM-RGB. The source code of HyTIP is available at https://github.com/NYCU-MAPL/HyTIP.

This paper focuses on task-agnostic prompt compression for better generalizability and efficiency. Considering the redundancy in natural language, existing approaches compress prompts by removing tokens or lexical units according to their information entropy obtained from a causal language model such as LLaMa-7B. The challenge is that information entropy may be a suboptimal compression metric: (i) it only leverages unidirectional context and may fail to capture all essential information needed for prompt compression; (ii) it is not aligned with the prompt compression objective. To address these issues, we propose a data distillation procedure to derive knowledge from an LLM to compress prompts without losing crucial information, and meantime, introduce an extractive text compression dataset. We formulate prompt compression as a token classification problem to guarantee the faithfulness of the compressed prompt to the original one, and use a Transformer encoder as the base architecture to capture all essential information for prompt compression from the full bidirectional context. Our approach leads to lower latency by explicitly learning the compression objective with smaller models such as XLM-RoBERTa-large and mBERT. We evaluate our method on both in-domain and out-of-domain datasets, including MeetingBank, LongBench, ZeroScrolls, GSM8K, and BBH. Despite its small size, our model shows significant performance gains over strong baselines and demonstrates robust generalization ability across different LLMs. Additionally, our model is 3x-6x faster than existing prompt compression methods, while accelerating the end-to-end latency by 1.6x-2.9x with compression ratios of 2x-5x.

We consider distributed image transmission over a noisy multiple access channel (MAC) using deep joint source-channel coding (DeepJSCC). It is known that Shannon's separation theorem holds when transmitting independent sources over a MAC in the asymptotic infinite block length regime. However, we are interested in the practical finite block length regime, in which case separate source and channel coding is known to be suboptimal. We introduce a novel joint image compression and transmission scheme, where the devices send their compressed image representations in a non-orthogonal manner. While non-orthogonal multiple access (NOMA) is known to achieve the capacity region, to the best of our knowledge, non-orthogonal joint source channel coding (JSCC) scheme for practical systems has not been studied before. Through extensive experiments, we show significant improvements in terms of the quality of the reconstructed images compared to orthogonal transmission employing current DeepJSCC approaches particularly for low bandwidth ratios. We publicly share source code to facilitate further research and reproducibility.

In this work, we conceptualize the learning process as information compression. We seek to equip generative pre-trained models with human-like learning capabilities that enable data compression during inference. We present a novel approach that utilizes the Generative Pre-trained Transformer (GPT) to approximate Kolmogorov complexity, with the aim of estimating the optimal Information Distance for few-shot learning. We first propose using GPT as a prior for lossless text compression, achieving a noteworthy compression ratio. Experiment with LLAMA2-7B backbone achieves a compression ratio of 15.5 on enwik9. We justify the pre-training objective of GPT models by demonstrating its equivalence to the compression length, and, consequently, its ability to approximate the information distance for texts. Leveraging the approximated information distance, our method allows the direct application of GPT models in quantitative text similarity measurements. Experiment results show that our method overall achieves superior performance compared to embedding and prompt baselines on challenging NLP tasks, including semantic similarity, zero and one-shot text classification, and zero-shot text ranking.

We study a distributed stochastic multi-armed bandit where a client supplies the learner with communication-constrained feedback based on the rewards for the corresponding arm pulls. In our setup, the client must encode the rewards such that the second moment of the encoded rewards is no more than P, and this encoded reward is further corrupted by additive Gaussian noise of variance sigma^2; the learner only has access to this corrupted reward. For this setting, we derive an information-theoretic lower bound of Omegaleft(frac{KT{SNR wedge1}} right) on the minimax regret of any scheme, where SNR := P{sigma^2}, and K and T are the number of arms and time horizon, respectively. Furthermore, we propose a multi-phase bandit algorithm, UEtext{-UCB++}, which matches this lower bound to a minor additive factor. UEtext{-UCB++} performs uniform exploration in its initial phases and then utilizes the {\em upper confidence bound }(UCB) bandit algorithm in its final phase. An interesting feature of UEtext{-UCB++} is that the coarser estimates of the mean rewards formed during a uniform exploration phase help to refine the encoding protocol in the next phase, leading to more accurate mean estimates of the rewards in the subsequent phase. This positive reinforcement cycle is critical to reducing the number of uniform exploration rounds and closely matching our lower bound.

