Daily Papers

This work analyzes the training dynamics of Image Restoration (IR) Transformers and uncovers a critical yet overlooked issue: conventional LayerNorm (LN) drives feature magnitudes to diverge to a million scale and collapses channel-wise entropy. We analyze this in the perspective of networks attempting to bypass LN's constraints that conflict with IR tasks. Accordingly, we address two misalignments between LN and IR: 1) per-token normalization disrupts spatial correlations, and 2) input-independent scaling discards input-specific statistics. To address this, we propose Image Restoration Transformer Tailored Layer Normalization i-LN, a simple drop-in replacement that normalizes features holistically and adaptively rescales them per input. We provide theoretical insights and empirical evidence that this simple design effectively leads to both improved training dynamics and thereby improved performance, validated by extensive experiments.

Recently, deep learning technology has been successfully applied in the field of image compression, leading to superior rate-distortion performance. It is crucial to design an effective and efficient entropy model to estimate the probability distribution of the latent representation. However, the majority of entropy models primarily focus on one-dimensional correlation processing between channel and spatial information. In this paper, we propose an Adaptive Channel-wise and Global-inter attention Context (ACGC) entropy model, which can efficiently achieve dual feature aggregation in both inter-slice and intraslice contexts. Specifically, we divide the latent representation into different slices and then apply the ACGC model in a parallel checkerboard context to achieve faster decoding speed and higher rate-distortion performance. In order to capture redundant global features across different slices, we utilize deformable attention in adaptive global-inter attention to dynamically refine the attention weights based on the actual spatial relationships and context. Furthermore, in the main transformation structure, we propose a high-performance S2LIC model. We introduce the residual SwinV2 Transformer model to capture global feature information and utilize a dense block network as the feature enhancement module to improve the nonlinear representation of the image within the transformation structure. Experimental results demonstrate that our method achieves faster encoding and decoding speeds and outperforms VTM-17.1 and some recent learned image compression methods in both PSNR and MS-SSIM metrics.

A model must adapt itself to generalize to new and different data during testing. In this setting of fully test-time adaptation the model has only the test data and its own parameters. We propose to adapt by test entropy minimization (tent): we optimize the model for confidence as measured by the entropy of its predictions. Our method estimates normalization statistics and optimizes channel-wise affine transformations to update online on each batch. Tent reduces generalization error for image classification on corrupted ImageNet and CIFAR-10/100 and reaches a new state-of-the-art error on ImageNet-C. Tent handles source-free domain adaptation on digit recognition from SVHN to MNIST/MNIST-M/USPS, on semantic segmentation from GTA to Cityscapes, and on the VisDA-C benchmark. These results are achieved in one epoch of test-time optimization without altering training.

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

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

Since the introduction of deep learning, a wide scope of representation properties, such as decorrelation, whitening, disentanglement, rank, isotropy, and mutual information, have been studied to improve the quality of representation. However, manipulating such properties can be challenging in terms of implementational effectiveness and general applicability. To address these limitations, we propose to regularize von Neumann entropy~(VNE) of representation. First, we demonstrate that the mathematical formulation of VNE is superior in effectively manipulating the eigenvalues of the representation autocorrelation matrix. Then, we demonstrate that it is widely applicable in improving state-of-the-art algorithms or popular benchmark algorithms by investigating domain-generalization, meta-learning, self-supervised learning, and generative models. In addition, we formally establish theoretical connections with rank, disentanglement, and isotropy of representation. Finally, we provide discussions on the dimension control of VNE and the relationship with Shannon entropy. Code is available at: https://github.com/jaeill/CVPR23-VNE.

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

Entropy and mutual information in neural networks provide rich information on the learning process, but they have proven difficult to compute reliably in high dimensions. Indeed, in noisy and high-dimensional data, traditional estimates in ambient dimensions approach a fixed entropy and are prohibitively hard to compute. To address these issues, we leverage data geometry to access the underlying manifold and reliably compute these information-theoretic measures. Specifically, we define diffusion spectral entropy (DSE) in neural representations of a dataset as well as diffusion spectral mutual information (DSMI) between different variables representing data. First, we show that they form noise-resistant measures of intrinsic dimensionality and relationship strength in high-dimensional simulated data that outperform classic Shannon entropy, nonparametric estimation, and mutual information neural estimation (MINE). We then study the evolution of representations in classification networks with supervised learning, self-supervision, or overfitting. We observe that (1) DSE of neural representations increases during training; (2) DSMI with the class label increases during generalizable learning but stays stagnant during overfitting; (3) DSMI with the input signal shows differing trends: on MNIST it increases, while on CIFAR-10 and STL-10 it decreases. Finally, we show that DSE can be used to guide better network initialization and that DSMI can be used to predict downstream classification accuracy across 962 models on ImageNet. The official implementation is available at https://github.com/ChenLiu-1996/DiffusionSpectralEntropy.

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

A high-performance image compression algorithm is crucial for real-time information transmission across numerous fields. Despite rapid progress in image compression, computational inefficiency and poor redundancy modeling still pose significant bottlenecks, limiting practical applications. Inspired by the effectiveness of state space models (SSMs) in capturing long-range dependencies, we leverage SSMs to address computational inefficiency in existing methods and improve image compression from multiple perspectives. In this paper, we integrate the advantages of SSMs for better efficiency-performance trade-off and propose an enhanced image compression approach through refined context modeling, which we term MambaIC. Specifically, we explore context modeling to adaptively refine the representation of hidden states. Additionally, we introduce window-based local attention into channel-spatial entropy modeling to reduce potential spatial redundancy during compression, thereby increasing efficiency. Comprehensive qualitative and quantitative results validate the effectiveness and efficiency of our approach, particularly for high-resolution image compression. Code is released at https://github.com/AuroraZengfh/MambaIC.

The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added subsequently to that original work, to explore the consequences of the purely statistical point of view. We show how standard methods in the equilibrium theory could have been derived simply from a description of the available problem information. In addition, our presentation leads to novel insights into questions associated with symmetry and non-equilibrium statistical mechanics. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a quantity related to the thermodynamic entropy production is found by considering information loss in non-equilibrium processes. Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complexity by successively adding information to create progressively more complex descriptions of a physical system. Our result is that such statistical mechanical descriptions can be used to create transparent, computable, experimentally-relevant models that may be informed by more detailed atomistic simulations. We also derive a theory for the kinetic behavior of this system, identifying the nonequilibrium `process' free energy functional. The Gibbs relation for this functional is a fluctuation-dissipation theorem applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient driving forces. Based on this work, it is clear that statistical mechanics is a general tool for constructing the relationships between constraints on system information.

Time series forecasting has attracted significant attention in recent decades. Previous studies have demonstrated that the Channel-Independent (CI) strategy improves forecasting performance by treating different channels individually, while it leads to poor generalization on unseen instances and ignores potentially necessary interactions between channels. Conversely, the Channel-Dependent (CD) strategy mixes all channels with even irrelevant and indiscriminate information, which, however, results in oversmoothing issues and limits forecasting accuracy. There is a lack of channel strategy that effectively balances individual channel treatment for improved forecasting performance without overlooking essential interactions between channels. Motivated by our observation of a correlation between the time series model's performance boost against channel mixing and the intrinsic similarity on a pair of channels, we developed a novel and adaptable Channel Clustering Module (CCM). CCM dynamically groups channels characterized by intrinsic similarities and leverages cluster information instead of individual channel identities, combining the best of CD and CI worlds. Extensive experiments on real-world datasets demonstrate that CCM can (1) boost the performance of CI and CD models by an average margin of 2.4% and 7.2% on long-term and short-term forecasting, respectively; (2) enable zero-shot forecasting with mainstream time series forecasting models; (3) uncover intrinsic time series patterns among channels and improve interpretability of complex time series models.

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

Recent advancements in learned image compression (LIC) have yielded impressive performance gains. Notably, the learned image compression models with multi-reference entropy models (MLIC series) have significantly outperformed existing traditional image codecs such as the Versatile Video Coding (VVC) Intra. In this paper, we present MLICv2 and MLICv2^+, enhanced versions of the MLIC series, featuring improved transform techniques, entropy modeling, and instance adaptability. For better transform, we introduce a simple token mixing transform block inspired by the meta transformer architecture, addressing the performance degradation at high bit-rates observed in previous MLIC series while maintaining computational efficiency. To enhance entropy modeling, we propose a hyperprior-guided global correlation prediction, enabling the capture of global contexts in the initial slice of the latent representation. We also develop a channel reweighting module to dynamically prioritize important channels within each context. Additionally, advanced positional embedding for context modeling and selective compression with guided optimization are investigated. To boost instance adaptability, we employ stochastic Gumbel annealing to iteratively refine the latent representation according to the rate-distortion optimization of a specific input image. This approach further enhances performance without impacting decoding speed. Experimental results demonstrate that our MLICv2 and MLICv2^+ achieve state-of-the-art performance, reducing Bjontegaard-Delta rate (BD-rate) by 16.54%, 21.61%, 16.05% and 20.46%, 24.35%, 19.14% respectively, compared to VTM-17.0 Intra on the Kodak, Tecnick, CLIC Pro Val dataset, respectively.

