Daily Papers

Implicit Neural Representation (INR), leveraging a neural network to transform coordinate input into corresponding attributes, has recently driven significant advances in several vision-related domains. However, the performance of INR is heavily influenced by the choice of the nonlinear activation function used in its multilayer perceptron (MLP) architecture. Multiple nonlinearities have been investigated; yet, current INRs face limitations in capturing high-frequency components, diverse signal types, and handling inverse problems. We have identified that these problems can be greatly alleviated by introducing a paradigm shift in INRs. We find that an architecture with learnable activations in initial layers can represent fine details in the underlying signals. Specifically, we propose SL^{2}A-INR, a hybrid network for INR with a single-layer learnable activation function, prompting the effectiveness of traditional ReLU-based MLPs. Our method performs superior across diverse tasks, including image representation, 3D shape reconstructions, inpainting, single image super-resolution, CT reconstruction, and novel view synthesis. Through comprehensive experiments, SL^{2}A-INR sets new benchmarks in accuracy, quality, and convergence rates for INR.

Kolmogorov-Arnold networks (KANs) are a remarkable innovation consisting of learnable activation functions with the potential to capture more complex relationships from data. Although KANs are useful in finding symbolic representations and continual learning of one-dimensional functions, their effectiveness in diverse machine learning (ML) tasks, such as vision, remains questionable. Presently, KANs are deployed by replacing multilayer perceptrons (MLPs) in deep network architectures, including advanced architectures such as vision Transformers (ViTs). In this paper, we are the first to design a general learnable Kolmogorov-Arnold Attention (KArAt) for vanilla ViTs that can operate on any choice of basis. However, the computing and memory costs of training them motivated us to propose a more modular version, and we designed particular learnable attention, called Fourier-KArAt. Fourier-KArAt and its variants either outperform their ViT counterparts or show comparable performance on CIFAR-10, CIFAR-100, and ImageNet-1K datasets. We dissect these architectures' performance and generalization capacity by analyzing their loss landscapes, weight distributions, optimizer path, attention visualization, and spectral behavior, and contrast them with vanilla ViTs. The goal of this paper is not to produce parameter- and compute-efficient attention, but to encourage the community to explore KANs in conjunction with more advanced architectures that require a careful understanding of learnable activations. Our open-source code and implementation details are available on: https://subhajitmaity.me/KArAt

Accurate air quality forecasts are vital for public health alerts, exposure assessment, and emissions control. In practice, observational data are often missing in varying proportions and patterns due to collection and transmission issues. These incomplete spatiotemporal records impede reliable inference and risk assessment and can lead to overconfident extrapolation. To address these challenges, we propose an end to end framework, the channel gated learning unit based spatiotemporal bayesian neural field (CGLUBNF). It uses Fourier features with a graph attention encoder to capture multiscale spatial dependencies and seasonal temporal dynamics. A channel gated learning unit, equipped with learnable activations and gated residual connections, adaptively filters and amplifies informative features. Bayesian inference jointly optimizes predictive distributions and parameter uncertainty, producing point estimates and calibrated prediction intervals. We conduct a systematic evaluation on two real world datasets, covering four typical missing data patterns and comparing against five state of the art baselines. CGLUBNF achieves superior prediction accuracy and sharper confidence intervals. In addition, we further validate robustness across multiple prediction horizons and analysis the contribution of extraneous variables. This research lays a foundation for reliable deep learning based spatio-temporal forecasting with incomplete observations in emerging sensing paradigms, such as real world vehicle borne mobile monitoring.

Existing parameter-efficient fine-tuning (PEFT) methods primarily adapt weight matrices while keeping activation functions fixed. We introduce NoRA, the first PEFT framework that directly adapts nonlinear activation functions in pretrained transformer-based models. NoRA replaces fixed activations with learnable rational functions and applies structured low-rank updates to numerator and denominator coefficients, with a group-wise design that localizes adaptation and improves stability at minimal cost. On vision transformers trained on CIFAR-10 and CIFAR-100, NoRA matches or exceeds full fine-tuning while updating only 0.4\% of parameters (0.02M), achieving accuracy gains of +0.17\% and +0.27\%. When combined with LoRA (NoRA++), it outperforms LoRA and DoRA under matched training budgets by adding fewer trainable parameters. On LLaMA3-8B instruction tuning, NoRA++ consistently improves generation quality, yielding average MMLU gains of +0.3\%--0.8\%, including +1.6\% on STEM (Alpaca) and +1.3\% on OpenOrca. We further show that NoRA constrains adaptation to a low-dimensional functional subspace, implicitly regularizing update magnitude and direction. These results establish activation-space tuning as a complementary and highly parameter-efficient alternative to weight-based PEFT, positioning activation functions as first-class objects for model adaptation.

Implicit neural representations (INRs) use neural networks to provide continuous and resolution-independent representations of complex signals with a small number of parameters. However, existing INR models often fail to capture important frequency components specific to each task. To address this issue, in this paper, we propose a Fourier Kolmogorov Arnold network (FKAN) for INRs. The proposed FKAN utilizes learnable activation functions modeled as Fourier series in the first layer to effectively control and learn the task-specific frequency components. In addition, the activation functions with learnable Fourier coefficients improve the ability of the network to capture complex patterns and details, which is beneficial for high-resolution and high-dimensional data. Experimental results show that our proposed FKAN model outperforms three state-of-the-art baseline schemes, and improves the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) for the image representation task and intersection over union (IoU) for the 3D occupancy volume representation task, respectively.

Quantization Aware Training (QAT) is a neural network quantization technique that compresses model size and improves operational efficiency while effectively maintaining model performance. The paradigm of QAT is to introduce fake quantization operators during the training process, allowing the model to autonomously compensate for information loss caused by quantization. Making quantization parameters trainable can significantly improve the performance of QAT, but at the cost of compromising the flexibility during inference, especially when dealing with activation values with substantially different distributions. In this paper, we propose an effective learnable adaptive neural network quantization method, called Adaptive Step Size Quantization (ASQ), to resolve this conflict. Specifically, the proposed ASQ method first dynamically adjusts quantization scaling factors through a trained module capable of accommodating different activations. Then, to address the rigid resolution issue inherent in Power of Two (POT) quantization, we propose an efficient non-uniform quantization scheme. We utilize the Power Of Square root of Two (POST) as the basis for exponential quantization, effectively handling the bell-shaped distribution of neural network weights across various bit-widths while maintaining computational efficiency through a Look-Up Table method (LUT). Extensive experimental results demonstrate that the proposed ASQ method is superior to the state-of-the-art QAT approaches. Notably that the ASQ is even competitive compared to full precision baselines, with its 4-bit quantized ResNet34 model improving accuracy by 1.2\% on ImageNet.

Training stability is a persistent challenge in the pre-training of large language models (LLMs), particularly for architectures such as Post-Norm Transformers, which are prone to gradient explosion and dissipation. In this paper, we propose Scale-Distribution Decoupling (SDD), a novel approach that stabilizes training by explicitly decoupling the scale and distribution of the weight matrix in fully-connected layers. SDD applies a normalization mechanism to regulate activations and a learnable scaling vector to maintain well-conditioned gradients, effectively preventing gradient explosion and dissipation. This separation improves optimization efficiency, particularly in deep networks, by ensuring stable gradient propagation. Experimental results demonstrate that our method stabilizes training across various LLM architectures and outperforms existing techniques in different normalization configurations. Furthermore, the proposed method is lightweight and compatible with existing frameworks, making it a practical solution for stabilizing LLM training. Code is available at https://github.com/kaihemo/SDD.

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

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

Large language models (LLMs) have revolutionized natural language processing tasks. However, their practical deployment is hindered by their immense memory and computation requirements. Although recent post-training quantization (PTQ) methods are effective in reducing memory footprint and improving the computational efficiency of LLM, they hand-craft quantization parameters, which leads to low performance and fails to deal with extremely low-bit quantization. To tackle this issue, we introduce an Omnidirectionally calibrated Quantization (OmniQuant) technique for LLMs, which achieves good performance in diverse quantization settings while maintaining the computational efficiency of PTQ by efficiently optimizing various quantization parameters. OmniQuant comprises two innovative components including Learnable Weight Clipping (LWC) and Learnable Equivalent Transformation (LET). LWC modulates the extreme values of weights by optimizing the clipping threshold. Meanwhile, LET tackles activation outliers by shifting the challenge of quantization from activations to weights through a learnable equivalent transformation. Operating within a differentiable framework using block-wise error minimization, OmniQuant can optimize the quantization process efficiently for both weight-only and weight-activation quantization. For instance, the LLaMA-2 model family with the size of 7-70B can be processed with OmniQuant on a single A100-40G GPU within 1-16 hours using 128 samples. Extensive experiments validate OmniQuant's superior performance across diverse quantization configurations such as W4A4, W6A6, W4A16, W3A16, and W2A16. Additionally, OmniQuant demonstrates effectiveness in instruction-tuned models and delivers notable improvements in inference speed and memory reduction on real devices. Codes and models are available at https://github.com/OpenGVLab/OmniQuant.

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

Fine-tuning pre-trained models has emerged as a powerful technique in numerous domains, owing to its ability to leverage enormous pre-existing knowledge and achieve remarkable performance on downstream tasks. However, updating the parameters of entire networks is computationally intensive. Although state-of-the-art parameter-efficient transfer learning (PETL) methods significantly reduce the trainable parameters and storage demand, almost all of them still need to back-propagate the gradients through large pre-trained networks. This memory-extensive characteristic extremely limits the applicability of PETL methods in real-world scenarios. To this end, we propose a new memory-efficient PETL strategy, dubbed Universal Parallel Tuning (UniPT). Specifically, we facilitate the transfer process via a lightweight learnable parallel network, which consists of two modules: 1) A parallel interaction module that decouples the inherently sequential connections and processes the intermediate activations detachedly of the pre-trained network. 2) A confidence aggregation module that learns optimal strategies adaptively for integrating cross-layer features. We evaluate UniPT with different backbones (e.g., VSEinfty, CLIP4Clip, Clip-ViL, and MDETR) on five challenging vision-and-language tasks (i.e., image-text retrieval, video-text retrieval, visual question answering, compositional question answering, and visual grounding). Extensive ablations on ten datasets have validated that our UniPT can not only dramatically reduce memory consumption and outperform the best memory-efficient competitor, but also achieve higher performance than existing PETL methods in a low-memory scenario on different architectures. Our code is publicly available at: https://github.com/Paranioar/UniPT.

This paper introduces the Univariate Gaussian Mixture Model Neural Network (uGMM-NN), a novel neural architecture that embeds probabilistic reasoning directly into the computational units of deep networks. Unlike traditional neurons, which apply weighted sums followed by fixed nonlinearities, each uGMM-NN node parameterizes its activations as a univariate Gaussian mixture, with learnable means, variances, and mixing coefficients. This design enables richer representations by capturing multimodality and uncertainty at the level of individual neurons, while retaining the scalability of standard feedforward networks. We demonstrate that uGMM-NN can achieve competitive discriminative performance compared to conventional multilayer perceptrons, while additionally offering a probabilistic interpretation of activations. The proposed framework provides a foundation for integrating uncertainty-aware components into modern neural architectures, opening new directions for both discriminative and generative modeling.

Deep learning approaches for black-box modelling of audio effects have shown promise, however, the majority of existing work focuses on nonlinear effects with behaviour on relatively short time-scales, such as guitar amplifiers and distortion. While recurrent and convolutional architectures can theoretically be extended to capture behaviour at longer time scales, we show that simply scaling the width, depth, or dilation factor of existing architectures does not result in satisfactory performance when modelling audio effects such as fuzz and dynamic range compression. To address this, we propose the integration of time-varying feature-wise linear modulation into existing temporal convolutional backbones, an approach that enables learnable adaptation of the intermediate activations. We demonstrate that our approach more accurately captures long-range dependencies for a range of fuzz and compressor implementations across both time and frequency domain metrics. We provide sound examples, source code, and pretrained models to faciliate reproducibility.

The Segment Anything Model 2 (SAM2) is a powerful foundation model for promptable segmentation. However, its high computational and memory costs are a major barrier to deployment on resource-constrained devices. In this paper, we present Q-SAM2, an accurate low-bit quantization method that achieves high compression and high fidelity. To address performance degradation arising from challenging weight and activation distributions during quantization, Q-SAM2 introduces two novel contributions: Variance-Reduced Calibration (VRC), an initialization method that reduces weight statistical variance by minimizing the Frobenius norm over a small calibration batch; and Learnable Statistical Clipping (LSC), a Quantization-Aware Training (QAT) method that learns momentum-stabilized clipping factors to manage outliers in weights and activations. Comprehensive experiments demonstrate that Q-SAM2 achieves highly accurate inference with substantial efficiency gains, significantly surpassing state-of-the-art general QAT schemes, particularly in the ultra-low 2-bit regime. Specifically, Q-SAM2 achieves an accuracy gain of up to 9.7 ppt in J&F on the video segmentation benchmark and 7.3 ppt in mIoU for instance segmentation over the best competing QAT model, all while achieving an 8x reduction in model size compared to the BF16 baseline.

Variational quantum circuits (VQCs) are central to quantum machine learning, while recent progress in Kolmogorov-Arnold networks (KANs) highlights the power of learnable activation functions. We unify these directions by introducing quantum variational activation functions (QVAFs), realized through single-qubit data re-uploading circuits called DatA Re-Uploading ActivatioNs (DARUANs). We show that DARUAN with trainable weights in data pre-processing possesses an exponentially growing frequency spectrum with data repetitions, enabling an exponential reduction in parameter size compared with Fourier-based activations without loss of expressivity. Embedding DARUAN into KANs yields quantum-inspired KANs (QKANs), which retain the interpretability of KANs while improving their parameter efficiency, expressivity, and generalization. We further introduce two novel techniques to enhance scalability, feasibility and computational efficiency, such as layer extension and hybrid QKANs (HQKANs) as drop-in replacements of multi-layer perceptrons (MLPs) for feed-forward networks in large-scale models. We provide theoretical analysis and extensive experiments on function regression, image classification, and autoregressive generative language modeling, demonstrating the efficiency and scalability of QKANs. DARUANs and QKANs offer a promising direction for advancing quantum machine learning on both noisy intermediate-scale quantum (NISQ) hardware and classical quantum simulators.