Inference-time optimization scales computation to derive deliberate reasoning steps for effective performance. While previous search-based strategies address the short-sightedness of auto-regressive generation, the vast search space leads to excessive exploration and insufficient exploitation. To strike an efficient balance to derive the optimal step, we frame the decoding strategy as foresight sampling, leveraging simulated future steps to obtain globally optimal step estimation. Built on it, we propose a novel decoding strategy, named phi-Decoding. To provide a precise and expressive estimation of step value, phi-Decoding approximates two distributions via foresight and clustering. Sampling from the joint distribution, the optimal steps can be selected for exploitation. To support adaptive computation allocation, we propose in-width and in-depth pruning strategies, featuring a light-weight solution to achieve inference efficiency. Extensive experiments across seven benchmarks show phi-Decoding outperforms strong baselines in both performance and efficiency. Additional analysis demonstrates its generalization across various LLMs and scalability across a wide range of computing budgets. The code will be released at https://github.com/xufangzhi/phi-Decoding, and the open-source PyPI package is coming soon.

Implicit neural representations (INRs) recently achieved great success in image representation and compression, offering high visual quality and fast rendering speeds with 10-1000 FPS, assuming sufficient GPU resources are available. However, this requirement often hinders their use on low-end devices with limited memory. In response, we propose a groundbreaking paradigm of image representation and compression by 2D Gaussian Splatting, named GaussianImage. We first introduce 2D Gaussian to represent the image, where each Gaussian has 8 parameters including position, covariance and color. Subsequently, we unveil a novel rendering algorithm based on accumulated summation. Remarkably, our method with a minimum of 3times lower GPU memory usage and 5times faster fitting time not only rivals INRs (e.g., WIRE, I-NGP) in representation performance, but also delivers a faster rendering speed of 1500-2000 FPS regardless of parameter size. Furthermore, we integrate existing vector quantization technique to build an image codec. Experimental results demonstrate that our codec attains rate-distortion performance comparable to compression-based INRs such as COIN and COIN++, while facilitating decoding speeds of approximately 1000 FPS. Additionally, preliminary proof of concept shows that our codec surpasses COIN and COIN++ in performance when using partial bits-back coding.

The input space of a neural network with ReLU-like activations is partitioned into multiple linear regions, each corresponding to a specific activation pattern of the included ReLU-like activations. We demonstrate that this partition exhibits the following encoding properties across a variety of deep learning models: (1) {\it determinism}: almost every linear region contains at most one training example. We can therefore represent almost every training example by a unique activation pattern, which is parameterized by a {\it neural code}; and (2) {\it categorization}: according to the neural code, simple algorithms, such as K-Means, K-NN, and logistic regression, can achieve fairly good performance on both training and test data. These encoding properties surprisingly suggest that {\it normal neural networks well-trained for classification behave as hash encoders without any extra efforts.} In addition, the encoding properties exhibit variability in different scenarios. {Further experiments demonstrate that {\it model size}, {\it training time}, {\it training sample size}, {\it regularization}, and {\it label noise} contribute in shaping the encoding properties, while the impacts of the first three are dominant.} We then define an {\it activation hash phase chart} to represent the space expanded by {model size}, training time, training sample size, and the encoding properties, which is divided into three canonical regions: {\it under-expressive regime}, {\it critically-expressive regime}, and {\it sufficiently-expressive regime}. The source code package is available at https://github.com/LeavesLei/activation-code.

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional subspaces challenging, especially for deep architectures. We argue that these difficulties come from suboptimal representation learning, where latent variables fail to balance expressivity and simplicity. This tension is closely related to the information bottleneck (IB) dilemma: constructing compressed representations that are both compact and predictive. Rethinking Koopman learning through this lens, we demonstrate that latent mutual information promotes simplicity, yet an overemphasis on simplicity may cause latent space to collapse onto a few dominant modes. In contrast, expressiveness is sustained by the von Neumann entropy, which prevents such collapse and encourages mode diversity. This insight leads us to propose an information-theoretic Lagrangian formulation that explicitly balances this tradeoff. Furthermore, we propose a new algorithm based on the Lagrangian formulation that encourages both simplicity and expressiveness, leading to a stable and interpretable Koopman representation. Beyond quantitative evaluations, we further visualize the learned manifolds under our representations, observing empirical results consistent with our theoretical predictions. Finally, we validate our approach across a diverse range of dynamical systems, demonstrating improved performance over existing Koopman learning methods. The implementation is publicly available at https://github.com/Wenxuan52/InformationKoopman.