With the rapid advancement of stereo vision technologies, stereo image compression has emerged as a crucial field that continues to draw significant attention. Previous approaches have primarily employed a unidirectional paradigm, where the compression of one view is dependent on the other, resulting in imbalanced compression. To address this issue, we introduce a symmetric bidirectional stereo image compression architecture, named BiSIC. Specifically, we propose a 3D convolution based codec backbone to capture local features and incorporate bidirectional attention blocks to exploit global features. Moreover, we design a novel cross-dimensional entropy model that integrates various conditioning factors, including the spatial context, channel context, and stereo dependency, to effectively estimate the distribution of latent representations for entropy coding. Extensive experiments demonstrate that our proposed BiSIC outperforms conventional image/video compression standards, as well as state-of-the-art learning-based methods, in terms of both PSNR and MS-SSIM.

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

Few-Shot Learning (FSL) requires vision models to quickly adapt to brand-new classification tasks with a shift in task distribution. Understanding the difficulties posed by this task distribution shift is central to FSL. In this paper, we show that a simple channel-wise feature transformation may be the key to unraveling this secret from a channel perspective. When facing novel few-shot tasks in the test-time datasets, this transformation can greatly improve the generalization ability of learned image representations, while being agnostic to the choice of training algorithms and datasets. Through an in-depth analysis of this transformation, we find that the difficulty of representation transfer in FSL stems from the severe channel bias problem of image representations: channels may have different importance in different tasks, while convolutional neural networks are likely to be insensitive, or respond incorrectly to such a shift. This points out a core problem of the generalization ability of modern vision systems and needs further attention in the future. Our code is available at https://github.com/Frankluox/Channel_Importance_FSL.

Unlike color photography images, which are consistently encoded into RGB channels, biological images encompass various modalities, where the type of microscopy and the meaning of each channel varies with each experiment. Importantly, the number of channels can range from one to a dozen and their correlation is often comparatively much lower than RGB, as each of them brings specific information content. This aspect is largely overlooked by methods designed out of the bioimage field, and current solutions mostly focus on intra-channel spatial attention, often ignoring the relationship between channels, yet crucial in most biological applications. Importantly, the variable channel type and count prevent the projection of several experiments to a unified representation for large scale pre-training. In this study, we propose ChAda-ViT, a novel Channel Adaptive Vision Transformer architecture employing an Inter-Channel Attention mechanism on images with an arbitrary number, order and type of channels. We also introduce IDRCell100k, a bioimage dataset with a rich set of 79 experiments covering 7 microscope modalities, with a multitude of channel types, and channel counts varying from 1 to 10 per experiment. Our proposed architecture, trained in a self-supervised manner, outperforms existing approaches in several biologically relevant downstream tasks. Additionally, it can be used to bridge the gap for the first time between assays with different microscopes, channel numbers or types by embedding various image and experimental modalities into a unified biological image representation. The latter should facilitate interdisciplinary studies and pave the way for better adoption of deep learning in biological image-based analyses. Code and Data to be released soon.

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

Designing an efficient model within the limited computational cost is challenging. We argue the accuracy of a lightweight model has been further limited by the design convention: a stage-wise configuration of the channel dimensions, which looks like a piecewise linear function of the network stage. In this paper, we study an effective channel dimension configuration towards better performance than the convention. To this end, we empirically study how to design a single layer properly by analyzing the rank of the output feature. We then investigate the channel configuration of a model by searching network architectures concerning the channel configuration under the computational cost restriction. Based on the investigation, we propose a simple yet effective channel configuration that can be parameterized by the layer index. As a result, our proposed model following the channel parameterization achieves remarkable performance on ImageNet classification and transfer learning tasks including COCO object detection, COCO instance segmentation, and fine-grained classifications. Code and ImageNet pretrained models are available at https://github.com/clovaai/rexnet.

Multivariate time series forecasting plays a crucial role in various fields such as finance, traffic management, energy, and healthcare. Recent studies have highlighted the advantages of channel independence to resist distribution drift but neglect channel correlations, limiting further enhancements. Several methods utilize mechanisms like attention or mixer to address this by capturing channel correlations, but they either introduce excessive complexity or rely too heavily on the correlation to achieve satisfactory results under distribution drifts, particularly with a large number of channels. Addressing this gap, this paper presents an efficient MLP-based model, the Series-cOre Fused Time Series forecaster (SOFTS), which incorporates a novel STar Aggregate-Redistribute (STAR) module. Unlike traditional approaches that manage channel interactions through distributed structures, e.g., attention, STAR employs a centralized strategy to improve efficiency and reduce reliance on the quality of each channel. It aggregates all series to form a global core representation, which is then dispatched and fused with individual series representations to facilitate channel interactions effectively.SOFTS achieves superior performance over existing state-of-the-art methods with only linear complexity. The broad applicability of the STAR module across different forecasting models is also demonstrated empirically. For further research and development, we have made our code publicly available at https://github.com/Secilia-Cxy/SOFTS.

StyleGAN has shown remarkable performance in unconditional image generation. However, its high computational cost poses a significant challenge for practical applications. Although recent efforts have been made to compress StyleGAN while preserving its performance, existing compressed models still lag behind the original model, particularly in terms of sample diversity. To overcome this, we propose a novel channel pruning method that leverages varying sensitivities of channels to latent vectors, which is a key factor in sample diversity. Specifically, by assessing channel importance based on their sensitivities to latent vector perturbations, our method enhances the diversity of samples in the compressed model. Since our method solely focuses on the channel pruning stage, it has complementary benefits with prior training schemes without additional training cost. Extensive experiments demonstrate that our method significantly enhances sample diversity across various datasets. Moreover, in terms of FID scores, our method not only surpasses state-of-the-art by a large margin but also achieves comparable scores with only half training iterations.

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

A fundamental problem in quantum information is to understand the operational significance of quantum resources. Quantum resource theories (QRTs) provide a powerful theoretical framework that aids in analyzing and comprehending the operational meaning of these resources. Early resource theories primarily focused on analyzing static quantum resources. Recently, there has been growing interest in the study of dynamic quantum resources. In this paper, we utilize superchannel theory to describe the dynamic resource theory of quantum coherence. In this dynamic resource theory, we treat classical channels as free channels and consider two classes of free superchannels that preserve channel incoherence (maximally incoherent superchannels (MISC) and dephasing-covariant incoherent superchannels (DISC)) as free resources. We regard the quantum Fourier transform as the golden unit of dynamic coherence resources. We first establish the one-shot theory of dynamic coherence cost and dynamic coherence distillation, which involves converting the quantum Fourier transform into an arbitrary quantum channel using MISC and DISC. Next, we introduce a class of free superchannels known as δ-MISC, which asymptotically generate negligible dynamic coherence. Finally, we provide upper and lower bounds for the one-shot catalytic dynamic coherence cost of quantum channels under the action of these δ-MISC superchannels.

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

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

We investigate the impact of channel-wise mixing via multi-layer perceptrons (MLPs) on the generalization capabilities of recurrent convolutional networks. Specifically, we compare two architectures: DARC (Depth Aware Recurrent Convolution), which employs a simple recurrent convolutional structure, and DAMP (Depth Aware Multi-layer Perceptron), which extends DARC with a gated MLP for channel mixing. Using the Re-ARC benchmark, we find that DAMP significantly outperforms DARC in both in-distribution and out-of-distribution generalization under exact-match grading criteria. These results suggest that explicit channel mixing through MLPs enables recurrent convolutional networks to learn more robust and generalizable computational patterns. Our findings have implications for neural program synthesis and highlight the potential of DAMP as a target architecture for hypernetwork approaches.

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

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

This work aims to predict channels in wireless communication systems based on noisy observations, utilizing sequence-to-sequence models with attention (Seq2Seq-attn) and transformer models. Both models are adapted from natural language processing to tackle the complex challenge of channel prediction. Additionally, a new technique called reverse positional encoding is introduced in the transformer model to improve the robustness of the model against varying sequence lengths. Similarly, the encoder outputs of the Seq2Seq-attn model are reversed before applying attention. Simulation results demonstrate that the proposed ordering techniques allow the models to better capture the relationships between the channel snapshots within the sequence, irrespective of the sequence length, as opposed to existing methods.