The success of powerful open source Large Language Models (LLMs) has enabled the community to create a vast collection of post-trained models adapted to specific tasks and domains. However, navigating and understanding these models remains challenging due to inconsistent metadata and unstructured repositories. We introduce Delta Activations, a method to represent finetuned models as vector embeddings by measuring shifts in their internal activations relative to a base model. This representation allows for effective clustering by domain and task, revealing structure in the model landscape. Delta Activations also demonstrate desirable properties: it is robust across finetuning settings and exhibits an additive property when finetuning datasets are mixed. In addition, we show that Delta Activations can embed tasks via few-shot finetuning, and further explore its use for model selection and merging. We hope Delta Activations can facilitate the practice of reusing publicly available models. Code is available at https://github.com/OscarXZQ/delta_activations.

Predictive modeling on web-scale tabular data with billions of instances and hundreds of heterogeneous numerical features faces significant scalability challenges. These features exhibit anisotropy, heavy-tailed distributions, and non-stationarity, creating bottlenecks for models like Gradient Boosting Decision Trees and requiring laborious manual feature engineering. We introduce KMLP, a hybrid deep architecture integrating a shallow Kolmogorov-Arnold Network (KAN) front-end with a Gated Multilayer Perceptron (gMLP) backbone. The KAN front-end uses learnable activation functions to automatically model complex non-linear transformations for each feature, while the gMLP backbone captures high-order interactions. Experiments on public benchmarks and an industrial dataset with billions of samples show KMLP achieves state-of-the-art performance, with advantages over baselines like GBDTs increasing at larger scales, validating KMLP as a scalable deep learning paradigm for large-scale web tabular data.

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable activation functions on edges ("weights"). KANs have no linear weights at all -- every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today's deep learning models which rely heavily on MLPs.

Reliably controlling the behavior of large language models is a pressing open problem. Existing methods include supervised finetuning, reinforcement learning from human feedback, prompt engineering and guided decoding. We instead investigate activation engineering: modifying activations at inference-time to predictably alter model behavior. We bias the forward pass with a 'steering vector' implicitly specified through natural language. Past work learned these steering vectors; our Activation Addition (ActAdd) method instead computes them by taking the activation differences which result from pairs of prompts. We demonstrate ActAdd on GPT-2 on OpenWebText and ConceptNet, and replicate the effect on Llama-13B and GPT-J-6B. Our approach yields inference-time control over high-level properties of output & preserves performance on off-target topics. The method requires far less compute and implementation effort than finetuning and RLHF, allows for natural language specification by users, and its overhead scales naturally with model size.

Transformers stand as the cornerstone of mordern deep learning. Traditionally, these models rely on multi-layer perceptron (MLP) layers to mix the information between channels. In this paper, we introduce the Kolmogorov-Arnold Transformer (KAT), a novel architecture that replaces MLP layers with Kolmogorov-Arnold Network (KAN) layers to enhance the expressiveness and performance of the model. Integrating KANs into transformers, however, is no easy feat, especially when scaled up. Specifically, we identify three key challenges: (C1) Base function. The standard B-spline function used in KANs is not optimized for parallel computing on modern hardware, resulting in slower inference speeds. (C2) Parameter and Computation Inefficiency. KAN requires a unique function for each input-output pair, making the computation extremely large. (C3) Weight initialization. The initialization of weights in KANs is particularly challenging due to their learnable activation functions, which are critical for achieving convergence in deep neural networks. To overcome the aforementioned challenges, we propose three key solutions: (S1) Rational basis. We replace B-spline functions with rational functions to improve compatibility with modern GPUs. By implementing this in CUDA, we achieve faster computations. (S2) Group KAN. We share the activation weights through a group of neurons, to reduce the computational load without sacrificing performance. (S3) Variance-preserving initialization. We carefully initialize the activation weights to make sure that the activation variance is maintained across layers. With these designs, KAT scales effectively and readily outperforms traditional MLP-based transformers.

Tabular data analysis presents unique challenges that arise from heterogeneous feature types, missing values, and complex feature interactions. While traditional machine learning methods like gradient boosting often outperform deep learning, recent advancements in neural architectures offer promising alternatives. In this study, we introduce TabKAN, a novel framework for tabular data modeling based on Kolmogorov-Arnold Networks (KANs). Unlike conventional deep learning models, KANs use learnable activation functions on edges, which improves both interpretability and training efficiency. TabKAN incorporates modular KAN-based architectures designed for tabular analysis and proposes a transfer learning framework for knowledge transfer across domains. Furthermore, we develop a model-specific interpretability approach that reduces reliance on post hoc explanations. Extensive experiments on public datasets show that TabKAN achieves superior performance in supervised learning and significantly outperforms classical and Transformer-based models in binary and multi-class classification. The results demonstrate the potential of KAN-based architectures to bridge the gap between traditional machine learning and deep learning for structured data.

The Mixture-of-Experts (MoE) approach has demonstrated outstanding scalability in multi-task learning including low-level upstream tasks such as concurrent removal of multiple adverse weather effects. However, the conventional MoE architecture with parallel Feed Forward Network (FFN) experts leads to significant parameter and computational overheads that hinder its efficient deployment. In addition, the naive MoE linear router is suboptimal in assigning task-specific features to multiple experts which limits its further scalability. In this work, we propose an efficient MoE architecture with weight sharing across the experts. Inspired by the idea of linear feature modulation (FM), our architecture implicitly instantiates multiple experts via learnable activation modulations on a single shared expert block. The proposed Feature Modulated Expert (FME) serves as a building block for the novel Mixture-of-Feature-Modulation-Experts (MoFME) architecture, which can scale up the number of experts with low overhead. We further propose an Uncertainty-aware Router (UaR) to assign task-specific features to different FM modules with well-calibrated weights. This enables MoFME to effectively learn diverse expert functions for multiple tasks. The conducted experiments on the multi-deweather task show that our MoFME outperforms the baselines in the image restoration quality by 0.1-0.2 dB and achieves SOTA-compatible performance while saving more than 72% of parameters and 39% inference time over the conventional MoE counterpart. Experiments on the downstream segmentation and classification tasks further demonstrate the generalizability of MoFME to real open-world applications.

To address the trade-off between computational efficiency and adherence to Kolmogorov-Arnold Network (KAN) principles, we propose TruKAN, a new architecture based on the KAN structure and learnable activation functions. TruKAN replaces the B-spline basis in KAN with a family of truncated power functions derived from k-order spline theory. This change maintains the KAN's expressiveness while enhancing accuracy and training time. Each TruKAN layer combines a truncated power term with a polynomial term and employs either shared or individual knots. TruKAN exhibits greater interpretability than other KAN variants due to its simplified basis functions and knot configurations. By prioritizing interpretable basis functions, TruKAN aims to balance approximation efficacy with transparency. We develop the TruKAN model and integrate it into an advanced EfficientNet-V2-based framework, which is then evaluated on computer vision benchmark datasets. To ensure a fair comparison, we develop various models: MLP-, KAN-, SineKAN and TruKAN-based EfficientNet frameworks and assess their training time and accuracy across small and deep architectures. The training phase uses hybrid optimization to improve convergence stability. Additionally, we investigate layer normalization techniques for all the models and assess the impact of shared versus individual knots in TruKAN. Overall, TruKAN outperforms other KAN models in terms of accuracy, computational efficiency and memory usage on the complex vision task, demonstrating advantages beyond the limited settings explored in prior KAN studies.

The multilayer perceptron (MLP), a fundamental paradigm in current artificial intelligence, is widely applied in fields such as computer vision and natural language processing. However, the recently proposed Kolmogorov-Arnold Network (KAN), based on nonlinear additive connections, has been proven to achieve performance comparable to MLPs with significantly fewer parameters. Despite this potential, the use of a single activation function space results in reduced performance of KAN and related works across different tasks. To address this issue, we propose an activation space Selectable KAN (S-KAN). S-KAN employs an adaptive strategy to choose the possible activation mode for data at each feedforward KAN node. Our approach outperforms baseline methods in seven representative function fitting tasks and significantly surpasses MLP methods with the same level of parameters. Furthermore, we extend the structure of S-KAN and propose an activation space selectable Convolutional KAN (S-ConvKAN), which achieves leading results on four general image classification datasets. Our method mitigates the performance variability of the original KAN across different tasks and demonstrates through extensive experiments that feedforward KANs with selectable activations can achieve or even exceed the performance of MLP-based methods. This work contributes to the understanding of the data-centric design of new AI paradigms and provides a foundational reference for innovations in KAN-based network architectures.

Interpreting the internal activations of neural networks can produce more faithful explanations of their behavior, but is difficult due to the complex structure of activation space. Existing approaches to scalable interpretability use hand-designed agents that make and test hypotheses about how internal activations relate to external behavior. We propose to instead turn this task into an end-to-end training objective, by training interpretability assistants to accurately predict model behavior from activations through a communication bottleneck. Specifically, an encoder compresses activations to a sparse list of concepts, and a decoder reads this list and answers a natural language question about the model. We show how to pretrain this assistant on large unstructured data, then finetune it to answer questions. The resulting architecture, which we call a Predictive Concept Decoder, enjoys favorable scaling properties: the auto-interp score of the bottleneck concepts improves with data, as does the performance on downstream applications. Specifically, PCDs can detect jailbreaks, secret hints, and implanted latent concepts, and are able to accurately surface latent user attributes.

The success of artificial neural networks (ANNs) hinges greatly on the judicious selection of an activation function, introducing non-linearity into network and enabling them to model sophisticated relationships in data. However, the search of activation functions has largely relied on empirical knowledge in the past, lacking theoretical guidance, which has hindered the identification of more effective activation functions. In this work, we offer a proper solution to such issue. Firstly, we theoretically demonstrate the existence of the worst activation function with boundary conditions (WAFBC) from the perspective of information entropy. Furthermore, inspired by the Taylor expansion form of information entropy functional, we propose the Entropy-based Activation Function Optimization (EAFO) methodology. EAFO methodology presents a novel perspective for designing static activation functions in deep neural networks and the potential of dynamically optimizing activation during iterative training. Utilizing EAFO methodology, we derive a novel activation function from ReLU, known as Correction Regularized ReLU (CRReLU). Experiments conducted with vision transformer and its variants on CIFAR-10, CIFAR-100 and ImageNet-1K datasets demonstrate the superiority of CRReLU over existing corrections of ReLU. Extensive empirical studies on task of large language model (LLM) fine-tuning, CRReLU exhibits superior performance compared to GELU, suggesting its broader potential for practical applications.

Parameter-efficient fine-tuning (PEFT) methods such as adapt large pretrained models by adding small weight-space updates. While effective, weight deltas are hard to interpret mechanistically, and they do not directly expose which internal computations are reused versus bypassed for a new task. We explore an alternative view inspired by neuromodulation: adaptation as a change in mode -- selecting and rescaling existing computations -- rather than rewriting the underlying weights. We propose , a simple activation-space PEFT technique that freezes base weights and learns per-neuron thresholds and gains. During training, a smooth gate decides whether a neuron's activation participates; at inference the gate can be hardened to yield explicit conditional computation and neuron-level attributions. As a proof of concept, we study ``mode specialization'' on MNIST (0^circ) versus rotated MNIST (45^circ). We pretrain a small MLP on a 50/50 mixture (foundation), freeze its weights, and then specialize to the rotated mode using . Across seeds, improves rotated accuracy over the frozen baseline while using only a few hundred trainable parameters per layer, and exhibits partial activation sparsity (a minority of units strongly active). Compared to , trades some accuracy for substantially fewer trainable parameters and a more interpretable ``which-neurons-fire'' mechanism. We discuss limitations, including reduced expressivity when the frozen base lacks features needed for the target mode.

Steering Large Language Models (LLMs) through activation interventions has emerged as a lightweight alternative to fine-tuning for alignment and personalization. Recent work on Bi-directional Preference Optimization (BiPO) shows that dense steering vectors can be learned directly from preference data in a Direct Preference Optimization (DPO) fashion, enabling control over truthfulness, hallucinations, and safety behaviors. However, dense steering vectors often entangle multiple latent factors due to neuron multi-semanticity, limiting their effectiveness and stability in fine-grained settings such as cultural alignment, where closely related values and behaviors (e.g., among Middle Eastern cultures) must be distinguished. In this paper, we propose Yet another Policy Optimization (YaPO), a reference-free method that learns sparse steering vectors in the latent space of a Sparse Autoencoder (SAE). By optimizing sparse codes, YaPO produces disentangled, interpretable, and efficient steering directions. Empirically, we show that YaPO converges faster, achieves stronger performance, and exhibits improved training stability compared to dense steering baselines. Beyond cultural alignment, YaPO generalizes to a range of alignment-related behaviors, including hallucination, wealth-seeking, jailbreak, and power-seeking. Importantly, YaPO preserves general knowledge, with no measurable degradation on MMLU. Overall, our results show that YaPO provides a general recipe for efficient, stable, and fine-grained alignment of LLMs, with broad applications to controllability and domain adaptation. The associated code and data are publicly availablehttps://github.com/MBZUAI-Paris/YaPO.