Dual encoders perform retrieval by encoding documents and queries into dense lowdimensional vectors, scoring each document by its inner product with the query. We investigate the capacity of this architecture relative to sparse bag-of-words models and attentional neural networks. Using both theoretical and empirical analysis, we establish connections between the encoding dimension, the margin between gold and lower-ranked documents, and the document length, suggesting limitations in the capacity of fixed-length encodings to support precise retrieval of long documents. Building on these insights, we propose a simple neural model that combines the efficiency of dual encoders with some of the expressiveness of more costly attentional architectures, and explore sparse-dense hybrids to capitalize on the precision of sparse retrieval. These models outperform strong alternatives in large-scale retrieval.

While recent neural codecs achieve strong performance at low bitrates when optimized for perceptual quality, their effectiveness deteriorates significantly under ultra-low bitrate conditions. To mitigate this, generative compression methods leveraging semantic priors from pretrained models have emerged as a promising paradigm. However, existing approaches are fundamentally constrained by a tradeoff between semantic faithfulness and perceptual realism. Methods based on explicit representations preserve content structure but often lack fine-grained textures, whereas implicit methods can synthesize visually plausible details at the cost of semantic drift. In this work, we propose a unified framework that bridges this gap by coherently integrating explicit and implicit representations in a training-free manner. Specifically, We condition a diffusion model on explicit high-level semantics while employing reverse-channel coding to implicitly convey fine-grained details. Moreover, we introduce a plug-in encoder that enables flexible control of the distortion-perception tradeoff by modulating the implicit information. Extensive experiments demonstrate that the proposed framework achieves state-of-the-art rate-perception performance, outperforming existing methods and surpassing DiffC by 29.92%, 19.33%, and 20.89% in DISTS BD-Rate on the Kodak, DIV2K, and CLIC2020 datasets, respectively.

Efficient deployment of Large Language Models (LLMs) requires batching multiple requests together to improve throughput. As the batch size, context length, or model size increases, the size of the key and value (KV) cache can quickly become the main contributor to GPU memory usage and the bottleneck of inference latency. Quantization has emerged as an effective technique for KV cache compression, but existing methods still fail at very low bit widths. We observe that distinct channels of a key/value activation embedding are highly inter-dependent, and the joint entropy of multiple channels grows at a slower rate than the sum of their marginal entropies. Based on this insight, we propose Coupled Quantization (CQ), which couples multiple key/value channels together to exploit their inter-dependency and encode the activations in a more information-efficient manner. Extensive experiments reveal that CQ outperforms or is competitive with existing baselines in preserving model quality. Furthermore, we demonstrate that CQ can preserve model quality with KV cache quantized down to 1-bit.

In distributed computing, slower nodes (stragglers) usually become a bottleneck. Gradient Coding (GC), introduced by Tandon et al., is an efficient technique that uses principles of error-correcting codes to distribute gradient computation in the presence of stragglers. In this paper, we consider the distributed computation of a sequence of gradients {g(1),g(2),ldots,g(J)}, where processing of each gradient g(t) starts in round-t and finishes by round-(t+T). Here Tgeq 0 denotes a delay parameter. For the GC scheme, coding is only across computing nodes and this results in a solution where T=0. On the other hand, having T>0 allows for designing schemes which exploit the temporal dimension as well. In this work, we propose two schemes that demonstrate improved performance compared to GC. Our first scheme combines GC with selective repetition of previously unfinished tasks and achieves improved straggler mitigation. In our second scheme, which constitutes our main contribution, we apply GC to a subset of the tasks and repetition for the remainder of the tasks. We then multiplex these two classes of tasks across workers and rounds in an adaptive manner, based on past straggler patterns. Using theoretical analysis, we demonstrate that our second scheme achieves significant reduction in the computational load. In our experiments, we study a practical setting of concurrently training multiple neural networks over an AWS Lambda cluster involving 256 worker nodes, where our framework naturally applies. We demonstrate that the latter scheme can yield a 16\% improvement in runtime over the baseline GC scheme, in the presence of naturally occurring, non-simulated stragglers.