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

Anomaly detection in multivariate time series is challenging as heterogeneous subsequence anomalies may occur. Reconstruction-based methods, which focus on learning normal patterns in the frequency domain to detect diverse abnormal subsequences, achieve promising results, while still falling short on capturing fine-grained frequency characteristics and channel correlations. To contend with the limitations, we introduce CATCH, a framework based on frequency patching. We propose to patchify the frequency domain into frequency bands, which enhances its ability to capture fine-grained frequency characteristics. To perceive appropriate channel correlations, we propose a Channel Fusion Module (CFM), which features a patch-wise mask generator and a masked-attention mechanism. Driven by a bi-level multi-objective optimization algorithm, the CFM is encouraged to iteratively discover appropriate patch-wise channel correlations, and to cluster relevant channels while isolating adverse effects from irrelevant channels. Extensive experiments on 10 real-world datasets and 12 synthetic datasets demonstrate that CATCH achieves state-of-the-art performance. We make our code and datasets available at https://github.com/decisionintelligence/CATCH.

State-of-the-art language generation models can degenerate when applied to open-ended generation problems such as text completion, story generation, or dialog modeling. This degeneration usually shows up in the form of incoherence, lack of vocabulary diversity, and self-repetition or copying from the context. In this paper, we postulate that ``human-like'' generations usually lie in a narrow and nearly flat entropy band, and violation of these entropy bounds correlates with degenerate behavior. Our experiments show that this stable narrow entropy zone exists across models, tasks, and domains and confirm the hypothesis that violations of this zone correlate with degeneration. We then use this insight to propose an entropy-aware decoding algorithm that respects these entropy bounds resulting in less degenerate, more contextual, and "human-like" language generation in open-ended text generation settings.

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

Extracting informative representations from videos is fundamental for effectively learning various downstream tasks. We present a novel approach for unsupervised learning of meaningful representations from videos, leveraging the concept of image spatial entropy (ISE) that quantifies the per-pixel information in an image. We argue that local entropy of pixel neighborhoods and their temporal evolution create valuable intrinsic supervisory signals for learning prominent features. Building on this idea, we abstract visual features into a concise representation of keypoints that act as dynamic information transmitters, and design a deep learning model that learns, purely unsupervised, spatially and temporally consistent representations directly from video frames. Two original information-theoretic losses, computed from local entropy, guide our model to discover consistent keypoint representations; a loss that maximizes the spatial information covered by the keypoints and a loss that optimizes the keypoints' information transportation over time. We compare our keypoint representation to strong baselines for various downstream tasks, \eg, learning object dynamics. Our empirical results show superior performance for our information-driven keypoints that resolve challenges like attendance to static and dynamic objects or objects abruptly entering and leaving the scene.

Understanding the training dynamics of deep neural networks remains a major open problem, with physics-inspired approaches offering promising insights. Building on this perspective, we develop a thermodynamic framework to describe the stationary distributions of stochastic gradient descent (SGD) with weight decay for scale-invariant neural networks, a setting that both reflects practical architectures with normalization layers and permits theoretical analysis. We establish analogies between training hyperparameters (e.g., learning rate, weight decay) and thermodynamic variables such as temperature, pressure, and volume. Starting with a simplified isotropic noise model, we uncover a close correspondence between SGD dynamics and ideal gas behavior, validated through theory and simulation. Extending to training of neural networks, we show that key predictions of the framework, including the behavior of stationary entropy, align closely with experimental observations. This framework provides a principled foundation for interpreting training dynamics and may guide future work on hyperparameter tuning and the design of learning rate schedulers.

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

Joint source-channel coding (JSCC) offers a promising avenue for enhancing transmission efficiency by jointly incorporating source and channel statistics into the system design. A key advancement in this area is the deep joint source and channel coding (DeepJSCC) technique that designs a direct mapping of input signals to channel symbols parameterized by a neural network, which can be trained for arbitrary channel models and semantic quality metrics. This paper advances the DeepJSCC framework toward a semantics-aligned, high-fidelity transmission approach, called semantics-guided diffusion DeepJSCC (SGD-JSCC). Existing schemes that integrate diffusion models (DMs) with JSCC face challenges in transforming random generation into accurate reconstruction and adapting to varying channel conditions. SGD-JSCC incorporates two key innovations: (1) utilizing some inherent information that contributes to the semantics of an image, such as text description or edge map, to guide the diffusion denoising process; and (2) enabling seamless adaptability to varying channel conditions with the help of a semantics-guided DM for channel denoising. The DM is guided by diverse semantic information and integrates seamlessly with DeepJSCC. In a slow fading channel, SGD-JSCC dynamically adapts to the instantaneous signal-to-noise ratio (SNR) directly estimated from the channel output, thereby eliminating the need for additional pilot transmissions for channel estimation. In a fast fading channel, we introduce a training-free denoising strategy, allowing SGD-JSCC to effectively adjust to fluctuations in channel gains. Numerical results demonstrate that, guided by semantic information and leveraging the powerful DM, our method outperforms existing DeepJSCC schemes, delivering satisfactory reconstruction performance even at extremely poor channel conditions.

We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as mathematical models of contextuality in classical and quantum settings. Each information structure can be regarded as a ringed site with trivial topology; the structure ring is generated by the observables themselves and its multiplication corresponds to joint measurement. We extend Baudot and Bennequin's definition of information cohomology to this setting, as a derived functor in the category of modules over the structure ring, and show explicitly that the bar construction gives a projective resolution in that category, recovering in this way the cochain complexes previously considered in the literature. Finally, we study the particular case of a one-parameter family of coefficients made of functions of probability distributions. The only 1-cocycles are Shannon entropy or Tsallis alpha-entropy, depending on the value of the parameter.

Learned image compression (LIC) has gained traction as an effective solution for image storage and transmission in recent years. However, existing LIC methods are redundant in latent representation due to limitations in capturing anisotropic frequency components and preserving directional details. To overcome these challenges, we propose a novel frequency-aware transformer (FAT) block that for the first time achieves multiscale directional ananlysis for LIC. The FAT block comprises frequency-decomposition window attention (FDWA) modules to capture multiscale and directional frequency components of natural images. Additionally, we introduce frequency-modulation feed-forward network (FMFFN) to adaptively modulate different frequency components, improving rate-distortion performance. Furthermore, we present a transformer-based channel-wise autoregressive (T-CA) model that effectively exploits channel dependencies. Experiments show that our method achieves state-of-the-art rate-distortion performance compared to existing LIC methods, and evidently outperforms latest standardized codec VTM-12.1 by 14.5%, 15.1%, 13.0% in BD-rate on the Kodak, Tecnick, and CLIC datasets.

Backpropagation, which uses the chain rule, is the de-facto standard algorithm for optimizing neural networks nowadays. Recently, Hinton (2022) proposed the forward-forward algorithm, a promising alternative that optimizes neural nets layer-by-layer, without propagating gradients throughout the network. Although such an approach has several advantages over back-propagation and shows promising results, the fact that each layer is being trained independently limits the optimization process. Specifically, it prevents the network's layers from collaborating to learn complex and rich features. In this work, we study layer collaboration in the forward-forward algorithm. We show that the current version of the forward-forward algorithm is suboptimal when considering information flow in the network, resulting in a lack of collaboration between layers of the network. We propose an improved version that supports layer collaboration to better utilize the network structure, while not requiring any additional assumptions or computations. We empirically demonstrate the efficacy of the proposed version when considering both information flow and objective metrics. Additionally, we provide a theoretical motivation for the proposed method, inspired by functional entropy theory.

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

Recently, channel attention mechanism has demonstrated to offer great potential in improving the performance of deep convolutional neural networks (CNNs). However, most existing methods dedicate to developing more sophisticated attention modules for achieving better performance, which inevitably increase model complexity. To overcome the paradox of performance and complexity trade-off, this paper proposes an Efficient Channel Attention (ECA) module, which only involves a handful of parameters while bringing clear performance gain. By dissecting the channel attention module in SENet, we empirically show avoiding dimensionality reduction is important for learning channel attention, and appropriate cross-channel interaction can preserve performance while significantly decreasing model complexity. Therefore, we propose a local cross-channel interaction strategy without dimensionality reduction, which can be efficiently implemented via 1D convolution. Furthermore, we develop a method to adaptively select kernel size of 1D convolution, determining coverage of local cross-channel interaction. The proposed ECA module is efficient yet effective, e.g., the parameters and computations of our modules against backbone of ResNet50 are 80 vs. 24.37M and 4.7e-4 GFLOPs vs. 3.86 GFLOPs, respectively, and the performance boost is more than 2% in terms of Top-1 accuracy. We extensively evaluate our ECA module on image classification, object detection and instance segmentation with backbones of ResNets and MobileNetV2. The experimental results show our module is more efficient while performing favorably against its counterparts.