Catastrophic forgetting remains a significant challenge to continual learning for decades. While recent works have proposed effective methods to mitigate this problem, they mainly focus on the algorithmic side. Meanwhile, we do not fully understand what architectural properties of neural networks lead to catastrophic forgetting. This study aims to fill this gap by studying the role of activation functions in the training dynamics of neural networks and their impact on catastrophic forgetting. Our study reveals that, besides sparse representations, the gradient sparsity of activation functions also plays an important role in reducing forgetting. Based on this insight, we propose a new class of activation functions, elephant activation functions, that can generate both sparse representations and sparse gradients. We show that by simply replacing classical activation functions with elephant activation functions, we can significantly improve the resilience of neural networks to catastrophic forgetting. Our method has broad applicability and benefits for continual learning in regression, class incremental learning, and reinforcement learning tasks. Specifically, we achieves excellent performance on Split MNIST dataset in just one single pass, without using replay buffer, task boundary information, or pre-training.

The growing computational demands of large language models (LLMs) make efficient inference and activation strategies increasingly critical. While recent approaches, such as Mixture-of-Experts (MoE), leverage selective activation but require specialized training, training-free sparse activation methods offer broader applicability and superior resource efficiency through their plug-and-play design. However, many existing methods rely solely on hidden state magnitudes to determine activation, resulting in high approximation errors and suboptimal inference accuracy. To address these limitations, we propose WINA (Weight Informed Neuron Activation), a novel, simple, and training-free sparse activation framework that jointly considers hidden state magnitudes and the column-wise ell_2-norms of weight matrices. We show that this leads to a sparsification strategy that obtains optimal approximation error bounds with theoretical guarantees tighter than existing techniques. Empirically, WINA also outperforms state-of-the-art methods (e.g., TEAL) by up to 2.94% in average performance at the same sparsity levels, across a diverse set of LLM architectures and datasets. These results position WINA as a new performance frontier for training-free sparse activation in LLM inference, advancing training-free sparse activation methods and setting a robust baseline for efficient inference. The source code is available at https://github.com/microsoft/wina.

The performance of deep network learning strongly depends on the choice of the non-linear activation function associated with each neuron. However, deciding on the best activation is non-trivial, and the choice depends on the architecture, hyper-parameters, and even on the dataset. Typically these activations are fixed by hand before training. Here, we demonstrate how to eliminate the reliance on first picking fixed activation functions by using flexible parametric rational functions instead. The resulting Pad\'e Activation Units (PAUs) can both approximate common activation functions and also learn new ones while providing compact representations. Our empirical evidence shows that end-to-end learning deep networks with PAUs can increase the predictive performance. Moreover, PAUs pave the way to approximations with provable robustness. https://github.com/ml-research/pau

The development of foundation models for functional magnetic resonance imaging (fMRI) time series holds significant promise for predicting phenotypes related to disease and cognition. Current models, however, are often trained using a mask-and-reconstruct objective on small brain regions. This focus on low-level information leads to representations that are sensitive to noise and temporal fluctuations, necessitating extensive fine-tuning for downstream tasks. We introduce Brain-Semantoks, a self-supervised framework designed specifically to learn abstract representations of brain dynamics. Its architecture is built on two core innovations: a semantic tokenizer that aggregates noisy regional signals into robust tokens representing functional networks, and a self-distillation objective that enforces representational stability across time. We show that this objective is stabilized through a novel training curriculum, ensuring the model robustly learns meaningful features from low signal-to-noise time series. We demonstrate that learned representations enable strong performance on a variety of downstream tasks even when only using a linear probe. Furthermore, we provide comprehensive scaling analyses indicating more unlabeled data reliably results in out-of-distribution performance gains without domain adaptation.

LLMs have shown remarkable capabilities, but precisely controlling their response behavior remains challenging. Existing activation steering methods alter LLM behavior indiscriminately, limiting their practical applicability in settings where selective responses are essential, such as content moderation or domain-specific assistants. In this paper, we propose Conditional Activation Steering (CAST), which analyzes LLM activation patterns during inference to selectively apply or withhold activation steering based on the input context. Our method is based on the observation that different categories of prompts activate distinct patterns in the model's hidden states. Using CAST, one can systematically control LLM behavior with rules like "if input is about hate speech or adult content, then refuse" or "if input is not about legal advice, then refuse." This allows for selective modification of responses to specific content while maintaining normal responses to other content, all without requiring weight optimization. We release an open-source implementation of our framework at github.com/IBM/activation-steering .

The instruction learning paradigm -- where a model learns to perform new tasks from task descriptions alone -- has become popular in general-purpose model research. The capabilities of large transformer models as instruction learners, however, remain poorly understood. We use a controlled synthetic environment to characterize such capabilities. Specifically, we use the task of deciding whether a given string matches a regular expression (viewed as an instruction) to identify properties of tasks, instructions, and instances that make instruction learning challenging. For instance, we find that our model, a fine-tuned T5-based text2text transformer, struggles with large regular languages, suggesting that less precise instructions are challenging for models. Additionally, instruction executions that require tracking longer contexts of prior steps are also more difficult. We use our findings to systematically construct a challenging instruction learning dataset, which we call Hard RegSet. Fine-tuning on Hard RegSet, our large transformer learns to correctly interpret only 65.6% of test instructions (with at least 90% accuracy), and 11%-24% of the instructions in out-of-distribution generalization settings. We propose Hard RegSet as a challenging instruction learning task, and a controlled environment for studying instruction learning.

We introduce stochastic activations. This novel strategy randomly selects between several non-linear functions in the feed-forward layer of a large language model. In particular, we choose between SILU or RELU depending on a Bernoulli draw. This strategy circumvents the optimization problem associated with RELU, namely, the constant shape for negative inputs that prevents the gradient flow. We leverage this strategy in two ways: (1) We use stochastic activations during pre-training and fine-tune the model with RELU, which is used at inference time to provide sparse latent vectors. This reduces the inference FLOPs and translates into a significant speedup in the CPU. Interestingly, this leads to much better results than training from scratch with the RELU activation function. (2) We evaluate stochastic activations for generation. This strategy performs reasonably well: it is only slightly inferior to the best deterministic non-linearity, namely SILU combined with temperature scaling. This offers an alternative to existing strategies by providing a controlled way to increase the diversity of the generated text.

Large language models (LLMs) excel at generating fluent text, but their internal reasoning remains opaque and difficult to control. Sparse autoencoders (SAEs) make hidden activations more interpretable by exposing latent features that often align with human concepts. Yet, these features are fragile and passive, offering no mechanism for systematic reasoning or model control. To address this, we introduce ActivationReasoning (AR), a framework that embeds explicit logical reasoning into the latent space of LLMs. It proceeds in three stages: (1) Finding latent representations, first latent concept representations are identified (e.g., via SAEs) and organized into a dictionary; (2) Activating propositions, at inference time AR detects activating concepts and maps them to logical propositions; and (3)Logical reasoning, applying logical rules over these propositions to infer higher-order structures, compose new concepts, and steer model behavior. We evaluate AR on multi-hop reasoning (PrOntoQA), abstraction and robustness to indirect concept cues (Rail2Country), reasoning over natural and diverse language (ProverQA), and context-sensitive safety (BeaverTails). Across all tasks, AR scales robustly with reasoning complexity, generalizes to abstract and context-sensitive tasks, and transfers across model backbones. These results demonstrate that grounding logical structure in latent activations not only improves transparency but also enables structured reasoning, reliable control, and alignment with desired behaviors, providing a path toward more reliable and auditable AI.

The choice of activation functions in deep networks has a significant effect on the training dynamics and task performance. Currently, the most successful and widely-used activation function is the Rectified Linear Unit (ReLU). Although various hand-designed alternatives to ReLU have been proposed, none have managed to replace it due to inconsistent gains. In this work, we propose to leverage automatic search techniques to discover new activation functions. Using a combination of exhaustive and reinforcement learning-based search, we discover multiple novel activation functions. We verify the effectiveness of the searches by conducting an empirical evaluation with the best discovered activation function. Our experiments show that the best discovered activation function, f(x) = x cdot sigmoid(beta x), which we name Swish, tends to work better than ReLU on deeper models across a number of challenging datasets. For example, simply replacing ReLUs with Swish units improves top-1 classification accuracy on ImageNet by 0.9\% for Mobile NASNet-A and 0.6\% for Inception-ResNet-v2. The simplicity of Swish and its similarity to ReLU make it easy for practitioners to replace ReLUs with Swish units in any neural network.

Massive activations are scalar values in transformer hidden states that achieve values orders of magnitude larger than typical activations and have been shown to be critical for model functionality. While prior work has characterized these phenomena in fully trained models, the temporal dynamics of their emergence during training remain poorly understood. We present the first comprehensive analysis of massive activation development throughout transformer training, using the Pythia model family as our testbed. Through systematic analysis of various model sizes across multiple training checkpoints, we demonstrate that massive activation emergence follows predictable mathematical patterns that can be accurately modeled using an exponentially-modulated logarithmic function with five key parameters. We develop a machine learning framework to predict these mathematical parameters from architectural specifications alone, achieving high accuracy for steady-state behavior and moderate accuracy for emergence timing and magnitude. These findings enable architects to predict and potentially control key aspects of massive activation emergence through design choices, with significant implications for model stability, training cycle length, interpretability, and optimization. Our findings demonstrate that the emergence of massive activations is governed by model design and can be anticipated, and potentially controlled, before training begins.

While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are optimal for classification, i.e., whether such models minimize the probability of misclassification for arbitrary data distributions. In this work, we identify and construct an explicit set of neural network classifiers that achieve optimality. Since effective neural networks in practice are typically both wide and deep, we analyze infinitely wide networks that are also infinitely deep. In particular, using the recent connection between infinitely wide neural networks and Neural Tangent Kernels, we provide explicit activation functions that can be used to construct networks that achieve optimality. Interestingly, these activation functions are simple and easy to implement, yet differ from commonly used activations such as ReLU or sigmoid. More generally, we create a taxonomy of infinitely wide and deep networks and show that these models implement one of three well-known classifiers depending on the activation function used: (1) 1-nearest neighbor (model predictions are given by the label of the nearest training example); (2) majority vote (model predictions are given by the label of the class with greatest representation in the training set); or (3) singular kernel classifiers (a set of classifiers containing those that achieve optimality). Our results highlight the benefit of using deep networks for classification tasks, in contrast to regression tasks, where excessive depth is harmful.

Activation steering has emerged as a cost-effective paradigm for modifying large language model (LLM) behaviors. Existing methods typically intervene at the block level, steering the bundled activations of selected attention heads, feedforward networks, or residual streams. However, we reveal that block-level activations are inherently heterogeneous, entangling beneficial, irrelevant, and harmful features, thereby rendering block-level steering coarse, inefficient, and intrusive. To investigate the root cause, we decompose block activations into fine-grained atomic unit (AU)-level activations, where each AU-level activation corresponds to a single dimension of the block activation, and each AU denotes a slice of the block weight matrix. Steering an AU-level activation is thus equivalent to steering its associated AU. Our theoretical and empirical analysis show that heterogeneity arises because different AUs or dimensions control distinct token distributions in LLM outputs. Hence, block-level steering inevitably moves helpful and harmful token directions together, which reduces efficiency. Restricting intervention to beneficial AUs yields more precise and effective steering. Building on this insight, we propose AUSteer, a simple and efficient method that operates at a finer granularity of the AU level. AUSteer first identifies discriminative AUs globally by computing activation momenta on contrastive samples. It then assigns adaptive steering strengths tailored to diverse inputs and selected AU activations. Comprehensive experiments on multiple LLMs and tasks show that AUSteer consistently surpasses advanced baselines while steering considerably fewer activations, demonstrating that steering less achieves more.

Exploiting activation sparsity is a promising approach to significantly accelerating the inference process of large language models (LLMs) without compromising performance. However, activation sparsity is determined by activation functions, and commonly used ones like SwiGLU and GeGLU exhibit limited sparsity. Simply replacing these functions with ReLU fails to achieve sufficient sparsity. Moreover, inadequate training data can further increase the risk of performance degradation. To address these challenges, we propose a novel dReLU function, which is designed to improve LLM activation sparsity, along with a high-quality training data mixture ratio to facilitate effective sparsification. Additionally, we leverage sparse activation patterns within the Feed-Forward Network (FFN) experts of Mixture-of-Experts (MoE) models to further boost efficiency. By applying our neuron sparsification method to the Mistral and Mixtral models, only 2.5 billion and 4.3 billion parameters are activated per inference iteration, respectively, while achieving even more powerful model performance. Evaluation results demonstrate that this sparsity achieves a 2-5x decoding speedup. Remarkably, on mobile phones, our TurboSparse-Mixtral-47B achieves an inference speed of 11 tokens per second. Our models are available at https://huggingface.co/PowerInfer

Large language models (LLMs) have achieved impressive results in natural language processing but are prone to memorizing portions of their training data, which can compromise evaluation metrics, raise privacy concerns, and limit generalization. Traditional methods for detecting memorization rely on output probabilities or loss functions, often lacking precision due to confounding factors like common language patterns. In this paper, we introduce an analytical method that precisely detects memorization by examining neuron activations within the LLM. By identifying specific activation patterns that differentiate between memorized and not memorized tokens, we train classification probes that achieve near-perfect accuracy. The approach can also be applied to other mechanisms, such as repetition, as demonstrated in this study, highlighting its versatility. Intervening on these activations allows us to suppress memorization without degrading overall performance, enhancing evaluation integrity by ensuring metrics reflect genuine generalization. Additionally, our method supports large-scale labeling of tokens and sequences, crucial for next-generation AI models, improving training efficiency and results. Our findings contribute to model interpretability and offer practical tools for analyzing and controlling internal mechanisms in LLMs.