In this paper, we consider the problem of bit allocation in Neural Video Compression (NVC). First, we reveal a fundamental relationship between bit allocation in NVC and Semi-Amortized Variational Inference (SAVI). Specifically, we show that SAVI with GoP (Group-of-Picture)-level likelihood is equivalent to pixel-level bit allocation with precise rate \& quality dependency model. Based on this equivalence, we establish a new paradigm of bit allocation using SAVI. Different from previous bit allocation methods, our approach requires no empirical model and is thus optimal. Moreover, as the original SAVI using gradient ascent only applies to single-level latent, we extend the SAVI to multi-level such as NVC by recursively applying back-propagating through gradient ascent. Finally, we propose a tractable approximation for practical implementation. Our method can be applied to scenarios where performance outweights encoding speed, and serves as an empirical bound on the R-D performance of bit allocation. Experimental results show that current state-of-the-art bit allocation algorithms still have a room of approx 0.5 dB PSNR to improve compared with ours. Code is available at https://github.com/tongdaxu/Bit-Allocation-Using-Optimization.

We argue that the estimation of mutual information between high dimensional continuous random variables can be achieved by gradient descent over neural networks. We present a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size, trainable through back-prop, and strongly consistent. We present a handful of applications on which MINE can be used to minimize or maximize mutual information. We apply MINE to improve adversarially trained generative models. We also use MINE to implement Information Bottleneck, applying it to supervised classification; our results demonstrate substantial improvement in flexibility and performance in these settings.

The pervasiveness of proprietary language models has raised critical privacy concerns, necessitating advancements in private inference (PI), where computations are performed directly on encrypted data without revealing users' sensitive information. While PI offers a promising solution, its practical deployment is hindered by substantial communication and latency overheads, primarily stemming from nonlinear operations. To address this, we introduce an information-theoretic framework to characterize the role of nonlinearities in decoder-only language models, laying a principled foundation for optimizing transformer-architectures tailored to the demands of PI. By leveraging Shannon's entropy as a quantitative measure, we uncover the previously unexplored dual significance of nonlinearities: beyond ensuring training stability, they are crucial for maintaining attention head diversity. Specifically, we find that their removal triggers two critical failure modes: {\em entropy collapse} in deeper layers that destabilizes training, and {\em entropic overload} in earlier layers that leads to under-utilization of Multi-Head Attention's (MHA) representational capacity. We propose an entropy-guided attention mechanism paired with a novel entropy regularization technique to mitigate entropic overload. Additionally, we explore PI-friendly alternatives to layer normalization for preventing entropy collapse and stabilizing the training of LLMs with reduced-nonlinearities. Our study bridges the gap between information theory and architectural design, establishing entropy dynamics as a principled guide for developing efficient PI architectures. The code and implementation are available at https://github.com/Nandan91/entropy-guided-attention-llm{entropy-guided-llm}.

Neural audio codecs are foundational to speech language models. It is expected to have a low frame rate and decoupled semantic and acoustic information. A lower frame rate codec can reduce the computational cost of speech language models by shortening the sequence length. Recent studies have developed 12.5Hz low-frame-rate audio codecs, but even lower frame rate codecs remain underexplored. We find that a major challenge for very low frame rate tokens is missing semantic information. This paper introduces FlexiCodec to address this limitation. FlexiCodec improves semantic preservation with a dynamic frame rate approach and introduces a novel architecture featuring an ASR feature-assisted dual stream encoding and Transformer bottlenecks. With dynamic frame rates, it uses less frames at information-sparse regions through adaptively merging semantically similar frames. A dynamic frame rate also allows FlexiCodec to support inference-time controllable frame rates between 3Hz and 12.5Hz. Experiments on 6.25Hz, 8.3Hz and 12.5Hz average frame rates confirm that FlexiCodec excels over baseline systems in semantic information preservation and delivers a high audio reconstruction quality. We also validate the effectiveness of FlexiCodec in language model-based TTS. Demos are available at: https://flexicodec.github.io

Neural speech codecs have gained great attention for their outstanding reconstruction with discrete token representations. It is a crucial component in generative tasks such as speech coding and large language models (LLM). However, most works based on residual vector quantization perform worse with fewer tokens due to low coding efficiency for modeling complex coupled information. In this paper, we propose a neural speech codec named FreeCodec which employs a more effective encoding framework by decomposing intrinsic properties of speech into different components: 1) a global vector is extracted as the timbre information, 2) a prosody encoder with a long stride level is used to model the prosody information, 3) the content information is from a content encoder. Using different training strategies, FreeCodec achieves state-of-the-art performance in reconstruction and disentanglement scenarios. Results from subjective and objective experiments demonstrate that our framework outperforms existing methods.