Attention mechanism, especially channel attention, has gained great success in the computer vision field. Many works focus on how to design efficient channel attention mechanisms while ignoring a fundamental problem, i.e., channel attention mechanism uses scalar to represent channel, which is difficult due to massive information loss. In this work, we start from a different view and regard the channel representation problem as a compression process using frequency analysis. Based on the frequency analysis, we mathematically prove that the conventional global average pooling is a special case of the feature decomposition in the frequency domain. With the proof, we naturally generalize the compression of the channel attention mechanism in the frequency domain and propose our method with multi-spectral channel attention, termed as FcaNet. FcaNet is simple but effective. We can change a few lines of code in the calculation to implement our method within existing channel attention methods. Moreover, the proposed method achieves state-of-the-art results compared with other channel attention methods on image classification, object detection, and instance segmentation tasks. Our method could consistently outperform the baseline SENet, with the same number of parameters and the same computational cost. Our code and models will are publicly available at https://github.com/cfzd/FcaNet.

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

Contemporary predictive models are hard to interpret as their deep nets exploit numerous complex relations between input elements. This work suggests a theoretical framework for model interpretability by measuring the contribution of relevant features to the functional entropy of the network with respect to the input. We rely on the log-Sobolev inequality that bounds the functional entropy by the functional Fisher information with respect to the covariance of the data. This provides a principled way to measure the amount of information contribution of a subset of features to the decision function. Through extensive experiments, we show that our method surpasses existing interpretability sampling-based methods on various data signals such as image, text, and audio.

Entropy serves as a critical metric for measuring the diversity of outputs generated by large language models (LLMs), providing valuable insights into their exploration capabilities. While recent studies increasingly focus on monitoring and adjusting entropy to better balance exploration and exploitation in reinforcement fine-tuning (RFT), a principled understanding of entropy dynamics during this process is yet to be thoroughly investigated. In this paper, we establish a theoretical framework for analyzing the entropy dynamics during the RFT process, which begins with a discriminant expression that quantifies entropy change under a single logit update. This foundation enables the derivation of a first-order expression for entropy change, which can be further extended to the update formula of Group Relative Policy Optimization (GRPO). The corollaries and insights drawn from the theoretical analysis inspire the design of entropy control methods, and also offer a unified lens for interpreting various entropy-based methods in existing studies. We provide empirical evidence to support the main conclusions of our analysis and demonstrate the effectiveness of the derived entropy-discriminator clipping methods. This study yields novel insights into RFT training dynamics, providing theoretical support and practical strategies for optimizing the exploration-exploitation balance during LLM fine-tuning.

We introduce the Structured Knowledge Accumulation (SKA) framework, which reinterprets entropy as a dynamic, layer-wise measure of knowledge alignment in neural networks. Instead of relying on traditional gradient-based optimization, SKA defines entropy in terms of knowledge vectors and their influence on decision probabilities across multiple layers. This formulation naturally leads to the emergence of activation functions such as the sigmoid as a consequence of entropy minimization. Unlike conventional backpropagation, SKA allows each layer to optimize independently by aligning its knowledge representation with changes in decision probabilities. As a result, total network entropy decreases in a hierarchical manner, allowing knowledge structures to evolve progressively. This approach provides a scalable, biologically plausible alternative to gradient-based learning, bridging information theory and artificial intelligence while offering promising applications in resource-constrained and parallel computing environments.

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.

We consider reversely-degraded wiretap channels, for which the secrecy capacity is zero if there is no channel feedback. This work focuses on a seeded modular code design for the Gaussian wiretap channel with channel output feedback, combining universal hash functions for security and learned feedback-based codes for reliability to achieve positive secrecy rates. We study the trade-off between communication reliability and information leakage, illustrating that feedback enables agreeing on a secret key shared between legitimate parties, overcoming the security advantage of the wiretapper. Our findings also motivate code designs for sensing-assisted secure communication, to be used in next-generation integrated sensing and communication methods.

Convolutional neural network (CNN) depth is of crucial importance for image super-resolution (SR). However, we observe that deeper networks for image SR are more difficult to train. The low-resolution inputs and features contain abundant low-frequency information, which is treated equally across channels, hence hindering the representational ability of CNNs. To solve these problems, we propose the very deep residual channel attention networks (RCAN). Specifically, we propose a residual in residual (RIR) structure to form very deep network, which consists of several residual groups with long skip connections. Each residual group contains some residual blocks with short skip connections. Meanwhile, RIR allows abundant low-frequency information to be bypassed through multiple skip connections, making the main network focus on learning high-frequency information. Furthermore, we propose a channel attention mechanism to adaptively rescale channel-wise features by considering interdependencies among channels. Extensive experiments show that our RCAN achieves better accuracy and visual improvements against state-of-the-art methods.

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using graph structures based on the relational inductive bias (homophily assumption). While GNNs have been commonly believed to outperform NNs in real-world tasks, recent work has identified a non-trivial set of datasets where their performance compared to NNs is not satisfactory. Heterophily has been considered the main cause of this empirical observation and numerous works have been put forward to address it. In this paper, we first revisit the widely used homophily metrics and point out that their consideration of only graph-label consistency is a shortcoming. Then, we study heterophily from the perspective of post-aggregation node similarity and define new homophily metrics, which are potentially advantageous compared to existing ones. Based on this investigation, we prove that some harmful cases of heterophily can be effectively addressed by local diversification operation. Then, we propose the Adaptive Channel Mixing (ACM), a framework to adaptively exploit aggregation, diversification and identity channels node-wisely to extract richer localized information for diverse node heterophily situations. ACM is more powerful than the commonly used uni-channel framework for node classification tasks on heterophilic graphs and is easy to be implemented in baseline GNN layers. When evaluated on 10 benchmark node classification tasks, ACM-augmented baselines consistently achieve significant performance gain, exceeding state-of-the-art GNNs on most tasks without incurring significant computational burden.

The central building block of convolutional neural networks (CNNs) is the convolution operator, which enables networks to construct informative features by fusing both spatial and channel-wise information within local receptive fields at each layer. A broad range of prior research has investigated the spatial component of this relationship, seeking to strengthen the representational power of a CNN by enhancing the quality of spatial encodings throughout its feature hierarchy. In this work, we focus instead on the channel relationship and propose a novel architectural unit, which we term the "Squeeze-and-Excitation" (SE) block, that adaptively recalibrates channel-wise feature responses by explicitly modelling interdependencies between channels. We show that these blocks can be stacked together to form SENet architectures that generalise extremely effectively across different datasets. We further demonstrate that SE blocks bring significant improvements in performance for existing state-of-the-art CNNs at slight additional computational cost. Squeeze-and-Excitation Networks formed the foundation of our ILSVRC 2017 classification submission which won first place and reduced the top-5 error to 2.251%, surpassing the winning entry of 2016 by a relative improvement of ~25%. Models and code are available at https://github.com/hujie-frank/SENet.

Informative features play a crucial role in the single image super-resolution task. Channel attention has been demonstrated to be effective for preserving information-rich features in each layer. However, channel attention treats each convolution layer as a separate process that misses the correlation among different layers. To address this problem, we propose a new holistic attention network (HAN), which consists of a layer attention module (LAM) and a channel-spatial attention module (CSAM), to model the holistic interdependencies among layers, channels, and positions. Specifically, the proposed LAM adaptively emphasizes hierarchical features by considering correlations among layers. Meanwhile, CSAM learns the confidence at all the positions of each channel to selectively capture more informative features. Extensive experiments demonstrate that the proposed HAN performs favorably against the state-of-the-art single image super-resolution approaches.

While Reinforcement Learning with Verifiable Rewards (RLVR) can enhance LLM reasoning, its training process poses a critical risk: entropy collapse. This phenomenon is a rapid loss of policy diversity, stemming from the exploration-exploitation imbalance and leading to a lack of generalization. Recent entropy-intervention methods aim to prevent entropy collapse, yet their underlying mechanisms remain unclear. In this paper, we conduct a quantitative analysis to reveal token-level entropy changes and how existing entropy intervention methods help avoid entropy collapse. Our findings point out a fundamental limitation of existing methods: they attempt to control entropy dynamics indirectly. By only affecting related factors, such as the advantage signal and generation probability, their effectiveness is inherently limited and could potentially fail. To address this limitation, we introduce an entropy-change-aware reweighting scheme, namely Stabilizing Token-level Entropy-changE via Reweighting (STEER), that adaptively stabilizes entropy dynamics through fine-grained token-level adjustments. Our approach mitigates over-exploitation while fostering robust exploration. Extensive experiments demonstrate that STEER significantly mitigates entropy collapse, stabilizes entropy dynamics, and achieves stronger downstream performance across various mathematical reasoning benchmarks \footnote{Our code is available at https://github.com/zz-haooo/STEER.