Activation functions are fundamental in deep neural networks and directly impact gradient flow, optimization stability, and generalization. Although ReLU remains standard because of its simplicity, it suffers from vanishing gradients and lacks adaptability. Alternatives like Swish and GELU introduce smooth transitions, but fail to dynamically adjust to input statistics. We propose VeLU, a Variance-enhanced Learning Unit as an activation function that dynamically scales based on input variance by integrating ArcTan-Sin transformations and Wasserstein-2 regularization, effectively mitigating covariate shifts and stabilizing optimization. Extensive experiments on ViT_B16, VGG19, ResNet50, DenseNet121, MobileNetV2, and EfficientNetB3 confirm VeLU's superiority over ReLU, ReLU6, Swish, and GELU on six vision benchmarks. The codes of VeLU are publicly available on GitHub.

We introduce Contrastive Activation Addition (CAA), an innovative method for steering language models by modifying activations during their forward passes. CAA computes ``steering vectors'' by averaging the difference in residual stream activations between pairs of positive and negative examples of a particular behavior such as factual versus hallucinatory responses. During inference, these steering vectors are added at all token positions after the user's prompt with either a positive or negative coefficient, allowing precise control over the degree of the targeted behavior. We evaluate CAA's effectiveness on Llama 2 Chat using both multiple-choice behavioral question datasets and open-ended generation tasks. We demonstrate that CAA significantly alters model behavior, outperforms traditional methods like finetuning and few-shot prompting, and minimally reduces capabilities. Moreover, by employing various activation space interpretation methods, we gain deeper insights into CAA's mechanisms. CAA both accurately steers model outputs and also sheds light on how high-level concepts are represented in Large Language Models (LLMs).

Modern neural networks rely on generic activation functions (ReLU, GELU, SiLU) that ignore the mathematical structure inherent in scientific data. We propose Neuro-Symbolic Activation Discovery, a framework that uses Genetic Programming to extract interpretable mathematical formulas from data and inject them as custom activation functions. Our key contribution is the discovery of a Geometric Transfer phenomenon: activation functions learned from particle physics data successfully generalize to ecological classification, outperforming standard activations (ReLU, GELU, SiLU) in both accuracy and parameter efficiency. On the Forest Cover dataset, our Hybrid Transfer model achieves 82.4% accuracy with only 5,825 parameters, compared to 83.4% accuracy requiring 31,801 parameters for a conventional heavy network -- a 5.5x parameter reduction with only 1% accuracy loss. We introduce a Parameter Efficiency Score (E_{param} = AUC / log_{10}(Params)) and demonstrate that lightweight hybrid architectures consistently achieve 18-21% higher efficiency than over-parameterized baselines. Crucially, we establish boundary conditions: while Physics to Ecology transfer succeeds (both involve continuous Euclidean measurements), Physics to Text transfer fails (discrete word frequencies require different mathematical structures). Our work opens pathways toward domain-specific activation libraries for efficient scientific machine learning.

The interpretation of deep learning models is a challenge due to their size, complexity, and often opaque internal state. In addition, many systems, such as image classifiers, operate on low-level features rather than high-level concepts. To address these challenges, we introduce Concept Activation Vectors (CAVs), which provide an interpretation of a neural net's internal state in terms of human-friendly concepts. The key idea is to view the high-dimensional internal state of a neural net as an aid, not an obstacle. We show how to use CAVs as part of a technique, Testing with CAVs (TCAV), that uses directional derivatives to quantify the degree to which a user-defined concept is important to a classification result--for example, how sensitive a prediction of "zebra" is to the presence of stripes. Using the domain of image classification as a testing ground, we describe how CAVs may be used to explore hypotheses and generate insights for a standard image classification network as well as a medical application.

Neural networks have proven to be a highly effective tool for solving complex problems in many areas of life. Recently, their importance and practical usability have further been reinforced with the advent of deep learning. One of the important conditions for the success of neural networks is the choice of an appropriate activation function introducing non-linearity into the model. Many types of these functions have been proposed in the literature in the past, but there is no single comprehensive source containing their exhaustive overview. The absence of this overview, even in our experience, leads to redundancy and the unintentional rediscovery of already existing activation functions. To bridge this gap, our paper presents an extensive survey involving 400 activation functions, which is several times larger in scale than previous surveys. Our comprehensive compilation also references these surveys; however, its main goal is to provide the most comprehensive overview and systematization of previously published activation functions with links to their original sources. The secondary aim is to update the current understanding of this family of functions.

Sparsely activated neural networks with conditional computation learn to route their inputs through different "expert" subnetworks, providing a form of modularity that densely activated models lack. Despite their possible benefits, models with learned routing often underperform their parameter-matched densely activated counterparts as well as models that use non-learned heuristic routing strategies. In this paper, we hypothesize that these shortcomings stem from the gradient estimation techniques used to train sparsely activated models that use non-differentiable discrete routing decisions. To address this issue, we introduce Soft Merging of Experts with Adaptive Routing (SMEAR), which avoids discrete routing by using a single "merged" expert constructed via a weighted average of all of the experts' parameters. By routing activations through a single merged expert, SMEAR does not incur a significant increase in computational costs and enables standard gradient-based training. We empirically validate that models using SMEAR outperform models that route based on metadata or learn sparse routing through gradient estimation. Furthermore, we provide qualitative analysis demonstrating that the experts learned via SMEAR exhibit a significant amount of specialization. All of the code used in our experiments is publicly available.

The increasing capabilities of large generative models and their ever more widespread deployment have raised concerns about their reliability, safety, and potential misuse. To address these issues, recent works have proposed to control model generation by steering model activations in order to effectively induce or prevent the emergence of concepts or behaviors in the generated output. In this paper we introduce Activation Transport (AcT), a general framework to steer activations guided by optimal transport theory that generalizes many previous activation-steering works. AcT is modality-agnostic and provides fine-grained control over the model behavior with negligible computational overhead, while minimally impacting model abilities. We experimentally show the effectiveness and versatility of our approach by addressing key challenges in large language models (LLMs) and text-to-image diffusion models (T2Is). For LLMs, we show that AcT can effectively mitigate toxicity, induce arbitrary concepts, and increase their truthfulness. In T2Is, we show how AcT enables fine-grained style control and concept negation.

In class incremental learning, neural networks typically suffer from catastrophic forgetting. We show that an MLP featuring a sparse activation function and an adaptive learning rate optimizer can compete with established regularization techniques in the Split-MNIST task. We highlight the effectiveness of the Adaptive SwisH (ASH) activation function in this context and introduce a novel variant, Hard Adaptive SwisH (Hard ASH) to further enhance the learning retention.

Sparse dictionary learning has been a rapidly growing technique in mechanistic interpretability to attack superposition and extract more human-understandable features from model activations. We ask a further question based on the extracted more monosemantic features: How do we recognize circuits connecting the enormous amount of dictionary features? We propose a circuit discovery framework alternative to activation patching. Our framework suffers less from out-of-distribution and proves to be more efficient in terms of asymptotic complexity. The basic unit in our framework is dictionary features decomposed from all modules writing to the residual stream, including embedding, attention output and MLP output. Starting from any logit, dictionary feature or attention score, we manage to trace down to lower-level dictionary features of all tokens and compute their contribution to these more interpretable and local model behaviors. We dig in a small transformer trained on a synthetic task named Othello and find a number of human-understandable fine-grained circuits inside of it.

Controlling undesirable Large Language Model (LLM) behaviors, such as the generation of unsafe content or failing to adhere to safety guidelines, often relies on costly fine-tuning. Activation steering provides an alternative for inference-time control, but existing methods typically lack fine-grained, adaptive mechanisms. We introduce a novel approach using a lightweight, trainable controller network integrated during inference. This controller network observes specific intermediate LLM activations and predicts both a global scaling factor and layer-specific weights. The predicted global scaling factor and layer-specific weights then dynamically modulate the intensity of a steering patch, derived from a pre-computed "refusal direction" vector, applied across the LLM's layers during generation. Trained on activations from both harmful and benign prompts, our controller learns to discriminatively apply nuanced, layer-aware interventions, activating steering primarily for harmful inputs. Experiments using safety benchmarks like ToxicChat & In-The-Wild Jailbreak Prompts demonstrate that our weighted steering controller significantly increases refusal rates compared to the base LLM, achieving targeted behavioral modification without altering the original model parameters. Our experiments with Llama-3.1-8B, Llama-3.2-1B & Mistral-7B show our approach outperforms existing methods, presenting an efficient and adaptive method for fine-grained control over LLM behavior at inference time.

Large language models are able to perform a task by conditioning on a few input-output demonstrations - a paradigm known as in-context learning. We show that language models can explicitly infer an underlying task from a few demonstrations by prompting them to generate a natural language instruction that fits the examples. To explore this ability, we introduce the instruction induction challenge, compile a dataset consisting of 24 tasks, and define a novel evaluation metric based on executing the generated instruction. We discover that, to a large extent, the ability to generate instructions does indeed emerge when using a model that is both large enough and aligned to follow instructions; InstructGPT achieves 65.7% of human performance in our execution-based metric, while the original GPT-3 model reaches only 9.8% of human performance. This surprising result suggests that instruction induction might be a viable learning paradigm in and of itself, where instead of fitting a set of latent continuous parameters to the data, one searches for the best description in the natural language hypothesis space.

Activation sparsity denotes the existence of substantial weakly-contributed elements within activation outputs that can be eliminated, benefiting many important applications concerned with large language models (LLMs). Although promoting greater activation sparsity within LLMs deserves deep studies, existing works lack comprehensive and quantitative research on the correlation between activation sparsity and potentially influential factors. In this paper, we present a comprehensive study on the quantitative scaling properties and influential factors of the activation sparsity within decoder-only Transformer-based LLMs. Specifically, we propose PPL-p% sparsity, a precise and performance-aware activation sparsity metric that is applicable to any activation function. Through extensive experiments, we find several important phenomena. Firstly, different activation functions exhibit comparable performance but opposite training-time sparsity trends. The activation ratio (i.e., 1-sparsity ratio) evolves as a convergent increasing power-law and decreasing logspace power-law with the amount of training data for SiLU-activated and ReLU-activated LLMs, respectively. These demonstrate that ReLU is more efficient as the activation function than SiLU and can leverage more training data to improve activation sparsity. Secondly, the activation ratio linearly increases with the width-depth ratio below a certain bottleneck point, indicating the potential advantage of a deeper architecture at a fixed parameter scale. Finally, at similar width-depth ratios, we surprisingly find that the limit value of activation sparsity varies weakly with the parameter scale, i.e., the activation patterns within LLMs are insensitive to the parameter scale. These empirical laws towards LLMs with greater activation sparsity have important implications for making LLMs more efficient and interpretable.

Kolmogorov-Arnold Networks (KANs) have gained significant attention as an alternative to traditional multilayer perceptrons, with proponents claiming superior interpretability and performance through learnable univariate activation functions. However, recent systematic evaluations reveal substantial discrepancies between theoretical claims and empirical evidence. This critical assessment examines KANs' actual performance across diverse domains using fair comparison methodologies that control for parameters and computational costs. Our analysis demonstrates that KANs outperform MLPs only in symbolic regression tasks, while consistently underperforming in machine learning, computer vision, and natural language processing benchmarks. The claimed advantages largely stem from B-spline activation functions rather than architectural innovations, and computational overhead (1.36-100x slower) severely limits practical deployment. Furthermore, theoretical claims about breaking the "curse of dimensionality" lack rigorous mathematical foundation. We systematically identify the conditions under which KANs provide value versus traditional approaches, establish evaluation standards for future research, and propose a priority-based roadmap for addressing fundamental limitations. This work provides researchers and practitioners with evidence-based guidance for the rational adoption of KANs while highlighting critical research gaps that must be addressed for broader applicability.

The choice of activation function plays a critical role in neural networks, yet most architectures still rely on fixed, uniform activation functions across all neurons. We introduce SmartMixed, a two-phase training strategy that allows networks to learn optimal per-neuron activation functions while preserving computational efficiency at inference. In the first phase, neurons adaptively select from a pool of candidate activation functions (ReLU, Sigmoid, Tanh, Leaky ReLU, ELU, SELU) using a differentiable hard-mixture mechanism. In the second phase, each neuron's activation function is fixed according to the learned selection, resulting in a computationally efficient network that supports continued training with optimized vectorized operations. We evaluate SmartMixed on the MNIST dataset using feedforward neural networks of varying depths. The analysis shows that neurons in different layers exhibit distinct preferences for activation functions, providing insights into the functional diversity within neural architectures.

We show the formal equivalence of linearised self-attention mechanisms and fast weight controllers from the early '90s, where a ``slow" neural net learns by gradient descent to program the ``fast weights" of another net through sequences of elementary programming instructions which are additive outer products of self-invented activation patterns (today called keys and values). Such Fast Weight Programmers (FWPs) learn to manipulate the contents of a finite memory and dynamically interact with it. We infer a memory capacity limitation of recent linearised softmax attention variants, and replace the purely additive outer products by a delta rule-like programming instruction, such that the FWP can more easily learn to correct the current mapping from keys to values. The FWP also learns to compute dynamically changing learning rates. We also propose a new kernel function to linearise attention which balances simplicity and effectiveness. We conduct experiments on synthetic retrieval problems as well as standard machine translation and language modelling tasks which demonstrate the benefits of our methods.

Activation steering is a promising technique for controlling LLM behavior by adding semantically meaningful vectors directly into a model's hidden states during inference. It is often framed as a precise, interpretable, and potentially safer alternative to fine-tuning. We demonstrate the opposite: steering systematically breaks model alignment safeguards, making it comply with harmful requests. Through extensive experiments on different model families, we show that even steering in a random direction can increase the probability of harmful compliance from 0% to 2-27%. Alarmingly, steering benign features from a sparse autoencoder (SAE), a common source of interpretable directions, increases these rates by a further 2-4%. Finally, we show that combining 20 randomly sampled vectors that jailbreak a single prompt creates a universal attack, significantly increasing harmful compliance on unseen requests. These results challenge the paradigm of safety through interpretability, showing that precise control over model internals does not guarantee precise control over model behavior.