Deep neural networks tend to exhibit a bias toward low-rank solutions during training, implicitly learning low-dimensional feature representations. This paper investigates how deep multilayer perceptrons (MLPs) encode these feature manifolds and connects this behavior to the Information Bottleneck (IB) theory. We introduce the concept of local rank as a measure of feature manifold dimensionality and demonstrate, both theoretically and empirically, that this rank decreases during the final phase of training. We argue that networks that reduce the rank of their learned representations also compress mutual information between inputs and intermediate layers. This work bridges the gap between feature manifold rank and information compression, offering new insights into the interplay between information bottlenecks and representation learning.

In this work, we present a naive initialization scheme for word vectors based on a dense, independent co-occurrence model and provide preliminary results that suggest it is competitive and warrants further investigation. Specifically, we demonstrate through information-theoretic minimum description length (MDL) probing that our model, EigenNoise, can approach the performance of empirically trained GloVe despite the lack of any pre-training data (in the case of EigenNoise). We present these preliminary results with interest to set the stage for further investigations into how this competitive initialization works without pre-training data, as well as to invite the exploration of more intelligent initialization schemes informed by the theory of harmonic linguistic structure. Our application of this theory likewise contributes a novel (and effective) interpretation of recent discoveries which have elucidated the underlying distributional information that linguistic representations capture from data and contrast distributions.

Large Language Models (LLMs) are increasingly used in applications requiring long context lengths, but the key-value (KV) cache often becomes a memory bottleneck on GPUs as context grows. To address this, we propose Commutative Vector Quantization (CommVQ) to significantly reduce memory usage for long-context LLM inference. We first introduce additive quantization with a lightweight encoder and codebook to compress the KV cache, which can be decoded via simple matrix multiplication. To further reduce computational costs during decoding, we design the codebook to be commutative with Rotary Position Embedding (RoPE) and train it using an Expectation-Maximization (EM) algorithm. This enables efficient integration of decoding into the self-attention mechanism. Our approach achieves high accuracy with additive quantization and low overhead via the RoPE-commutative codebook. Experiments on long-context benchmarks and GSM8K show that our method reduces FP16 KV cache size by 87.5% with 2-bit quantization, while outperforming state-of-the-art KV cache quantization methods. Notably, it enables 1-bit KV cache quantization with minimal accuracy loss, allowing a LLaMA-3.1 8B model to run with a 128K context length on a single RTX 4090 GPU. The source code is available at: https://github.com/UMass-Embodied-AGI/CommVQ.

Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in the high-dimensional, undersampled regimes typical of modern experiments. Recent machine learning-based estimators show promise, but their accuracy depends sensitively on dataset size, structure, and hyperparameters, with no accepted tests to detect failures. We close these gaps through a systematic evaluation of classical and neural MI estimators across standard benchmarks and new synthetic datasets tailored to challenging high-dimensional, undersampled regimes. We contribute: (i) a practical protocol for reliable MI estimation with explicit checks for statistical consistency; (ii) confidence intervals (error bars around estimates) that existing neural MI estimator do not provide; and (iii) a new class of probabilistic critics designed for high-dimensional, high-information settings. We demonstrate the effectiveness of our protocol with computational experiments, showing that it consistently matches or surpasses existing methods while uniquely quantifying its own reliability. We show that reliable MI estimation is sometimes achievable even in severely undersampled, high-dimensional datasets, provided they admit accurate low-dimensional representations. This broadens the scope of applicability of neural MI estimators and clarifies when such estimators can be trusted.

The uniform information density (UID) hypothesis states that humans tend to distribute information roughly evenly across an utterance or discourse. Early evidence in support of the UID hypothesis came from Genzel & Charniak (2002), which proposed an entropy rate constancy principle based on the probability of English text under n-gram language models. We re-evaluate the claims of Genzel & Charniak (2002) with neural language models, failing to find clear evidence in support of entropy rate constancy. We conduct a range of experiments across datasets, model sizes, and languages and discuss implications for the uniform information density hypothesis and linguistic theories of efficient communication more broadly.