We propose a fully data-driven approach to designing mutual information (MI) estimators. Since any MI estimator is a function of the observed sample from two random variables, we parameterize this function with a neural network (MIST) and train it end-to-end to predict MI values. Training is performed on a large meta-dataset of 625,000 synthetic joint distributions with known ground-truth MI. To handle variable sample sizes and dimensions, we employ a two-dimensional attention scheme ensuring permutation invariance across input samples. To quantify uncertainty, we optimize a quantile regression loss, enabling the estimator to approximate the sampling distribution of MI rather than return a single point estimate. This research program departs from prior work by taking a fully empirical route, trading universal theoretical guarantees for flexibility and efficiency. Empirically, the learned estimators largely outperform classical baselines across sample sizes and dimensions, including on joint distributions unseen during training. The resulting quantile-based intervals are well-calibrated and more reliable than bootstrap-based confidence intervals, while inference is orders of magnitude faster than existing neural baselines. Beyond immediate empirical gains, this framework yields trainable, fully differentiable estimators that can be embedded into larger learning pipelines. Moreover, exploiting MI's invariance to invertible transformations, meta-datasets can be adapted to arbitrary data modalities via normalizing flows, enabling flexible training for diverse target meta-distributions.

Collective motion in fish schools exemplifies emergent self-organization in active matter systems, yet computational tools for simulating and analyzing these dynamics remain fragmented across research groups. We present dewi-kadita, an open-source Python library implementing the three-dimensional Couzin zone-based model with comprehensive entropy diagnostics tailored for marine collective behavior research. The library introduces seven information-theoretic metrics -- school cohesion entropy, polarization entropy, depth stratification entropy, angular momentum entropy, nearest-neighbor entropy, velocity correlation entropy, and school shape entropy -- that characterize distinct organizational features inaccessible to classical order parameters. These metrics combine into an Oceanic Schooling Index (OSI) providing a single scalar measure of collective disorder. Validation across four canonical configurations (swarm, torus, dynamic parallel, highly parallel) confirms correct reproduction of known phase behaviors: the swarm maintains disorder with polarization P < 0.1 and OSI approx 0.71, while the highly parallel state achieves P = 0.998 with OSI = 0.24 and velocity correlation entropy vanishing to zero. The entropy framework successfully discriminates the torus and dynamic parallel configurations that exhibit comparable order parameter magnitudes through different organizational mechanisms. Numba just-in-time (JIT) compilation accelerates pairwise interaction calculations by 10--100times, enabling simulations of 150--250 agents over 1000--2000 time steps within five minutes on standard workstation hardware. NetCDF4 output ensures interoperability with oceanographic analysis tools. The library addresses the need for standardized, reproducible infrastructure in collective behavior modeling analogous to established molecular dynamics codes.

Large Language Models (LLMs) excel in NLP, but their demands hinder their widespread deployment. While Quantization-Aware Training (QAT) offers a solution, its extensive training costs make Post-Training Quantization (PTQ) a more practical approach for LLMs. In existing studies, activation outliers in particular channels are identified as the bottleneck to PTQ accuracy. They propose to transform the magnitudes from activations to weights, which however offers limited alleviation or suffers from unstable gradients, resulting in a severe performance drop at low-bitwidth. In this paper, we propose QLLM, an accurate and efficient low-bitwidth PTQ method designed for LLMs. QLLM introduces an adaptive channel reassembly technique that reallocates the magnitude of outliers to other channels, thereby mitigating their impact on the quantization range. This is achieved by channel disassembly and channel assembly, which first breaks down the outlier channels into several sub-channels to ensure a more balanced distribution of activation magnitudes. Then similar channels are merged to maintain the original channel number for efficiency. Additionally, an adaptive strategy is designed to autonomously determine the optimal number of sub-channels for channel disassembly. To further compensate for the performance loss caused by quantization, we propose an efficient tuning method that only learns a small number of low-rank weights while freezing the pre-trained quantized model. After training, these low-rank parameters can be fused into the frozen weights without affecting inference. Extensive experiments on LLaMA-1 and LLaMA-2 show that QLLM can obtain accurate quantized models efficiently. For example, QLLM quantizes the 4-bit LLaMA-2-70B within 10 hours on a single A100-80G GPU, outperforming the previous state-of-the-art method by 7.89% on the average accuracy across five zero-shot tasks.

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

We investigate the time evolution of the Boltzmann entropy of a dilute gas of N particles, N>>1, as it undergoes a free expansion doubling its volume. The microstate of the system, a point in the 4N dimensional phase space, changes in time via Hamiltonian dynamics. Its entropy, at any time t, is given by the logarithm of the phase space volume of all the microstates giving rise to its macrostate at time t. The macrostates that we consider are defined by coarse graining the one-particle phase space into cells Δ_α. The initial and final macrostates of the system are equilibrium states in volumes V and 2V, with the same energy E and particle number N. Their entropy per particle is given, for sufficiently large systems, by the thermodynamic entropy as a function of the particle and energy density, whose leading term is independent of the size of the Δ_α. The intermediate (non-equilibrium) entropy does however depend on the size of the cells Δ_α. Its change with time is due to (i) dispersal in physical space from free motion and to (ii) the collisions between particles which change their velocities. The former depends strongly on the size of the velocity coarse graining Δv: it produces entropy at a rate proportional to Δv. This dependence is investigated numerically and analytically for a dilute two-dimensional gas of hard discs. It becomes significant when the mean free path between collisions is of the same order or larger than the length scale of the initial spatial inhomogeneity. In the opposite limit, the rate of entropy production is essentially independent of Δv and is given by the Boltzmann equation for the limit Δvrightarrow 0. We show that when both processes are active the time dependence of the entropy has a scaling form involving the ratio of the rates of its production by the two processes.

This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of almost-zero eigenvalues in the Hessian with very few positive or negative eigenvalues. We leverage upon this observation to construct a local-entropy-based objective function that favors well-generalizable solutions lying in large flat regions of the energy landscape, while avoiding poorly-generalizable solutions located in the sharp valleys. Conceptually, our algorithm resembles two nested loops of SGD where we use Langevin dynamics in the inner loop to compute the gradient of the local entropy before each update of the weights. We show that the new objective has a smoother energy landscape and show improved generalization over SGD using uniform stability, under certain assumptions. Our experiments on convolutional and recurrent networks demonstrate that Entropy-SGD compares favorably to state-of-the-art techniques in terms of generalization error and training time.

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

Gaussian quantum channels constitute a cornerstone of continuous-variable quantum information science, underpinning a wide array of protocols in quantum optics and quantum metrology. While the action of such channels on arbitrary states is well-characterized under full channel knowledge, we address the inverse problem, namely, the precise estimation of fundamental channel parameters, including the beam splitter transmissivity and the two-mode squeezing amplitude. Employing the quantum Fisher information (QFI) as a benchmark for metrological sensitivity, we demonstrate that the symmetry inherent in mode mixing critically governs the amplification of QFI, thereby enabling high-precision parameter estimation. In addition, we investigate quantum thermometry by estimating the average photon number of thermal states, revealing that the transmissivity parameter significantly modulates estimation precision. Our results underscore the metrological utility of two-mode Gaussian states and establish a robust framework for parameter inference in noisy and dynamically evolving quantum systems.

Real-world multichannel time series prediction faces growing demands for efficiency across edge and cloud environments, making channel compression a timely and essential problem. Motivated by success of Multiple-Input Multiple-Output (MIMO) methods, we propose a predictability-aware compression-decompression framework to reduce runtime, lower communication cost, and maintain prediction accuracy across diverse predictors. The core idea involves using a circular periodicity key matrix with orthogonality to capture underlying time series predictability during compression and to mitigate reconstruction errors during decompression by relaxing oversimplified data assumptions. Theoretical and empirical analyses show that the proposed framework is both time-efficient and scalable under a large number of channels. Extensive experiments on six datasets across various predictors demonstrate that the proposed method achieves superior overall performance by jointly considering prediction accuracy and runtime, while maintaining strong compatibility with diverse predictors.

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

A number of different architectures and loss functions have been applied to the problem of self-supervised learning (SSL), with the goal of developing embeddings that provide the best possible pre-training for as-yet-unknown, lightly supervised downstream tasks. One of these SSL criteria is to maximize the entropy of a set of embeddings in some compact space. But the goal of maximizing the embedding entropy often depends--whether explicitly or implicitly--upon high dimensional entropy estimates, which typically perform poorly in more than a few dimensions. In this paper, we motivate an effective entropy maximization criterion (E2MC), defined in terms of easy-to-estimate, low-dimensional constraints. We demonstrate that using it to continue training an already-trained SSL model for only a handful of epochs leads to a consistent and, in some cases, significant improvement in downstream performance. We perform careful ablation studies to show that the improved performance is due to the proposed add-on criterion. We also show that continued pre-training with alternative criteria does not lead to notable improvements, and in some cases, even degrades performance.