The growing use of generative models in daily life calls for efficient mechanisms to control their generation, to e.g., produce safe content or provide users with tools to explore style changes. Ideally, such mechanisms should require low volume of unpaired data (i.e., without explicit preference), and should be cheap, both at train and inference time, while preserving output quality. Recent research has shown that such mechanisms can be obtained by intervening exclusively on model activations, with the goal of correcting distributional differences between activations seen when using prompts from a source vs. a target set (e.g., toxic and non-toxic sentences). While cheap, these fast methods are inherently crude: their maps are tuned locally, not accounting for their impact on downstream layers, resulting in interventions that cause unintended shifts when used out-of-sample. We propose in this work linear end-to-end activation steering (LinEAS), an approach trained with a global loss that accounts simultaneously for all layer-wise distributional shifts. In addition to being more robust, the loss used to train LinEAS can be regularized with sparsifying norms, which can automatically carry out neuron selection. LinEAS only requires a handful of unpaired samples to be effective, and beats similar baselines on toxicity mitigation in language models, becoming competitive with oracle-dependent methods that have access to strong supervision. LinEAS is modality-agnostic and we empirically find that it outperforms existing activation steering methods at mitigating and including new concepts at the output of single-step text-to-image generation models.

Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically "similar" data points and "negative samples," the learner forces the inner product of representations of similar pairs with each other to be higher on average than with negative samples. The current paper uses the term contrastive learning for such algorithms and presents a theoretical framework for analyzing them by introducing latent classes and hypothesizing that semantically similar points are sampled from the same latent class. This framework allows us to show provable guarantees on the performance of the learned representations on the average classification task that is comprised of a subset of the same set of latent classes. Our generalization bound also shows that learned representations can reduce (labeled) sample complexity on downstream tasks. We conduct controlled experiments in both the text and image domains to support the theory.

The widely used ReLU is favored for its hardware efficiency, {as the implementation at inference is a one bit sign case,} yet suffers from issues such as the ``dying ReLU'' problem, where during training, neurons fail to activate and constantly remain at zero, as highlighted by Lu et al. Traditional approaches to mitigate this issue often introduce more complex and less hardware-friendly activation functions. In this work, we propose a Hysteresis Rectified Linear Unit (HeLU), an efficient activation function designed to address the ``dying ReLU'' problem with minimal complexity. Unlike traditional activation functions with fixed thresholds for training and inference, HeLU employs a variable threshold that refines the backpropagation. This refined mechanism allows simpler activation functions to achieve competitive performance comparable to their more complex counterparts without introducing unnecessary complexity or requiring inductive biases. Empirical evaluations demonstrate that HeLU enhances model generalization across diverse datasets, offering a promising solution for efficient and effective inference suitable for a wide range of neural network architectures.

Well-known activation functions like ReLU or Leaky ReLU are non-differentiable at the origin. Over the years, many smooth approximations of ReLU have been proposed using various smoothing techniques. We propose new smooth approximations of a non-differentiable activation function by convolving it with approximate identities. In particular, we present smooth approximations of Leaky ReLU and show that they outperform several well-known activation functions in various datasets and models. We call this function Smooth Activation Unit (SAU). Replacing ReLU by SAU, we get 5.12% improvement with ShuffleNet V2 (2.0x) model on CIFAR100 dataset.

Real-world analog systems intrinsically suffer from noise that can impede model convergence and accuracy on a variety of deep learning models. We demonstrate that differentiable activations like GELU and SiLU enable robust propagation of gradients which help to mitigate analog quantization error that is ubiquitous to all analog systems. We perform analysis and training of convolutional, linear, and transformer networks in the presence of quantized noise. Here, we are able to demonstrate that continuously differentiable activation functions are significantly more noise resilient over conventional rectified activations. As in the case of ReLU, the error in gradients are 100x higher than those in GELU near zero. Our findings provide guidance for selecting appropriate activations to realize performant and reliable hardware implementations across several machine learning domains such as computer vision, signal processing, and beyond.

We frame the problem of unifying representations in neural models as one of sparse model recovery and introduce a framework that extends sparse autoencoders (SAEs) to lifted spaces and infinite-dimensional function spaces, enabling mechanistic interpretability of large neural operators (NO). While the Platonic Representation Hypothesis suggests that neural networks converge to similar representations across architectures, the representational properties of neural operators remain underexplored despite their growing importance in scientific computing. We compare the inference and training dynamics of SAEs, lifted-SAE, and SAE neural operators. We highlight how lifting and operator modules introduce beneficial inductive biases, enabling faster recovery, improved recovery of smooth concepts, and robust inference across varying resolutions, a property unique to neural operators.

The activation function plays a crucial role in model optimisation, yet the optimal choice remains unclear. For example, the Sigmoid activation is the de-facto activation in balanced classification tasks, however, in imbalanced classification, it proves inappropriate due to bias towards frequent classes. In this work, we delve deeper in this phenomenon by performing a comprehensive statistical analysis in the classification and intermediate layers of both balanced and imbalanced networks and we empirically show that aligning the activation function with the data distribution, enhances the performance in both balanced and imbalanced tasks. To this end, we propose the Adaptive Parametric Activation (APA) function, a novel and versatile activation function that unifies most common activation functions under a single formula. APA can be applied in both intermediate layers and attention layers, significantly outperforming the state-of-the-art on several imbalanced benchmarks such as ImageNet-LT, iNaturalist2018, Places-LT, CIFAR100-LT and LVIS and balanced benchmarks such as ImageNet1K, COCO and V3DET. The code is available at https://github.com/kostas1515/AGLU.

Activation steering methods were shown to be effective in conditioning language model generation by additively intervening over models' intermediate representations. However, the evaluation of these techniques has so far been limited to single conditioning properties and synthetic settings. In this work, we conduct a comprehensive evaluation of various activation steering strategies, highlighting the property-dependent nature of optimal parameters to ensure a robust effect throughout generation. To address this issue, we propose Dynamic Activation Composition, an information-theoretic approach to modulate the steering intensity of one or more properties throughout generation. Our experiments on multi-property steering show that our method successfully maintains high conditioning while minimizing the impact of conditioning on generation fluency.

The training process of neural networks usually optimize weights and bias parameters of linear transformations, while nonlinear activation functions are pre-specified and fixed. This work develops a systematic approach to constructing matrix activation functions whose entries are generalized from ReLU. The activation is based on matrix-vector multiplications using only scalar multiplications and comparisons. The proposed activation functions depend on parameters that are trained along with the weights and bias vectors. Neural networks based on this approach are simple and efficient and are shown to be robust in numerical experiments.

Transformers have found extensive applications across various domains due to the powerful fitting capabilities. This success can be partially attributed to their inherent nonlinearity. Thus, in addition to the ReLU function employed in the original transformer architecture, researchers have explored alternative modules such as GeLU and SwishGLU to enhance nonlinearity and thereby augment representational capacity. In this paper, we propose a novel category of polynomial composition activations (PolyCom), designed to optimize the dynamics of transformers. Theoretically, we provide a comprehensive mathematical analysis of PolyCom, highlighting its enhanced expressivity and efficacy relative to other activation functions. Notably, we demonstrate that networks incorporating PolyCom achieve the optimal approximation rate, indicating that PolyCom networks require minimal parameters to approximate general smooth functions in Sobolev spaces. We conduct empirical experiments on the pre-training configurations of large language models (LLMs), including both dense and sparse architectures. By substituting conventional activation functions with PolyCom, we enable LLMs to capture higher-order interactions within the data, thus improving performance metrics in terms of accuracy and convergence rates. Extensive experimental results demonstrate the effectiveness of our method, showing substantial improvements over other activation functions. Code is available at https://github.com/BryceZhuo/PolyCom.

We introduce and train distributed neural architectures (DNA) in vision and language domains. DNAs are initialized with a proto-architecture that consists of (transformer, MLP, attention, etc.) modules and routers. Any token (or patch) can traverse any series of modules in any order. DNAs are a natural generalization of the sparse methods such as Mixture-of-Experts, Mixture-of-Depths, parameter sharing, etc. Computation and communication patterns of DNA modules are learnt end-to-end during training and depend on the content and context of each token (or patch). These patterns can be shaped by further requirements added to the optimization objective such as compute/memory efficiency or load balancing. We empirically show that (i) trained DNAs are competitive with the dense baselines in both domains and (ii) compute efficiency/parameter sharing can be learnt from data. Next, we analyze the emergent connectivity and computation patterns in the trained DNAs. We find that the paths that tokens take through the models are themselves distributed according to a power-law. We show that some paths (or, equivalently, groups of modules) show emergent specialization. Finally, we demonstrate that models learn to allocate compute and active parameters in an interpretable way.

Can a mere next-token predictor faithfully model human intelligence? We crystallize this intuitive concern, which is fragmented in the literature. As a starting point, we argue that the two often-conflated phases of next-token prediction -- autoregressive inference and teacher-forced training -- must be treated distinctly. The popular criticism that errors can compound during autoregressive inference, crucially assumes that teacher-forcing has learned an accurate next-token predictor. This assumption sidesteps a more deep-rooted problem we expose: in certain classes of tasks, teacher-forcing can simply fail to learn an accurate next-token predictor in the first place. We describe a general mechanism of how teacher-forcing can fail, and design a minimal planning task where both the Transformer and the Mamba architecture empirically fail in that manner -- remarkably, despite the task being straightforward to learn. We provide preliminary evidence that this failure can be resolved when training to predict multiple tokens in advance. We hope this finding can ground future debates and inspire explorations beyond the next-token prediction paradigm. We make our code available under https://github.com/gregorbachmann/Next-Token-Failures

"Induction heads" are attention heads that implement a simple algorithm to complete token sequences like [A][B] ... [A] -> [B]. In this work, we present preliminary and indirect evidence for a hypothesis that induction heads might constitute the mechanism for the majority of all "in-context learning" in large transformer models (i.e. decreasing loss at increasing token indices). We find that induction heads develop at precisely the same point as a sudden sharp increase in in-context learning ability, visible as a bump in the training loss. We present six complementary lines of evidence, arguing that induction heads may be the mechanistic source of general in-context learning in transformer models of any size. For small attention-only models, we present strong, causal evidence; for larger models with MLPs, we present correlational evidence.

We present the Mixture-of-Tunable-Experts (MoTE), a method that extends the Mixture-of-Experts architecture of Large Language Models (LLMs). Without additional training, MoTE enables meaningful and focused behavior changes in LLMs on-the-fly during inference time. By analyzing the digital LLM brain of DeepSeek-R1 using a technique we dub 'functional Token Resonance Imaging' (fTRI) -- inspired by fMRI and using prompts designed to elicit specific behavior (e.g., 'What happened {time}{place}?') -- we empirically identify distinctive experts associated with behaviors like refusal responses. Using MoTE we are able to intervene and control such specific behavior. We switched off the top 10 most refusal-relevant experts (0.07% of R1's 14,848 routed experts), achieving a 52% refusal reduction on sensitive reference prompts without performance degradation on MT-Bench. Random expert deactivation resulted in smaller behavioral shifts with increased noise, whereas forced expert activation led to significantly higher refusal rates. Our approach shares similarities with sparse autoencoders (SAEs) in terms of explainability and steerability. Unlike SAEs, MoTE does not require large training efforts, as within MoEs with a vast number of experts, specialization already emerged naturally during pretraining. Our findings suggest that significant functional mechanisms in Mixture-of-Experts architectures can at least partially be localized in a small number of specific experts, rather than being distributed throughout the model's weights. Expert subgroups can be tuned to trigger significant behavior variations, providing insights into the inner workings of LLMs.

Large language models based on transformers have achieved great empirical successes. However, as they are deployed more widely, there is a growing need to better understand their internal mechanisms in order to make them more reliable. These models appear to store vast amounts of knowledge from their training data, and to adapt quickly to new information provided in their context or prompt. We study how transformers balance these two types of knowledge by considering a synthetic setup where tokens are generated from either global or context-specific bigram distributions. By a careful empirical analysis of the training process on a simplified two-layer transformer, we illustrate the fast learning of global bigrams and the slower development of an "induction head" mechanism for the in-context bigrams. We highlight the role of weight matrices as associative memories, provide theoretical insights on how gradients enable their learning during training, and study the role of data-distributional properties.

Recent work by Anthropic on Mechanistic interpretability claims to understand and control Large Language Models by extracting human-interpretable features from their neural activation patterns using sparse autoencoders (SAEs). If successful, this approach offers one of the most promising routes for human oversight in AI safety. We conduct an initial stress-test of these claims by replicating their main results with open-source SAEs for Llama 3.1. While we successfully reproduce basic feature extraction and steering capabilities, our investigation suggests that major caution is warranted regarding the generalizability of these claims. We find that feature steering exhibits substantial fragility, with sensitivity to layer selection, steering magnitude, and context. We observe non-standard activation behavior and demonstrate the difficulty to distinguish thematically similar features from one another. While SAE-based interpretability produces compelling demonstrations in selected cases, current methods often fall short of the systematic reliability required for safety-critical applications. This suggests a necessary shift in focus from prioritizing interpretability of internal representations toward reliable prediction and control of model output. Our work contributes to a more nuanced understanding of what mechanistic interpretability has achieved and highlights fundamental challenges for AI safety that remain unresolved.

We propose ERA, a new paradigm that constrains the sampling entropy above given thresholds by applying specially designed activations to the outputs of models. Our approach demonstrates broad effectiveness across different domains: 1) for large language models(LLMs), boosting the AIME 2025 score for Qwen2.5-Math-7B by 37.4%; 2) for continuous control reinforcement learning agents, improving performance by more than 30% over strong baselines such as SAC on the challenging HumanoidBench; 3) for image classification, enhancing ImageNet top-1 accuracy by 0.69% for ResNet-50. These gains are achieved with a computational overhead of less than 7%. Our work validates output activation as a powerful tool for entropy control, opening a new direction for designing simpler and more robust algorithms.