There has been much interest in deploying deep learning algorithms on low-powered devices, including smartphones, drones, and medical sensors. However, full-scale deep neural networks are often too resource-intensive in terms of energy and storage. As a result, the bulk part of the machine learning operation is therefore often carried out on an edge server, where the data is compressed and transmitted. However, compressing data (such as images) leads to transmitting information irrelevant to the supervised task. Another popular approach is to split the deep network between the device and the server while compressing intermediate features. To date, however, such split computing strategies have barely outperformed the aforementioned naive data compression baselines due to their inefficient approaches to feature compression. This paper adopts ideas from knowledge distillation and neural image compression to compress intermediate feature representations more efficiently. Our supervised compression approach uses a teacher model and a student model with a stochastic bottleneck and learnable prior for entropy coding (Entropic Student). We compare our approach to various neural image and feature compression baselines in three vision tasks and found that it achieves better supervised rate-distortion performance while maintaining smaller end-to-end latency. We furthermore show that the learned feature representations can be tuned to serve multiple downstream tasks.

Modern data compression methods are slowly reaching their limits after 80 years of research, millions of papers, and wide range of applications. Yet, the extravagant 6G communication speed requirement raises a major open question for revolutionary new ideas of data compression. We have previously shown all understanding or learning are compression, under reasonable assumptions. Large language models (LLMs) understand data better than ever before. Can they help us to compress data? The LLMs may be seen to approximate the uncomputable Solomonoff induction. Therefore, under this new uncomputable paradigm, we present LMCompress. LMCompress shatters all previous lossless compression algorithms, doubling the lossless compression ratios of JPEG-XL for images, FLAC for audios, and H.264 for videos, and quadrupling the compression ratio of bz2 for texts. The better a large model understands the data, the better LMCompress compresses.

We introduce a practical real-time neural video codec (NVC) designed to deliver high compression ratio, low latency and broad versatility. In practice, the coding speed of NVCs depends on 1) computational costs, and 2) non-computational operational costs, such as memory I/O and the number of function calls. While most efficient NVCs prioritize reducing computational cost, we identify operational cost as the primary bottleneck to achieving higher coding speed. Leveraging this insight, we introduce a set of efficiency-driven design improvements focused on minimizing operational costs. Specifically, we employ implicit temporal modeling to eliminate complex explicit motion modules, and use single low-resolution latent representations rather than progressive downsampling. These innovations significantly accelerate NVC without sacrificing compression quality. Additionally, we implement model integerization for consistent cross-device coding and a module-bank-based rate control scheme to improve practical adaptability. Experiments show our proposed DCVC-RT achieves an impressive average encoding/decoding speed at 125.2/112.8 fps (frames per second) for 1080p video, while saving an average of 21% in bitrate compared to H.266/VTM. The code is available at https://github.com/microsoft/DCVC.

The Information Bottleneck (IB) principle has emerged as a promising approach for enhancing the generalization, robustness, and interpretability of deep neural networks, demonstrating efficacy across image segmentation, document clustering, and semantic communication. Among IB implementations, the IB Lagrangian method, employing Lagrangian multipliers, is widely adopted. While numerous methods for the optimizations of IB Lagrangian based on variational bounds and neural estimators are feasible, their performance is highly dependent on the quality of their design, which is inherently prone to errors. To address this limitation, we introduce Structured IB, a framework for investigating potential structured features. By incorporating auxiliary encoders to extract missing informative features, we generate more informative representations. Our experiments demonstrate superior prediction accuracy and task-relevant information preservation compared to the original IB Lagrangian method, even with reduced network size.

Standardized lossy video coding is at the core of almost all real-world video processing pipelines. Rate control is used to enable standard codecs to adapt to different network bandwidth conditions or storage constraints. However, standard video codecs (e.g., H.264) and their rate control modules aim to minimize video distortion w.r.t. human quality assessment. We demonstrate empirically that standard-coded videos vastly deteriorate the performance of deep vision models. To overcome the deterioration of vision performance, this paper presents the first end-to-end learnable deep video codec control that considers both bandwidth constraints and downstream deep vision performance, while adhering to existing standardization. We demonstrate that our approach better preserves downstream deep vision performance than traditional standard video coding.

Code generation is a latency-sensitive task that demands high timeliness, but the autoregressive decoding mechanism of Large Language Models (LLMs) leads to poor inference efficiency. Existing LLM inference acceleration methods mainly focus on standalone functions using only built-in components. Moreover, they treat code like natural language sequences, ignoring its unique syntax and semantic characteristics. As a result, the effectiveness of these approaches in code generation tasks remains limited and fails to align with real-world programming scenarios. To alleviate this issue, we propose CodeSwift, a simple yet highly efficient inference acceleration approach specifically designed for code generation, without comprising the quality of the output. CodeSwift constructs a multi-source datastore, providing access to both general and project-specific knowledge, facilitating the retrieval of high-quality draft sequences. Moreover, CodeSwift reduces retrieval cost by controlling retrieval timing, and enhances efficiency through parallel retrieval and a context- and LLM preference-aware cache. Experimental results show that CodeSwift can reach up to 2.53x and 2.54x speedup compared to autoregressive decoding in repository-level and standalone code generation tasks, respectively, outperforming state-of-the-art inference acceleration approaches by up to 88%.