Recent studies have demonstrated the great power of Transformer models for time series forecasting. One of the key elements that lead to the transformer's success is the channel-independent (CI) strategy to improve the training robustness. However, the ignorance of the correlation among different channels in CI would limit the model's forecasting capacity. In this work, we design a special Transformer, i.e., Channel Aligned Robust Blend Transformer (CARD for short), that addresses key shortcomings of CI type Transformer in time series forecasting. First, CARD introduces a channel-aligned attention structure that allows it to capture both temporal correlations among signals and dynamical dependence among multiple variables over time. Second, in order to efficiently utilize the multi-scale knowledge, we design a token blend module to generate tokens with different resolutions. Third, we introduce a robust loss function for time series forecasting to alleviate the potential overfitting issue. This new loss function weights the importance of forecasting over a finite horizon based on prediction uncertainties. Our evaluation of multiple long-term and short-term forecasting datasets demonstrates that CARD significantly outperforms state-of-the-art time series forecasting methods. The code is available at the following repository:https://github.com/wxie9/CARD

We discovered the underlying physics in Next-token Prediction (NTP). We identified the law of information conservation within NTP and proposed the First Law of Information Capacity (IC-1), demonstrating that the essence of intelligence emergence in auto-regressive models is fundamentally a process of information transfer. We also introduced Landauer's Principle into NTP, formulating the Second Law of Information Capacity (IC-2), which establishes the relationship between auto-regressive model training and energy consumption. Additionally, we presented several corollaries, which hold practical significance for production practices. Finally, we validated the compatibility and complementarity of our findings with existing theories.

We present VCNAC, a variable channel neural audio codec. Our approach features a single encoder and decoder parametrization that enables native inference for different channel setups, from mono speech to cinematic 5.1 channel surround audio. Channel compatibility objectives ensure that multi-channel content maintains perceptual quality when decoded to fewer channels. The shared representation enables training of generative language models on a single set of codebooks while supporting inference-time scalability across modalities and channel configurations. Evaluation using objective spatial audio metrics and subjective listening tests demonstrates that our unified approach maintains high reconstruction quality across mono, stereo, and surround audio configurations.

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

Masked Diffusion Models (MDMs) offer flexible, non-autoregressive generation, but this freedom introduces a challenge: final output quality is highly sensitive to the decoding order. We are the first to formalize this issue, attributing the variability in output quality to the cumulative predictive uncertainty along a generative path. To quantify this uncertainty, we introduce Denoising Entropy, a computable metric that serves as an internal signal for evaluating generative process. Leveraging this metric, we propose two algorithms designed to optimize the decoding path: a post-hoc selection method and a real-time guidance strategy. Experiments demonstrate that our entropy-guided methods significantly improve generation quality, consistently boosting accuracy on challenging reasoning, planning, and code benchmarks. Our work establishes Denoising Entropy as a principled tool for understanding and controlling generation, effectively turning the uncertainty in MDMs from a liability into a key advantage for discovering high-quality solutions.

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

Deep learning based channel code designs have recently gained interest as an alternative to conventional coding algorithms, particularly for channels for which existing codes do not provide effective solutions. Communication over a feedback channel is one such problem, for which promising results have recently been obtained by employing various deep learning architectures. In this paper, we introduce a novel learning-aided code design for feedback channels, called generalized block attention feedback (GBAF) codes, which i) employs a modular architecture that can be implemented using different neural network architectures; ii) provides order-of-magnitude improvements in the probability of error compared to existing designs; and iii) can transmit at desired code rates.

Long-term training of large language models (LLMs) requires maintaining stable exploration to prevent the model from collapsing into sub-optimal behaviors. Entropy is crucial in this context, as it controls exploration and helps avoid premature convergence to sub-optimal solutions. However, existing reinforcement learning methods struggle to maintain an appropriate level of entropy, as the training process involves a mix of positive and negative samples, each affecting entropy in different ways across steps. To address this, we propose Entropy stablilization via Proportional-Integral Control (EntroPIC), a novel method that adaptively adjusts the influence of positive and negative samples by dynamically tuning their loss coefficients. This approach stabilizes entropy throughout training, ensuring efficient exploration and steady progress. We provide a comprehensive theoretical analysis for both on-policy and off-policy learning settings, demonstrating that EntroPIC is effective at controlling entropy in large-scale LLM training. Experimental results show that our method successfully maintains desired entropy levels, enabling stable and optimal RL training for LLMs.

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

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

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

Channel state information (CSI) is a fundamental component in both wireless communication and sensing systems, enabling critical functions such as radio resource optimization and environmental perception. In wireless sensing, data scarcity and packet loss hinder efficient model training, while in wireless communication, high-dimensional CSI matrices and short coherent times caused by high mobility present challenges in CSI estimation.To address these issues, we propose a unified framework named CSI-BERT2 for CSI prediction and classification tasks. Building on CSI-BERT, we introduce a two-stage training method that first uses a mask language model (MLM) to enable the model to learn general feature extraction from scarce datasets in an unsupervised manner, followed by fine-tuning for specific downstream tasks. Specifically, we extend MLM into a mask prediction model (MPM), which efficiently addresses the CSI prediction task. We also introduce an adaptive re-weighting layer (ARL) to enhance subcarrier representation and a multi-layer perceptron (MLP) based temporal embedding module to mitigate permutation invariance issues in time-series CSI data. This significantly improves the CSI classification performance of the original CSI-BERT model. Extensive experiments on both real-world collected and simulated datasets demonstrate that CSI-BERT2 achieves state-of-the-art performance across all tasks. Our results further show that CSI-BERT2 generalizes effectively across varying sampling rates and robustly handles discontinuous CSI sequences caused by packet loss-challenges that conventional methods fail to address.

Large language models (LLMs) have revolutionized the field of natural language processing, extending their strong capabilities into multi-modal domains. Thus, it is vital to define proper and diversified metrics for the evaluation of LLMs. In this paper, we introduce matrix entropy, a novel metric rooted in information theory and geometry principles to quantify the data compression proficiency in LLMs. It reflects the model's ability to extract relevant information and eliminate unnecessary elements, thereby providing insight into the language model's intrinsic capability. Specifically, we demonstrate its applicability in both single-modal (language) and multi-modal settings. For language models, our findings reveal that the matrix entropy of representations follows a scaling law type reduction when the model scales up, serving as a complement to the traditional loss scaling law. For the multi-modal setting, we also propose an evaluation method based on matrix entropy for assessing alignment quality and we find that modern large multi-modal models exhibit great alignment performance.

We introduce a differentiable estimator of range-partition entropy, a recent concept from computational geometry that enables algorithms to adapt to the "sortedness" of their input. While range-partition entropy provides strong guarantees in algorithm design, it has not yet been made accessible to deep learning. In this work, we (i) propose the first differentiable approximation of range-partition entropy, enabling its use as a trainable loss or regularizer; (ii) design EntropyNet, a neural module that restructures data into low-entropy forms to accelerate downstream instance-optimal algorithms; and (iii) extend this principle beyond geometry by applying entropy regularization directly to Transformer attention. Across tasks, we demonstrate that differentiable entropy improves efficiency without degrading correctness: in geometry, our method achieves up to 4.1times runtime speedups with negligible error (<0.2%); in deep learning, it induces structured attention patterns that yield 6% higher accuracy at 80% sparsity compared to L1 baselines. Our theoretical analysis provides approximation bounds for the estimator, and extensive ablations validate design choices. These results suggest that entropy-bounded computation is not only theoretically elegant but also a practical mechanism for adaptive learning, efficiency, and structured representation.

Autoregressive language models are trained by minimizing the cross-entropy of the model distribution Q relative to the data distribution P -- that is, minimizing the forward cross-entropy, which is equivalent to maximum likelihood estimation (MLE). We have observed that models trained in this way may "over-generalize", in the sense that they produce non-human-like text. Moreover, we believe that reverse cross-entropy, i.e., the cross-entropy of P relative to Q, is a better reflection of how a human would evaluate text generated by a model. Hence, we propose learning with MixCE, an objective that mixes the forward and reverse cross-entropies. We evaluate models trained with this objective on synthetic data settings (where P is known) and real data, and show that the resulting models yield better generated text without complex decoding strategies. Our code and models are publicly available at https://github.com/bloomberg/mixce-acl2023

Prior work using Masked Autoencoders (MAEs) typically relies on random patch masking based on the assumption that images have significant redundancies across different channels, allowing for the reconstruction of masked content using cross-channel correlations. However, this assumption does not hold in Multi-Channel Imaging (MCI), where channels may provide complementary information with minimal feature overlap. Thus, these MAEs primarily learn local structures within individual channels from patch reconstruction, failing to fully leverage cross-channel interactions and limiting their MCI effectiveness. In this paper, we present ChA-MAEViT, an MAE-based method that enhances feature learning across MCI channels via four key strategies: (1) dynamic channel-patch masking, which compels the model to reconstruct missing channels in addition to masked patches, thereby enhancing cross-channel dependencies and improving robustness to varying channel configurations; (2) memory tokens, which serve as long-term memory aids to promote information sharing across channels, addressing the challenges of reconstructing structurally diverse channels; (3) hybrid token fusion module, which merges fine-grained patch tokens with a global class token to capture richer representations; and (4) Channel-Aware Decoder, a lightweight decoder utilizes channel tokens to effectively reconstruct image patches. Experiments on satellite and microscopy datasets, CHAMMI, JUMP-CP, and So2Sat, show that ChA-MAEViT significantly outperforms state-of-the-art MCI-ViTs by 3.0-21.5%, highlighting the importance of cross-channel interactions in MCI. Our code is publicly available at https://github.com/chaudatascience/cha_mae_vit.