Transformer models exhibit in-context learning: the ability to accurately predict the response to a novel query based on illustrative examples in the input sequence. In-context learning contrasts with traditional in-weights learning of query-output relationships. What aspects of the training data distribution and architecture favor in-context vs in-weights learning? Recent work has shown that specific distributional properties inherent in language, such as burstiness, large dictionaries and skewed rank-frequency distributions, control the trade-off or simultaneous appearance of these two forms of learning. We first show that these results are recapitulated in a minimal attention-only network trained on a simplified dataset. In-context learning (ICL) is driven by the abrupt emergence of an induction head, which subsequently competes with in-weights learning. By identifying progress measures that precede in-context learning and targeted experiments, we construct a two-parameter model of an induction head which emulates the full data distributional dependencies displayed by the attention-based network. A phenomenological model of induction head formation traces its abrupt emergence to the sequential learning of three nested logits enabled by an intrinsic curriculum. We propose that the sharp transitions in attention-based networks arise due to a specific chain of multi-layer operations necessary to achieve ICL, which is implemented by nested nonlinearities sequentially learned during training.

Despite their impressive capabilities, current Text-to-Image (T2I) models remain prone to generating unsafe and toxic content. While activation steering offers a promising inference-time intervention, we observe that linear activation steering frequently degrades image quality when applied to benign prompts. To address this trade-off, we first construct SafeSteerDataset, a contrastive dataset containing 2300 safe and unsafe prompt pairs with high cosine similarity. Leveraging this data, we propose Conditioned Activation Transport (CAT), a framework that employs a geometry-based conditioning mechanism and nonlinear transport maps. By conditioning transport maps to activate only within unsafe activation regions, we minimize interference with benign queries. We validate our approach on two state-of-the-art architectures: Z-Image and Infinity. Experiments demonstrate that CAT generalizes effectively across these backbones, significantly reducing Attack Success Rate while maintaining image fidelity compared to unsteered generations. Warning: This paper contains potentially offensive text and images.

We study the problem of learning a single neuron with respect to the L_2^2-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal L_2^2-error within a constant factor. Our algorithm applies under much milder distributional assumptions compared to prior work. The key ingredient enabling our results is a novel connection to local error bounds from optimization theory.

Deep neural networks (DNNs) have demonstrated state-of-the-art results on many pattern recognition tasks, especially vision classification problems. Understanding the inner workings of such computational brains is both fascinating basic science that is interesting in its own right - similar to why we study the human brain - and will enable researchers to further improve DNNs. One path to understanding how a neural network functions internally is to study what each of its neurons has learned to detect. One such method is called activation maximization (AM), which synthesizes an input (e.g. an image) that highly activates a neuron. Here we dramatically improve the qualitative state of the art of activation maximization by harnessing a powerful, learned prior: a deep generator network (DGN). The algorithm (1) generates qualitatively state-of-the-art synthetic images that look almost real, (2) reveals the features learned by each neuron in an interpretable way, (3) generalizes well to new datasets and somewhat well to different network architectures without requiring the prior to be relearned, and (4) can be considered as a high-quality generative method (in this case, by generating novel, creative, interesting, recognizable images).

Having reliable specifications is an unavoidable challenge in achieving verifiable correctness, robustness, and interpretability of AI systems. Existing specifications for neural networks are in the paradigm of data as specification. That is, the local neighborhood centering around a reference input is considered to be correct (or robust). While existing specifications contribute to verifying adversarial robustness, a significant problem in many research domains, our empirical study shows that those verified regions are somewhat tight, and thus fail to allow verification of test set inputs, making them impractical for some real-world applications. To this end, we propose a new family of specifications called neural representation as specification, which uses the intrinsic information of neural networks - neural activation patterns (NAPs), rather than input data to specify the correctness and/or robustness of neural network predictions. We present a simple statistical approach to mining neural activation patterns. To show the effectiveness of discovered NAPs, we formally verify several important properties, such as various types of misclassifications will never happen for a given NAP, and there is no ambiguity between different NAPs. We show that by using NAP, we can verify a significant region of the input space, while still recalling 84% of the data on MNIST. Moreover, we can push the verifiable bound to 10 times larger on the CIFAR10 benchmark. Thus, we argue that NAPs can potentially be used as a more reliable and extensible specification for neural network verification.

We present a framework for using transformer networks as universal computers by programming them with specific weights and placing them in a loop. Our input sequence acts as a punchcard, consisting of instructions and memory for data read/writes. We demonstrate that a constant number of encoder layers can emulate basic computing blocks, including embedding edit operations, non-linear functions, function calls, program counters, and conditional branches. Using these building blocks, we emulate a small instruction-set computer. This allows us to map iterative algorithms to programs that can be executed by a looped, 13-layer transformer. We show how this transformer, instructed by its input, can emulate a basic calculator, a basic linear algebra library, and in-context learning algorithms that employ backpropagation. Our work highlights the versatility of the attention mechanism, and demonstrates that even shallow transformers can execute full-fledged, general-purpose programs.

Recent advancements in large language models (LLMs) have resulted in increasingly anthropomorphic language concerning the ability of LLMs to reason. Whether reasoning in LLMs should be understood to be inherently different is, however, widely debated. We propose utilizing a representation engineering approach wherein model activations are read from the residual stream of an LLM when processing a reasoning task. The activations are used to derive a control vector that is applied to the model as an inference-time intervention, modulating the representational space of the model, to improve performance on the specified task. We publish the code for deriving control vectors and analyzing model representations. The method allows us to improve performance on reasoning benchmarks and assess how control vectors influence the final logit distribution of a model via metrics such as KL divergence and entropy. We apply control vectors to Mistral-7B-Instruct and a range of Pythia models on an inductive, a deductive and mathematical reasoning task. We show that an LLM can, to a certain degree, be controlled to improve its perceived reasoning ability by modulating activations. The intervention is dependent upon the ability to reliably extract the model's typical state when correctly solving a task. Our results suggest that reasoning performance can be modulated in the same manner as other information-processing tasks performed by LLMs and demonstrate that we are capable of improving performance on specific tasks via a simple intervention on the residual stream with no additional training.

The study of representation universality in AI models reveals growing convergence across domains, modalities, and architectures. However, the practical applications of representation universality remain largely unexplored. We bridge this gap by demonstrating that safety interventions can be transferred between models through learned mappings of their shared activation spaces. We demonstrate this approach on two well-established AI safety tasks: backdoor removal and refusal of harmful prompts, showing successful transfer of steering vectors that alter the models' outputs in a predictable way. Additionally, we propose a new task, corrupted capabilities, where models are fine-tuned to embed knowledge tied to a backdoor. This tests their ability to separate useful skills from backdoors, reflecting real-world challenges. Extensive experiments across Llama, Qwen and Gemma model families show that our method enables using smaller models to efficiently align larger ones. Furthermore, we demonstrate that autoencoder mappings between base and fine-tuned models can serve as reliable ``lightweight safety switches", allowing dynamic toggling between model behaviors.

Certain statistical models are capable of interpreting input strings as instructions, or prompts, and carry out tasks based on them. Many approaches to prompting and pre-training these models involve the automated generation of these prompts. We call these approaches meta-prompting, or prompting to obtain prompts. We propose a theoretical framework based on category theory to generalize and describe them. This framework is flexible enough to account for LLM stochasticity; and allows us to obtain formal results around task agnosticity and equivalence of various meta-prompting approaches. We experiment with meta-prompting in two active areas of model research: creativity and ideation. We find that user preference favors (p < 0.01) the prompts generated under meta-prompting, as well as their corresponding outputs, over a series of hardcoded baseline prompts that include the original task prompt. Using our framework, we argue that meta-prompting is more effective than basic prompting at generating desirable outputs.

Automated interpretability pipelines generate natural language descriptions for the concepts represented by features in large language models (LLMs), such as plants or the first word in a sentence. These descriptions are derived using inputs that activate the feature, which may be a dimension or a direction in the model's representation space. However, identifying activating inputs is costly, and the mechanistic role of a feature in model behavior is determined both by how inputs cause a feature to activate and by how feature activation affects outputs. Using steering evaluations, we reveal that current pipelines provide descriptions that fail to capture the causal effect of the feature on outputs. To fix this, we propose efficient, output-centric methods for automatically generating feature descriptions. These methods use the tokens weighted higher after feature stimulation or the highest weight tokens after applying the vocabulary "unembedding" head directly to the feature. Our output-centric descriptions better capture the causal effect of a feature on model outputs than input-centric descriptions, but combining the two leads to the best performance on both input and output evaluations. Lastly, we show that output-centric descriptions can be used to find inputs that activate features previously thought to be "dead".

We present a framework for the unsupervised learning of neurosymbolic encoders, which are encoders obtained by composing neural networks with symbolic programs from a domain-specific language. Our framework naturally incorporates symbolic expert knowledge into the learning process, which leads to more interpretable and factorized latent representations compared to fully neural encoders. We integrate modern program synthesis techniques with the variational autoencoding (VAE) framework, in order to learn a neurosymbolic encoder in conjunction with a standard decoder. The programmatic descriptions from our encoders can benefit many analysis workflows, such as in behavior modeling where interpreting agent actions and movements is important. We evaluate our method on learning latent representations for real-world trajectory data from animal biology and sports analytics. We show that our approach offers significantly better separation of meaningful categories than standard VAEs and leads to practical gains on downstream analysis tasks, such as for behavior classification.

We present a unified representation of the most popular neural network activation functions. Adopting Mittag-Leffler functions of fractional calculus, we propose a flexible and compact functional form that is able to interpolate between various activation functions and mitigate common problems in training neural networks such as vanishing and exploding gradients. The presented gated representation extends the scope of fixed-shape activation functions to their adaptive counterparts whose shape can be learnt from the training data. The derivatives of the proposed functional form can also be expressed in terms of Mittag-Leffler functions making it a suitable candidate for gradient-based backpropagation algorithms. By training multiple neural networks of different complexities on various datasets with different sizes, we demonstrate that adopting a unified gated representation of activation functions offers a promising and affordable alternative to individual built-in implementations of activation functions in conventional machine learning frameworks.

Recent advances in mechanistic interpretability have revealed that large language models (LLMs) develop internal representations corresponding not only to concrete entities but also distinct, human-understandable abstract concepts and behaviour. Moreover, these hidden features can be directly manipulated to steer model behaviour. However, it remains an open question whether this phenomenon is unique to models trained on inherently structured data (ie. language, images) or if it is a general property of foundation models. In this work, we investigate the internal representations of a large physics-focused foundation model. Inspired by recent work identifying single directions in activation space for complex behaviours in LLMs, we extract activation vectors from the model during forward passes over simulation datasets for different physical regimes. We then compute "delta" representations between the two regimes. These delta tensors act as concept directions in activation space, encoding specific physical features. By injecting these concept directions back into the model during inference, we can steer its predictions, demonstrating causal control over physical behaviours, such as inducing or removing some particular physical feature from a simulation. These results suggest that scientific foundation models learn generalised representations of physical principles. They do not merely rely on superficial correlations and patterns in the simulations. Our findings open new avenues for understanding and controlling scientific foundation models and has implications for AI-enabled scientific discovery.

Deep networks are gradually penetrating almost every domain in our lives due to their amazing success. However, with substantive performance accuracy improvements comes the price of irreproducibility. Two identical models, trained on the exact same training dataset may exhibit large differences in predictions on individual examples even when average accuracy is similar, especially when trained on highly distributed parallel systems. The popular Rectified Linear Unit (ReLU) activation has been key to recent success of deep networks. We demonstrate, however, that ReLU is also a catalyzer to irreproducibility in deep networks. We show that not only can activations smoother than ReLU provide better accuracy, but they can also provide better accuracy-reproducibility tradeoffs. We propose a new family of activations; Smooth ReLU (SmeLU), designed to give such better tradeoffs, while also keeping the mathematical expression simple, and thus implementation cheap. SmeLU is monotonic, mimics ReLU, while providing continuous gradients, yielding better reproducibility. We generalize SmeLU to give even more flexibility and then demonstrate that SmeLU and its generalized form are special cases of a more general methodology of REctified Smooth Continuous Unit (RESCU) activations. Empirical results demonstrate the superior accuracy-reproducibility tradeoffs with smooth activations, SmeLU in particular.

A central goal for mechanistic interpretability has been to identify the right units of analysis in large language models (LLMs) that causally explain their outputs. While early work focused on individual neurons, evidence that neurons often encode multiple concepts has motivated a shift toward analyzing directions in activation space. A key question is how to find directions that capture interpretable features in an unsupervised manner. Current methods rely on dictionary learning with sparse autoencoders (SAEs), commonly trained over residual stream activations to learn directions from scratch. However, SAEs often struggle in causal evaluations and lack intrinsic interpretability, as their learning is not explicitly tied to the computations of the model. Here, we tackle these limitations by directly decomposing MLP activations with semi-nonnegative matrix factorization (SNMF), such that the learned features are (a) sparse linear combinations of co-activated neurons, and (b) mapped to their activating inputs, making them directly interpretable. Experiments on Llama 3.1, Gemma 2 and GPT-2 show that SNMF derived features outperform SAEs and a strong supervised baseline (difference-in-means) on causal steering, while aligning with human-interpretable concepts. Further analysis reveals that specific neuron combinations are reused across semantically-related features, exposing a hierarchical structure in the MLP's activation space. Together, these results position SNMF as a simple and effective tool for identifying interpretable features and dissecting concept representations in LLMs.