"Compression Tells Intelligence", is supported by research in artificial intelligence, particularly concerning (multimodal) large language models (LLMs/MLLMs), where compression efficiency often correlates with improved model performance and capabilities. For compression, classical visual coding based on traditional information theory has developed over decades, achieving great success with numerous international industrial standards widely applied in multimedia (e.g., image/video) systems. Except that, the recent emergingvisual token technology of generative multi-modal large models also shares a similar fundamental objective like visual coding: maximizing semantic information fidelity during the representation learning while minimizing computational cost. Therefore, this paper provides a comprehensive overview of two dominant technique families first -- Visual Coding and Vision Token Technology -- then we further unify them from the aspect of optimization, discussing the essence of compression efficiency and model performance trade-off behind. Next, based on the proposed unified formulation bridging visual coding andvisual token technology, we synthesize bidirectional insights of themselves and forecast the next-gen visual codec and token techniques. Last but not least, we experimentally show a large potential of the task-oriented token developments in the more practical tasks like multimodal LLMs (MLLMs), AI-generated content (AIGC), and embodied AI, as well as shedding light on the future possibility of standardizing a general token technology like the traditional codecs (e.g., H.264/265) with high efficiency for a wide range of intelligent tasks in a unified and effective manner.

In recent years, neural network-driven image compression (NIC) has gained significant attention. Some works adopt deep generative models such as GANs and diffusion models to enhance perceptual quality (realism). A critical obstacle of these generative NIC methods is that each model is optimized for a single bit rate. Consequently, multiple models are required to compress images to different bit rates, which is impractical for real-world applications. To tackle this issue, we propose a variable-rate generative NIC model. Specifically, we explore several discriminator designs tailored for the variable-rate approach and introduce a novel adversarial loss. Moreover, by incorporating the newly proposed multi-realism technique, our method allows the users to adjust the bit rate, distortion, and realism with a single model, achieving ultra-controllability. Unlike existing variable-rate generative NIC models, our method matches or surpasses the performance of state-of-the-art single-rate generative NIC models while covering a wide range of bit rates using just one model. Code will be available at https://github.com/iwa-shi/CRDR

Recent advances in generative compression methods have demonstrated remarkable progress in enhancing the perceptual quality of compressed data, especially in scenarios with low bitrates. However, their efficacy and applicability to achieve extreme compression ratios (<0.05 bpp) remain constrained. In this work, we propose a simple yet effective coding framework by introducing vector quantization (VQ)--based generative models into the image compression domain. The main insight is that the codebook learned by the VQGAN model yields a strong expressive capacity, facilitating efficient compression of continuous information in the latent space while maintaining reconstruction quality. Specifically, an image can be represented as VQ-indices by finding the nearest codeword, which can be encoded using lossless compression methods into bitstreams. We propose clustering a pre-trained large-scale codebook into smaller codebooks through the K-means algorithm, yielding variable bitrates and different levels of reconstruction quality within the coding framework. Furthermore, we introduce a transformer to predict lost indices and restore images in unstable environments. Extensive qualitative and quantitative experiments on various benchmark datasets demonstrate that the proposed framework outperforms state-of-the-art codecs in terms of perceptual quality-oriented metrics and human perception at extremely low bitrates (le 0.04 bpp). Remarkably, even with the loss of up to 20% of indices, the images can be effectively restored with minimal perceptual loss.

Few neural architectures lend themselves to provable learning with gradient based methods. One popular model is the single-index model, in which labels are produced by composing an unknown linear projection with a possibly unknown scalar link function. Learning this model with SGD is relatively well-understood, whereby the so-called information exponent of the link function governs a polynomial sample complexity rate. However, extending this analysis to deeper or more complicated architectures remains challenging. In this work, we consider single index learning in the setting of symmetric neural networks. Under analytic assumptions on the activation and maximum degree assumptions on the link function, we prove that gradient flow recovers the hidden planted direction, represented as a finitely supported vector in the feature space of power sum polynomials. We characterize a notion of information exponent adapted to our setting that controls the efficiency of learning.