Multivariate time series forecasting tasks are usually conducted in a channel-dependent (CD) way since it can incorporate more variable-relevant information. However, it may also involve a lot of irrelevant variables, and this even leads to worse performance than the channel-independent (CI) strategy. This paper combines the strengths of both strategies and proposes the Deep Graph Clustering Transformer (DGCformer) for multivariate time series forecasting. Specifically, it first groups these relevant variables by a graph convolutional network integrated with an autoencoder, and a former-latter masked self-attention mechanism is then considered with the CD strategy being applied to each group of variables while the CI one for different groups. Extensive experimental results on eight datasets demonstrate the superiority of our method against state-of-the-art models, and our code will be publicly available upon acceptance.

Channel pruning approaches for convolutional neural networks (ConvNets) deactivate the channels, statically or dynamically, and require special implementation. In addition, channel squeezing in representative ConvNets is carried out via 1x1 convolutions which dominates a large portion of computations and network parameters. Given these challenges, we propose an effective multi-purpose module for dynamic channel sampling, namely Pick-or-Mix (PiX), which does not require special implementation. PiX divides a set of channels into subsets and then picks from them, where the picking decision is dynamically made per each pixel based on the input activations. We plug PiX into prominent ConvNet architectures and verify its multi-purpose utilities. After replacing 1x1 channel squeezing layers in ResNet with PiX, the network becomes 25% faster without losing accuracy. We show that PiX allows ConvNets to learn better data representation than widely adopted approaches to enhance networks' representation power (e.g., SE, CBAM, AFF, SKNet, and DWP). We also show that PiX achieves state-of-the-art performance on network downscaling and dynamic channel pruning applications.

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

Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance tradeoffs. We theoretically show that, under some conditions, estimators such as MINE exhibit variance that could grow exponentially with the true amount of underlying MI. We also empirically demonstrate that existing estimators fail to satisfy basic self-consistency properties of MI, such as data processing and additivity under independence. Based on a unified perspective of variational approaches, we develop a new estimator that focuses on variance reduction. Empirical results on standard benchmark tasks demonstrate that our proposed estimator exhibits improved bias-variance trade-offs on standard benchmark tasks.

Discrete video tokenization is essential for efficient autoregressive generative modeling due to the high dimensionality of video data. This work introduces a state-of-the-art discrete video tokenizer with two key contributions. First, we propose a novel Mamba-based encoder-decoder architecture that overcomes the limitations of previous sequencebased tokenizers. Second, we introduce a new quantization scheme, channel-split quantization, which significantly enhances the representational power of quantized latents while preserving the token count. Our model sets a new state-of-the-art, outperforming both causal 3D convolutionbased and Transformer-based approaches across multiple datasets. Experimental results further demonstrate its robustness as a tokenizer for autoregressive video generation.

Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability distribution. In this paper we propose goodness-of-fit statistics for the multivariate Student and multivariate Pearson type II distributions, based on the maximum entropy principle and a class of estimators for Renyi entropy based on nearest neighbour distances. We prove the L2-consistency of these statistics using results on the subadditivity of Euclidean functionals on nearest neighbour graphs, and investigate their rate of convergence and asymptotic distribution using Monte Carlo methods.

Network pruning reduces the computation costs of an over-parameterized network without performance damage. Prevailing pruning algorithms pre-define the width and depth of the pruned networks, and then transfer parameters from the unpruned network to pruned networks. To break the structure limitation of the pruned networks, we propose to apply neural architecture search to search directly for a network with flexible channel and layer sizes. The number of the channels/layers is learned by minimizing the loss of the pruned networks. The feature map of the pruned network is an aggregation of K feature map fragments (generated by K networks of different sizes), which are sampled based on the probability distribution.The loss can be back-propagated not only to the network weights, but also to the parameterized distribution to explicitly tune the size of the channels/layers. Specifically, we apply channel-wise interpolation to keep the feature map with different channel sizes aligned in the aggregation procedure. The maximum probability for the size in each distribution serves as the width and depth of the pruned network, whose parameters are learned by knowledge transfer, e.g., knowledge distillation, from the original networks. Experiments on CIFAR-10, CIFAR-100 and ImageNet demonstrate the effectiveness of our new perspective of network pruning compared to traditional network pruning algorithms. Various searching and knowledge transfer approaches are conducted to show the effectiveness of the two components. Code is at: https://github.com/D-X-Y/NAS-Projects.

The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability --- via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.

In this paper I apply newly-proposed information-theoretic principles to thermodynamic work extraction. I show that if it is possible to extract work deterministically from a physical system prepared in any one of a set of states, then those states must be distinguishable from one another. This result is formulated independently of scale and of particular dynamical laws; it also provides a novel connection between thermodynamics and information theory, established via the law of conservation of energy (rather than the second law of thermodynamics). Albeit compatible with these conclusions, existing thermodynamics approaches cannot provide a result of such generality, because they are scale-dependent (relying on ensembles or coarse-graining) or tied to particular dynamical laws. This paper thus provides a broader foundation for thermodynamics, with implications for the theory of von Neumann's universal constructor

This paper aims to extend the Structured Knowledge Accumulation (SKA) framework recently proposed by mahi2025ska. We introduce two core concepts: the Tensor Net function and the characteristic time property of neural learning. First, we reinterpret the learning rate as a time step in a continuous system. This transforms neural learning from discrete optimization into continuous-time evolution. We show that learning dynamics remain consistent when the product of learning rate and iteration steps stays constant. This reveals a time-invariant behavior and identifies an intrinsic timescale of the network. Second, we define the Tensor Net function as a measure that captures the relationship between decision probabilities, entropy gradients, and knowledge change. Additionally, we define its zero-crossing as the equilibrium state between decision probabilities and entropy gradients. We show that the convergence of entropy and knowledge flow provides a natural stopping condition, replacing arbitrary thresholds with an information-theoretic criterion. We also establish that SKA dynamics satisfy a variational principle based on the Euler-Lagrange equation. These findings extend SKA into a continuous and self-organizing learning model. The framework links computational learning with physical systems that evolve by natural laws. By understanding learning as a time-based process, we open new directions for building efficient, robust, and biologically-inspired AI systems.

This paper aims to overcome a major obstacle in scaling RL for reasoning with LLMs, namely the collapse of policy entropy. Such phenomenon is consistently observed across vast RL runs without entropy intervention, where the policy entropy dropped sharply at the early training stage, this diminished exploratory ability is always accompanied with the saturation of policy performance. In practice, we establish a transformation equation R=-a*e^H+b between entropy H and downstream performance R. This empirical law strongly indicates that, the policy performance is traded from policy entropy, thus bottlenecked by its exhaustion, and the ceiling is fully predictable H=0, R=-a+b. Our finding necessitates entropy management for continuous exploration toward scaling compute for RL. To this end, we investigate entropy dynamics both theoretically and empirically. Our derivation highlights that, the change in policy entropy is driven by the covariance between action probability and the change in logits, which is proportional to its advantage when using Policy Gradient-like algorithms. Empirical study shows that, the values of covariance term and entropy differences matched exactly, supporting the theoretical conclusion. Moreover, the covariance term stays mostly positive throughout training, further explaining why policy entropy would decrease monotonically. Through understanding the mechanism behind entropy dynamics, we motivate to control entropy by restricting the update of high-covariance tokens. Specifically, we propose two simple yet effective techniques, namely Clip-Cov and KL-Cov, which clip and apply KL penalty to tokens with high covariances respectively. Experiments show that these methods encourage exploration, thus helping policy escape entropy collapse and achieve better downstream performance.

Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. These systems generically involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the magnitude of the steady-state probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry and the strength of nonequilibrium transport of measure. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework that estimates the score of this density. We show that the score, together with the microscopic equations of motion, gives direct access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles, spatial regions, and degrees of freedom. To represent the score, we introduce a novel, spatially-local transformer-based network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of interacting active particles undergoing motility-induced phase separation (MIPS). We show that a single instance of our network trained on a system of 4096 particles at one packing fraction can generalize to other regions of the phase diagram, including systems with as many as 32768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.