The mechanisms by which reasoning training reshapes LLMs' internal computations remain unclear. We study lightweight steering vectors inserted into the base model's residual stream and trained with a reinforcement-learning objective. These vectors match full fine-tuning performance while preserving the interpretability of small, additive interventions. Using logit-lens readouts and path-patching analyses on two models, we find that (i) the last-layer steering vector acts like a token-substitution bias concentrated on the first generated token, consistently boosting tokens such as "To" and "Step"; (ii) the penultimate-layer vector leaves attention patterns largely intact and instead operates through the MLP and unembedding, preferentially up-weighting process words and structure symbols; and (iii) middle layers de-emphasize non-English tokens. Next, we show that a SAE isolates features associated with correct generations. We also show that steering vectors (i) transfer to other models, (ii) combine across layers when trained in isolation, and (iii) concentrate magnitude on meaningful prompt segments under adaptive token-wise scaling. Taken together, these results deepen understanding of how trained steering vectors shape computation and should inform future work in activation engineering and the study of reasoning models.

In order to understand the in-context learning phenomenon, recent works have adopted a stylized experimental framework and demonstrated that Transformers can learn gradient-based learning algorithms for various classes of real-valued functions. However, the limitations of Transformers in implementing learning algorithms, and their ability to learn other forms of algorithms are not well understood. Additionally, the degree to which these capabilities are confined to attention-based models is unclear. Furthermore, it remains to be seen whether the insights derived from these stylized settings can be extrapolated to pretrained Large Language Models (LLMs). In this work, we take a step towards answering these questions by demonstrating the following: (a) On a test-bed with a variety of Boolean function classes, we find that Transformers can nearly match the optimal learning algorithm for 'simpler' tasks, while their performance deteriorates on more 'complex' tasks. Additionally, we find that certain attention-free models perform (almost) identically to Transformers on a range of tasks. (b) When provided a teaching sequence, i.e. a set of examples that uniquely identifies a function in a class, we show that Transformers learn more sample-efficiently. Interestingly, our results show that Transformers can learn to implement two distinct algorithms to solve a single task, and can adaptively select the more sample-efficient algorithm depending on the sequence of in-context examples. (c) Lastly, we show that extant LLMs, e.g. LLaMA-2, GPT-4, can compete with nearest-neighbor baselines on prediction tasks that are guaranteed to not be in their training set.

Recent work on domain-specific reasoning with large language models (LLMs) often relies on training-intensive approaches that require parameter updates. While activation steering has emerged as a parameter efficient alternative, existing methods apply static, manual interventions that fail to adapt to the dynamic nature of complex reasoning. To address this limitation, we propose RISER (Router-based Intervention for Steerable Enhancement of Reasoning), a plug-and-play intervention framework that adaptively steers LLM reasoning in activation space. RISER constructs a library of reusable reasoning vectors and employs a lightweight Router to dynamically compose them for each input. The Router is optimized via reinforcement learning under task-level rewards, activating latent cognitive primitives in an emergent and compositional manner. Across seven diverse benchmarks, RISER yields 3.4-6.5% average zero-shot accuracy improvements over the base model while surpassing CoT-style reasoning with 2-3x higher token efficiency and robust accuracy gains. Further analysis shows that RISER autonomously combines multiple vectors into interpretable, precise control strategies, pointing toward more controllable and efficient LLM reasoning.

Activation patching is a standard method in mechanistic interpretability for localizing the components of a model responsible for specific behaviors, but it is computationally expensive to apply at scale. Attribution patching offers a faster, gradient-based approximation, yet suffers from noise and reduced reliability in deep, highly non-linear networks. In this work, we introduce Relevance Patching (RelP), which replaces the local gradients in attribution patching with propagation coefficients derived from Layer-wise Relevance Propagation (LRP). LRP propagates the network's output backward through the layers, redistributing relevance to lower-level components according to local propagation rules that ensure properties such as relevance conservation or improved signal-to-noise ratio. Like attribution patching, RelP requires only two forward passes and one backward pass, maintaining computational efficiency while improving faithfulness. We validate RelP across a range of models and tasks, showing that it more accurately approximates activation patching than standard attribution patching, particularly when analyzing residual stream and MLP outputs in the Indirect Object Identification (IOI) task. For instance, for MLP outputs in GPT-2 Large, attribution patching achieves a Pearson correlation of 0.006, whereas RelP reaches 0.956, highlighting the improvement offered by RelP. Additionally, we compare the faithfulness of sparse feature circuits identified by RelP and Integrated Gradients (IG), showing that RelP achieves comparable faithfulness without the extra computational cost associated with IG.

Large multimodal models have achieved remarkable progress in both understanding and generation. Recent efforts pursue unified multimodal models that integrate heterogeneous components to support both capabilities within a single framework. However, such unification introduces inference inefficiencies, e.g., specific tasks or samples may not require the full knowledge or capacity of the unified model. Yet, a systematic understanding of how these inefficiencies manifest across different components remains limited. In this work, we first conduct a systematic analysis of unified multimodal model components using training-free pruning as a probing methodology, considering both depth pruning and width reduction. Our study reveals that the understanding component exhibits notable compressibility in both understanding and generation tasks, which is more pronounced in the latter. In contrast, the generation components are highly sensitive to compression, with performance deteriorating sharply even under moderate compression ratios. To address this limitation, we propose the Mixture-of-Experts (MoE) Adaptation, inspired by the dynamic activation patterns observed across different samples. This approach partitions the generation module into multiple experts and enables sparse activation to restore generation quality. We validate the effectiveness of sparse activation through expert-frozen tuning and further demonstrate that a fully trainable adaptation delivers additional gains. As a result, the adapted BAGEL model achieves performance comparable to the full model while activating only about half of its parameters. The code is released at https://github.com/Shwai-He/SparseUnifiedModel{this link}.

In-context learning (ICL) is a type of prompting where a transformer model operates on a sequence of (input, output) examples and performs inference on-the-fly. In this work, we formalize in-context learning as an algorithm learning problem where a transformer model implicitly constructs a hypothesis function at inference-time. We first explore the statistical aspects of this abstraction through the lens of multitask learning: We obtain generalization bounds for ICL when the input prompt is (1) a sequence of i.i.d. (input, label) pairs or (2) a trajectory arising from a dynamical system. The crux of our analysis is relating the excess risk to the stability of the algorithm implemented by the transformer. We characterize when transformer/attention architecture provably obeys the stability condition and also provide empirical verification. For generalization on unseen tasks, we identify an inductive bias phenomenon in which the transfer learning risk is governed by the task complexity and the number of MTL tasks in a highly predictable manner. Finally, we provide numerical evaluations that (1) demonstrate transformers can indeed implement near-optimal algorithms on classical regression problems with i.i.d. and dynamic data, (2) provide insights on stability, and (3) verify our theoretical predictions.

We observe an empirical phenomenon in Large Language Models (LLMs) -- very few activations exhibit significantly larger values than others (e.g., 100,000 times larger). We call them massive activations. First, we demonstrate the widespread existence of massive activations across various LLMs and characterize their locations. Second, we find their values largely stay constant regardless of the input, and they function as indispensable bias terms in LLMs. Third, these massive activations lead to the concentration of attention probabilities to their corresponding tokens, and further, implicit bias terms in the self-attention output. Last, we also study massive activations in Vision Transformers. Code is available at https://github.com/locuslab/massive-activations.

What is the right supervisory signal to train visual representations? Current approaches in computer vision use category labels from datasets such as ImageNet to train ConvNets. However, in case of biological agents, visual representation learning does not require millions of semantic labels. We argue that biological agents use physical interactions with the world to learn visual representations unlike current vision systems which just use passive observations (images and videos downloaded from web). For example, babies push objects, poke them, put them in their mouth and throw them to learn representations. Towards this goal, we build one of the first systems on a Baxter platform that pushes, pokes, grasps and observes objects in a tabletop environment. It uses four different types of physical interactions to collect more than 130K datapoints, with each datapoint providing supervision to a shared ConvNet architecture allowing us to learn visual representations. We show the quality of learned representations by observing neuron activations and performing nearest neighbor retrieval on this learned representation. Quantitatively, we evaluate our learned ConvNet on image classification tasks and show improvements compared to learning without external data. Finally, on the task of instance retrieval, our network outperforms the ImageNet network on recall@1 by 3%

This paper studies the curious phenomenon for machine learning models with Transformer architectures that their activation maps are sparse. By activation map we refer to the intermediate output of the multi-layer perceptrons (MLPs) after a ReLU activation function, and by sparse we mean that on average very few entries (e.g., 3.0% for T5-Base and 6.3% for ViT-B16) are nonzero for each input to MLP. Moreover, larger Transformers with more layers and wider MLP hidden dimensions are sparser as measured by the percentage of nonzero entries. Through extensive experiments we demonstrate that the emergence of sparsity is a prevalent phenomenon that occurs for both natural language processing and vision tasks, on both training and evaluation data, for Transformers of various configurations, at layers of all depth levels, as well as for other architectures including MLP-mixers and 2-layer MLPs. We show that sparsity also emerges using training datasets with random labels, or with random inputs, or with infinite amount of data, demonstrating that sparsity is not a result of a specific family of datasets. We discuss how sparsity immediately implies a way to significantly reduce the FLOP count and improve efficiency for Transformers. Moreover, we demonstrate perhaps surprisingly that enforcing an even sparser activation via Top-k thresholding with a small value of k brings a collection of desired but missing properties for Transformers, namely less sensitivity to noisy training data, more robustness to input corruptions, and better calibration for their prediction confidence.

Activation decomposition methods in language models are tightly coupled to geometric assumptions on how concepts are realized in activation space. Existing approaches search for individual global directions, implicitly assuming linear separability, which overlooks concepts with nonlinear or multi-dimensional structure. In this work, we leverage Mixture of Factor Analyzers (MFA) as a scalable, unsupervised alternative that models the activation space as a collection of Gaussian regions with their local covariance structure. MFA decomposes activations into two compositional geometric objects: the region's centroid in activation space, and the local variation from the centroid. We train large-scale MFAs for Llama-3.1-8B and Gemma-2-2B, and show they capture complex, nonlinear structures in activation space. Moreover, evaluations on localization and steering benchmarks show that MFA outperforms unsupervised baselines, is competitive with supervised localization methods, and often achieves stronger steering performance than sparse autoencoders. Together, our findings position local geometry, expressed through subspaces, as a promising unit of analysis for scalable concept discovery and model control, accounting for complex structures that isolated directions fail to capture.

Transformer models encounter challenges in scaling hidden dimensions efficiently, as uniformly increasing them inflates computational and memory costs while failing to emphasize the most relevant features for each token. For further understanding, we study hidden dimension sparsity and observe that trained Transformers utilize only a small fraction of token dimensions, revealing an "activation flow" pattern. Notably, there are shared sub-dimensions with sustained activation across multiple consecutive tokens and specialized sub-dimensions uniquely activated for each token. To better model token-relevant sub-dimensions, we propose MoHD (Mixture of Hidden Dimensions), a sparse conditional activation architecture. Particularly, MoHD employs shared sub-dimensions for common token features and a routing mechanism to dynamically activate specialized sub-dimensions. To mitigate potential information loss from sparsity, we design activation scaling and group fusion mechanisms to preserve activation flow. In this way, MoHD expands hidden dimensions with negligible increases in computation or parameters, efficient training and inference while maintaining performance. Evaluations across 10 NLP tasks show that MoHD surpasses Vanilla Transformers in parameter efficiency and task performance. It achieves 1.7% higher performance with 50% fewer activation parameters and 3.7% higher performance with a 3x parameter expansion at constant activation cost. MOHD offers a new perspective for scaling the model, showcasing the potential of hidden dimension sparsity to boost efficiency

A major problem with Active Learning (AL) is high training costs since models are typically retrained from scratch after every query round. We start by demonstrating that standard AL on neural networks with warm starting fails, both to accelerate training and to avoid catastrophic forgetting when using fine-tuning over AL query rounds. We then develop a new class of techniques, circumventing this problem, by biasing further training towards previously labeled sets. We accomplish this by employing existing, and developing novel, replay-based Continual Learning (CL) algorithms that are effective at quickly learning the new without forgetting the old, especially when data comes from an evolving distribution. We call this paradigm Continual Active Learning (CAL). We show CAL achieves significant speedups using a plethora of replay schemes that use model distillation and that select diverse, uncertain points from the history. We conduct experiments across many data domains, including natural language, vision, medical imaging, and computational biology, each with different neural architectures and dataset sizes. CAL consistently provides a 3x reduction in training time, while retaining performance.

We investigate the learning of implicit neural representation (INR) using an overparameterized multilayer perceptron (MLP) via a novel nonparametric teaching perspective. The latter offers an efficient example selection framework for teaching nonparametrically defined (viz. non-closed-form) target functions, such as image functions defined by 2D grids of pixels. To address the costly training of INRs, we propose a paradigm called Implicit Neural Teaching (INT) that treats INR learning as a nonparametric teaching problem, where the given signal being fitted serves as the target function. The teacher then selects signal fragments for iterative training of the MLP to achieve fast convergence. By establishing a connection between MLP evolution through parameter-based gradient descent and that of function evolution through functional gradient descent in nonparametric teaching, we show for the first time that teaching an overparameterized MLP is consistent with teaching a nonparametric learner. This new discovery readily permits a convenient drop-in of nonparametric teaching algorithms to broadly enhance INR training efficiency, demonstrating 30%+ training time savings across various input modalities.

We can better understand deep neural networks by identifying which features each of their neurons have learned to detect. To do so, researchers have created Deep Visualization techniques including activation maximization, which synthetically generates inputs (e.g. images) that maximally activate each neuron. A limitation of current techniques is that they assume each neuron detects only one type of feature, but we know that neurons can be multifaceted, in that they fire in response to many different types of features: for example, a grocery store class neuron must activate either for rows of produce or for a storefront. Previous activation maximization techniques constructed images without regard for the multiple different facets of a neuron, creating inappropriate mixes of colors, parts of objects, scales, orientations, etc. Here, we introduce an algorithm that explicitly uncovers the multiple facets of each neuron by producing a synthetic visualization of each of the types of images that activate a neuron. We also introduce regularization methods that produce state-of-the-art results in terms of the interpretability of images obtained by activation maximization. By separately synthesizing each type of image a neuron fires in response to, the visualizations have more appropriate colors and coherent global structure. Multifaceted feature visualization thus provides a clearer and more comprehensive description of the role of each neuron.