Code-switching, the alternation of languages within a single discourse, presents a significant challenge for Automatic Speech Recognition. Despite the unique nature of the task, performance is commonly measured with established metrics such as Word-Error-Rate (WER). However, in this paper, we question whether these general metrics accurately assess performance on code-switching. Specifically, using both Connectionist-Temporal-Classification and Encoder-Decoder models, we show fine-tuning on non-code-switched data from both matrix and embedded language improves classical metrics on code-switching test sets, although actual code-switched words worsen (as expected). Therefore, we propose Point-of-Interest Error Rate (PIER), a variant of WER that focuses only on specific words of interest. We instantiate PIER on code-switched utterances and show that this more accurately describes the code-switching performance, showing huge room for improvement in future work. This focused evaluation allows for a more precise assessment of model performance, particularly in challenging aspects such as inter-word and intra-word code-switching.

Idempotence is the stability of image codec to re-compression. At the first glance, it is unrelated to perceptual image compression. However, we find that theoretically: 1) Conditional generative model-based perceptual codec satisfies idempotence; 2) Unconditional generative model with idempotence constraint is equivalent to conditional generative codec. Based on this newfound equivalence, we propose a new paradigm of perceptual image codec by inverting unconditional generative model with idempotence constraints. Our codec is theoretically equivalent to conditional generative codec, and it does not require training new models. Instead, it only requires a pre-trained mean-square-error codec and unconditional generative model. Empirically, we show that our proposed approach outperforms state-of-the-art methods such as HiFiC and ILLM, in terms of Fr\'echet Inception Distance (FID). The source code is provided in https://github.com/tongdaxu/Idempotence-and-Perceptual-Image-Compression.

The present work explores the theoretical limits of Machine Learning (ML) within the framework of Kolmogorov's theory of Algorithmic Probability, which clarifies the notion of entropy as Expected Kolmogorov Complexity and formalizes other fundamental concepts such as Occam's razor via Levin's Universal Distribution. As a fundamental application, we develop Maximum Entropy methods that allow us to derive the Erdos--Kac Law in Probabilistic Number Theory, and establish the impossibility of discovering a formula for primes using Machine Learning via the Prime Coding Theorem.

Existing multimodal large model-based image compression frameworks often rely on a fragmented integration of semantic retrieval, latent compression, and generative models, resulting in suboptimal performance in both reconstruction fidelity and coding efficiency. To address these challenges, we propose a residual-guided ultra lowrate image compression named ResULIC, which incorporates residual signals into both semantic retrieval and the diffusion-based generation process. Specifically, we introduce Semantic Residual Coding (SRC) to capture the semantic disparity between the original image and its compressed latent representation. A perceptual fidelity optimizer is further applied for superior reconstruction quality. Additionally, we present the Compression-aware Diffusion Model (CDM), which establishes an optimal alignment between bitrates and diffusion time steps, improving compression-reconstruction synergy. Extensive experiments demonstrate the effectiveness of ResULIC, achieving superior objective and subjective performance compared to state-of-the-art diffusion-based methods with - 80.7%, -66.3% BD-rate saving in terms of LPIPS and FID. Project page is available at https: //njuvision.github.io/ResULIC/.

Large language models demonstrate remarkable in-context learning capabilities, adapting to new tasks without parameter updates. While this phenomenon has been successfully modeled as implicit Bayesian inference, recent empirical findings reveal a fundamental contradiction: transformers systematically violate the martingale property, a cornerstone requirement of Bayesian updating on exchangeable data. This violation challenges the theoretical foundations underlying uncertainty quantification in critical applications. Our theoretical analysis establishes four key results: (1) positional encodings induce martingale violations of order Theta(log n / n); (2) transformers achieve information-theoretic optimality with excess risk O(n^{-1/2}) in expectation over orderings; (3) the implicit posterior representation converges to the true Bayesian posterior in the space of sufficient statistics; and (4) we derive the optimal chain-of-thought length as k^* = Theta(nlog(1/varepsilon)) with explicit constants, providing a principled approach to reduce inference costs while maintaining performance. Empirical validation on GPT-3 confirms predictions (1)-(3), with transformers reaching 99\% of theoretical entropy limits within 20 examples. Our framework provides practical methods for extracting calibrated uncertainty estimates from position-aware architectures and optimizing computational efficiency in deployment.