Representation learning, and interpreting learned representations, are key areas of focus in machine learning and neuroscience. Both fields generally use representations as a means to understand or improve a system's computations. In this work, however, we explore surprising dissociations between representation and computation that may pose challenges for such efforts. We create datasets in which we attempt to match the computational role that different features play, while manipulating other properties of the features or the data. We train various deep learning architectures to compute these multiple abstract features about their inputs. We find that their learned feature representations are systematically biased towards representing some features more strongly than others, depending upon extraneous properties such as feature complexity, the order in which features are learned, and the distribution of features over the inputs. For example, features that are simpler to compute or learned first tend to be represented more strongly and densely than features that are more complex or learned later, even if all features are learned equally well. We also explore how these biases are affected by architectures, optimizers, and training regimes (e.g., in transformers, features decoded earlier in the output sequence also tend to be represented more strongly). Our results help to characterize the inductive biases of gradient-based representation learning. These results also highlight a key challenge for interpretability - or for comparing the representations of models and brains - disentangling extraneous biases from the computationally important aspects of a system's internal representations.

We explore a class of adversarial attacks targeting the activations of language models. By manipulating a relatively small subset of model activations, a, we demonstrate the ability to control the exact prediction of a significant number (in some cases up to 1000) of subsequent tokens t. We empirically verify a scaling law where the maximum number of target tokens t_max predicted depends linearly on the number of tokens a whose activations the attacker controls as t_max = kappa a. We find that the number of bits of control in the input space needed to control a single bit in the output space (what we call attack resistance chi) is remarkably constant between approx 16 and approx 25 over 2 orders of magnitude of model sizes for different language models. Compared to attacks on tokens, attacks on activations are predictably much stronger, however, we identify a surprising regularity where one bit of input steered either via activations or via tokens is able to exert control over a similar amount of output bits. This gives support for the hypothesis that adversarial attacks are a consequence of dimensionality mismatch between the input and output spaces. A practical implication of the ease of attacking language model activations instead of tokens is for multi-modal and selected retrieval models, where additional data sources are added as activations directly, sidestepping the tokenized input. This opens up a new, broad attack surface. By using language models as a controllable test-bed to study adversarial attacks, we were able to experiment with input-output dimensions that are inaccessible in computer vision, especially where the output dimension dominates.

We propose NEURONA, a neuro-symbolic framework for fMRI decoding and concept grounding in neural activity. Leveraging image- and video-based fMRI question-answering datasets, NEURONA learns to decode interacting concepts from visual stimuli based on patterns of fMRI responses, integrating symbolic reasoning and compositional execution with fMRI grounding across brain regions. We demonstrate that incorporating structural priors (e.g., compositional predicate-argument dependencies between concepts) into the decoding process significantly improves both decoding accuracy over precise queries, and notably, generalization to unseen queries at test time. With NEURONA, we highlight neuro-symbolic frameworks as promising tools for understanding neural activity.

When learning an input-output mapping from very few examples, is it better to first infer a latent function that explains the examples, or is it better to directly predict new test outputs, e.g. using a neural network? We study this question on ARC by training neural models for induction (inferring latent functions) and transduction (directly predicting the test output for a given test input). We train on synthetically generated variations of Python programs that solve ARC training tasks. We find inductive and transductive models solve different kinds of test problems, despite having the same training problems and sharing the same neural architecture: Inductive program synthesis excels at precise computations, and at composing multiple concepts, while transduction succeeds on fuzzier perceptual concepts. Ensembling them approaches human-level performance on ARC.

Because learning sometimes involves sensitive data, machine learning algorithms have been extended to offer privacy for training data. In practice, this has been mostly an afterthought, with privacy-preserving models obtained by re-running training with a different optimizer, but using the model architectures that already performed well in a non-privacy-preserving setting. This approach leads to less than ideal privacy/utility tradeoffs, as we show here. Instead, we propose that model architectures are chosen ab initio explicitly for privacy-preserving training. To provide guarantees under the gold standard of differential privacy, one must bound as strictly as possible how individual training points can possibly affect model updates. In this paper, we are the first to observe that the choice of activation function is central to bounding the sensitivity of privacy-preserving deep learning. We demonstrate analytically and experimentally how a general family of bounded activation functions, the tempered sigmoids, consistently outperform unbounded activation functions like ReLU. Using this paradigm, we achieve new state-of-the-art accuracy on MNIST, FashionMNIST, and CIFAR10 without any modification of the learning procedure fundamentals or differential privacy analysis.

Latest insights from biology show that intelligence not only emerges from the connections between neurons but that individual neurons shoulder more computational responsibility than previously anticipated. This perspective should be critical in the context of constantly changing distinct reinforcement learning environments, yet current approaches still primarily employ static activation functions. In this work, we motivate why rationals are suitable for adaptable activation functions and why their inclusion into neural networks is crucial. Inspired by recurrence in residual networks, we derive a condition under which rational units are closed under residual connections and formulate a naturally regularised version: the recurrent-rational. We demonstrate that equipping popular algorithms with (recurrent-)rational activations leads to consistent improvements on Atari games, especially turning simple DQN into a solid approach, competitive to DDQN and Rainbow.

It is known that the learning rate is the most important hyper-parameter to tune for training deep neural networks. This paper describes a new method for setting the learning rate, named cyclical learning rates, which practically eliminates the need to experimentally find the best values and schedule for the global learning rates. Instead of monotonically decreasing the learning rate, this method lets the learning rate cyclically vary between reasonable boundary values. Training with cyclical learning rates instead of fixed values achieves improved classification accuracy without a need to tune and often in fewer iterations. This paper also describes a simple way to estimate "reasonable bounds" -- linearly increasing the learning rate of the network for a few epochs. In addition, cyclical learning rates are demonstrated on the CIFAR-10 and CIFAR-100 datasets with ResNets, Stochastic Depth networks, and DenseNets, and the ImageNet dataset with the AlexNet and GoogLeNet architectures. These are practical tools for everyone who trains neural networks.

The ability to learn tasks in a sequential fashion is crucial to the development of artificial intelligence. Neural networks are not, in general, capable of this and it has been widely thought that catastrophic forgetting is an inevitable feature of connectionist models. We show that it is possible to overcome this limitation and train networks that can maintain expertise on tasks which they have not experienced for a long time. Our approach remembers old tasks by selectively slowing down learning on the weights important for those tasks. We demonstrate our approach is scalable and effective by solving a set of classification tasks based on the MNIST hand written digit dataset and by learning several Atari 2600 games sequentially.

This paper introduces the sparse modular addition task and examines how transformers learn it. We focus on transformers with embeddings in R^2 and introduce a visual sandbox that provides comprehensive visualizations of each layer throughout the training process. We reveal a type of circuit, called "clustering heads," which learns the problem's invariants. We analyze the training dynamics of these circuits, highlighting two-stage learning, loss spikes due to high curvature or normalization layers, and the effects of initialization and curriculum learning.

Neural sequence models, especially transformers, exhibit a remarkable capacity for in-context learning. They can construct new predictors from sequences of labeled examples (x, f(x)) presented in the input without further parameter updates. We investigate the hypothesis that transformer-based in-context learners implement standard learning algorithms implicitly, by encoding smaller models in their activations, and updating these implicit models as new examples appear in the context. Using linear regression as a prototypical problem, we offer three sources of evidence for this hypothesis. First, we prove by construction that transformers can implement learning algorithms for linear models based on gradient descent and closed-form ridge regression. Second, we show that trained in-context learners closely match the predictors computed by gradient descent, ridge regression, and exact least-squares regression, transitioning between different predictors as transformer depth and dataset noise vary, and converging to Bayesian estimators for large widths and depths. Third, we present preliminary evidence that in-context learners share algorithmic features with these predictors: learners' late layers non-linearly encode weight vectors and moment matrices. These results suggest that in-context learning is understandable in algorithmic terms, and that (at least in the linear case) learners may rediscover standard estimation algorithms. Code and reference implementations are released at https://github.com/ekinakyurek/google-research/blob/master/incontext.

Continual learning can incrementally absorb new concepts without interfering with previously learned knowledge. Motivated by the characteristics of neural networks, in which information is stored in weights on connections, we investigated how to design an Innately Forgetting-Free Network (IF2Net) for continual learning context. This study proposed a straightforward yet effective learning paradigm by ingeniously keeping the weights relative to each seen task untouched before and after learning a new task. We first presented the novel representation-level learning on task sequences with random weights. This technique refers to tweaking the drifted representations caused by randomization back to their separate task-optimal working states, but the involved weights are frozen and reused (opposite to well-known layer-wise updates of weights). Then, sequential decision-making without forgetting can be achieved by projecting the output weight updates into the parsimonious orthogonal space, making the adaptations not disturb old knowledge while maintaining model plasticity. IF2Net allows a single network to inherently learn unlimited mapping rules without telling task identities at test time by integrating the respective strengths of randomization and orthogonalization. We validated the effectiveness of our approach in the extensive theoretical analysis and empirical study.

The goal of lifelong learning is to continuously learn from non-stationary distributions, where the non-stationarity is typically imposed by a sequence of distinct tasks. Prior works have mostly considered idealistic settings, where the identity of tasks is known at least at training. In this paper we focus on a fundamentally harder, so-called task-agnostic setting where the task identities are not known and the learning machine needs to infer them from the observations. Our algorithm, which we call TAME (Task-Agnostic continual learning using Multiple Experts), automatically detects the shift in data distributions and switches between task expert networks in an online manner. At training, the strategy for switching between tasks hinges on an extremely simple observation that for each new coming task there occurs a statistically-significant deviation in the value of the loss function that marks the onset of this new task. At inference, the switching between experts is governed by the selector network that forwards the test sample to its relevant expert network. The selector network is trained on a small subset of data drawn uniformly at random. We control the growth of the task expert networks as well as selector network by employing online pruning. Our experimental results show the efficacy of our approach on benchmark continual learning data sets, outperforming the previous task-agnostic methods and even the techniques that admit task identities at both training and testing, while at the same time using a comparable model size.

People perceive the world with multiple senses (e.g., through hearing sounds, reading words and seeing objects). However, most existing AI systems only process an individual modality. This paper presents an approach that excels at handling multiple modalities of information with a single model. In our "{SkillNet}" model, different parts of the parameters are specialized for processing different modalities. Unlike traditional dense models that always activate all the model parameters, our model sparsely activates parts of the parameters whose skills are relevant to the task. Such model design enables SkillNet to learn skills in a more interpretable way. We develop our model for five modalities including text, image, sound, video and code. Results show that, SkillNet performs comparably to five modality-specific fine-tuned models. Moreover, our model supports self-supervised pretraining with the same sparsely activated way, resulting in better initialized parameters for different modalities. We find that pretraining significantly improves the performance of SkillNet on five modalities, on par with or even better than baselines with modality-specific pretraining. On the task of Chinese text-to-image retrieval, our final system achieves higher accuracy than existing leading systems including Wukong{ViT-B} and Wenlan 2.0 while using less number of activated parameters.

Despite advances in transformer-based language models (LMs), a fundamental question remains largely unanswered: Are all layers activated during inference? We investigate this question by detecting unactivated layers (which we refer to as Voids) using a non-trainable and parameter-free adaptive computation method called L2 Adaptive Computation (LAC). We adapt LAC from its original efficiency-focused application to trace activated layers during inference. This method monitors changes in the L2-norm of activations to identify voids. We analyze layer activation in instruction-tuned LMs across two phases: Prompt Processing (PP), where we trace activated layers for each token in the input prompts, and Response Generation (RG), where we trace activated layers for each generated token. We further demonstrate that distinct layers are activated during these two phases. To show the effectiveness of our method, we evaluated three distinct instruction-tuned LMs from the Llama, Mistral, and Qwen families on three benchmarks: MMLU, GPQA Diamond, and BoolQ. For example, on MMLU with a zero-shot setting, skipping voids in Qwen2.5-7B-Instruct resulted in an improvement from 69.24 to 71.29 while the model uses only 30% of the layers. Similarly, Mistral-7B-Instruct-v0.3 on GPQA Diamond improved from 13.88 to 18.36 when using 70% of the layers during both the PP and RG phases. These results show that not all layers contribute equally during inference, and that selectively skipping most of them can improve the performance of models on certain tasks.

Large Language Models (LLMs), while demonstrating remarkable capabilities across various applications, present significant challenges during inference due to their substantial model size, especially when deployed on edge devices. Activation sparsity offers a promising solution to reduce computation and memory movement, enabling more efficient inference, particularly for small-batch on-device applications. However, current approaches face limitations with non-ReLU activation function, which are foundational to most advanced LLMs, or require heavy continual training. Additionally, the difficulty in predicting active channels and limited achievable sparsity ratios constrain the effectiveness of activation sparsity-based methods. In this paper, we introduce R-Sparse, a training-free activation sparsity approach capable of achieving high sparsity levels in advanced LLMs. We conducted two preliminary investigations into how different components contribute to the output within a single linear layer and found two key observations: (i) the non-sparse components of the input function can be regarded as a few bias terms, and (ii) The full computation can be effectively approximated by an appropriate combination of input channels and weight singular values. Building on this, we replace the linear layers in LLMs with a rank-aware sparse inference method that leverages the sparsity of input channels and singular value components, eliminating the need for active channel prediction like the output sparsity based approaches. Experiments on Llama-2/3 and Mistral models across ten diverse tasks demonstrate that R-Sparse achieves comparable performance at 50% model-level sparsity, resulting in a significant 43% end-to-end efficient improvements with customized kernels.