We present an open-source Python implementation of an idealized high-order pseudo-spectral solver for the one-dimensional nonlinear Schr\"odinger equation (NLSE). The solver combines Fourier spectral spatial discretization with an adaptive eighth-order Dormand-Prince time integration scheme to achieve machine-precision conservation of mass and near-perfect preservation of momentum and energy for smooth solutions. The implementation accurately reproduces fundamental NLSE phenomena including soliton collisions with analytically predicted phase shifts, Akhmediev breather dynamics, and the development of modulation instability from noisy initial conditions. Four canonical test cases validate the numerical scheme: single soliton propagation, two-soliton elastic collision, breather evolution, and noise-seeded modulation instability. The solver employs a 2/3 dealiasing rule with exponential filtering to prevent aliasing errors from the cubic nonlinearity. Statistical analysis using Shannon, R\'enyi, and Tsallis entropies quantifies the spatio-temporal complexity of solutions, while phase space representations reveal the underlying coherence structure. The implementation prioritizes code transparency and educational accessibility over computational performance, providing a valuable pedagogical tool for exploring nonlinear wave dynamics. Complete source code, documentation, and example configurations are freely available, enabling reproducible computational experiments across diverse physical contexts where the NLSE governs wave evolution, including nonlinear optics, Bose-Einstein condensates, and ocean surface waves.

Entropy minimization (EM) trains the model to concentrate even more probability mass on its most confident outputs. We show that this simple objective alone, without any labeled data, can substantially improve large language models' (LLMs) performance on challenging math, physics, and coding tasks. We explore three approaches: (1) EM-FT minimizes token-level entropy similarly to instruction finetuning, but on unlabeled outputs drawn from the model; (2) EM-RL: reinforcement learning with negative entropy as the only reward to maximize; (3) EM-INF: inference-time logit adjustment to reduce entropy without any training data or parameter updates. On Qwen-7B, EM-RL, without any labeled data, achieves comparable or better performance than strong RL baselines such as GRPO and RLOO that are trained on 60K labeled examples. Furthermore, EM-INF enables Qwen-32B to match or exceed the performance of proprietary models like GPT-4o, Claude 3 Opus, and Gemini 1.5 Pro on the challenging SciCode benchmark, while being 3x more efficient than self-consistency and sequential refinement. Our findings reveal that many pretrained LLMs possess previously underappreciated reasoning capabilities that can be effectively elicited through entropy minimization alone, without any labeled data or even any parameter updates.

Energy-based models (EBMs) are known in the Machine Learning community for decades. Since the seminal works devoted to EBMs dating back to the noughties, there have been a lot of efficient methods which solve the generative modelling problem by means of energy potentials (unnormalized likelihood functions). In contrast, the realm of Optimal Transport (OT) and, in particular, neural OT solvers is much less explored and limited by few recent works (excluding WGAN-based approaches which utilize OT as a loss function and do not model OT maps themselves). In our work, we bridge the gap between EBMs and Entropy-regularized OT. We present a novel methodology which allows utilizing the recent developments and technical improvements of the former in order to enrich the latter. From the theoretical perspective, we prove generalization bounds for our technique. In practice, we validate its applicability in toy 2D and image domains. To showcase the scalability, we empower our method with a pre-trained StyleGAN and apply it to high-res AFHQ 512times 512 unpaired I2I translation. For simplicity, we choose simple short- and long-run EBMs as a backbone of our Energy-guided Entropic OT approach, leaving the application of more sophisticated EBMs for future research. Our code is available at: https://github.com/PetrMokrov/Energy-guided-Entropic-OT

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

Continual learning aims to emulate the human ability to continually accumulate knowledge over sequential tasks. The main challenge is to maintain performance on previously learned tasks after learning new tasks, i.e., to avoid catastrophic forgetting. We propose a Channel-wise Lightweight Reprogramming (CLR) approach that helps convolutional neural networks (CNNs) overcome catastrophic forgetting during continual learning. We show that a CNN model trained on an old task (or self-supervised proxy task) could be ``reprogrammed" to solve a new task by using our proposed lightweight (very cheap) reprogramming parameter. With the help of CLR, we have a better stability-plasticity trade-off to solve continual learning problems: To maintain stability and retain previous task ability, we use a common task-agnostic immutable part as the shared ``anchor" parameter set. We then add task-specific lightweight reprogramming parameters to reinterpret the outputs of the immutable parts, to enable plasticity and integrate new knowledge. To learn sequential tasks, we only train the lightweight reprogramming parameters to learn each new task. Reprogramming parameters are task-specific and exclusive to each task, which makes our method immune to catastrophic forgetting. To minimize the parameter requirement of reprogramming to learn new tasks, we make reprogramming lightweight by only adjusting essential kernels and learning channel-wise linear mappings from anchor parameters to task-specific domain knowledge. We show that, for general CNNs, the CLR parameter increase is less than 0.6\% for any new task. Our method outperforms 13 state-of-the-art continual learning baselines on a new challenging sequence of 53 image classification datasets. Code and data are available at https://github.com/gyhandy/Channel-wise-Lightweight-Reprogramming

Statistical channel models are instrumental to design and evaluate wireless communication systems. In the millimeter wave bands, such models become acutely challenging; they must capture the delay, directions, and path gains, for each link and with high resolution. This paper presents a general modeling methodology based on training generative neural networks from data. The proposed generative model consists of a two-stage structure that first predicts the state of each link (line-of-sight, non-line-of-sight, or outage), and subsequently feeds this state into a conditional variational autoencoder that generates the path losses, delays, and angles of arrival and departure for all its propagation paths. Importantly, minimal prior assumptions are made, enabling the model to capture complex relationships within the data. The methodology is demonstrated for 28GHz air-to-ground channels in an urban environment, with training datasets produced by means of ray tracing.

KV cache stores key and value states from previous tokens to avoid re-computation, yet it demands substantial storage space, especially for long sequences. Adaptive KV cache compression seeks to discern the saliency of tokens, preserving vital information while aggressively compressing those of less importance. However, previous methods of this approach exhibit significant performance degradation at high compression ratios due to inaccuracies in identifying salient tokens. In this paper, we present ZipCache, an accurate and efficient KV cache quantization method for LLMs. First, we construct a strong baseline for quantizing KV cache. Through the proposed channel-separable tokenwise quantization scheme, the memory overhead of quantization parameters are substantially reduced compared to fine-grained groupwise quantization. To enhance the compression ratio, we propose normalized attention score as an effective metric for identifying salient tokens by considering the lower triangle characteristics of the attention matrix. Moreover, we develop an efficient approximation method that decouples the saliency metric from full attention scores, enabling compatibility with fast attention implementations like FlashAttention. Extensive experiments demonstrate that ZipCache achieves superior compression ratios, fast generation speed and minimal performance losses compared with previous KV cache compression methods. For instance, when evaluating Mistral-7B model on GSM8k dataset, ZipCache is capable of compressing the KV cache by 4.98times, with only a 0.38% drop in accuracy. In terms of efficiency, ZipCache also showcases a 37.3% reduction in prefill-phase latency, a 56.9% reduction in decoding-phase latency, and a 19.8% reduction in GPU memory usage when evaluating LLaMA3-8B model with a input length of 4096.

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

Quantization effectively reduces the serving costs of Large Language Models (LLMs) by speeding up data movement through compressed parameters and enabling faster operations via integer arithmetic. However, activating integer arithmetic requires quantizing both weights and activations, which poses challenges due to the significant outliers in LLMs that increase quantization error. In this work, we investigate these outliers with an emphasis on their effect on layer-wise quantization error, then examine how smoothing and rotation transform the observed values. Our primary contributions include introducing a new metric to measure and visualize quantization difficulty based on channel magnitudes, as well as proposing a hybrid approach that applies channel-wise scaling before rotation, supported by a mathematical formulation of its benefits.

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al.(2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has mathcal{O}(H^3S^2A/varepsilon^2) sample complexity thus improving the varepsilon-dependence upon existing results, where S is a number of states, A is a number of actions, H is an episode length, and varepsilon is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order mathcal{O}(poly(S,A,H)/varepsilon). Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to mathcal{O}(H^2SA/varepsilon^2), yielding a statistical separation between maximum entropy exploration and reward-free exploration.

In this work, we develop a joint denoising and feedback strategy for channel state information in frequency division duplex systems. In such systems, the biggest challenge is the overhead incurred when the mobile terminal has to send the downlink channel state information or corresponding partial information to the base station, where the complete estimates can subsequently be restored. To this end, we propose a novel learning-based framework for denoising and compression of channel estimates. Unlike existing studies, we extend a recently proposed approach and show that based solely on noisy uplink data available at the base station, it is possible to learn an autoencoder neural network that generalizes to downlink data. Subsequently, half of the autoencoder can be offloaded to the mobile terminals to generate channel feedback there as efficiently as possible, without any training effort at the terminals or corresponding transfer of training data. Numerical simulations demonstrate the excellent performance of the proposed method.

Zero-shot quantization (ZSQ) enables neural network compression without training data, which is crucial in restricted data access environments. However, existing ZSQ methods suffer from significant activation loss in low-bit environments owing to their coarse-grained scaling strategy. To address this issue, we propose GranQ, a novel ZSQ approach that leverages layer-channel awareness to minimize the quantization error. Unlike conventional layer- or channel-wise quantization, GranQ dynamically adjusts quantization granularity by considering both layer- and channel-level activation distributions. This enables fine-grained quantization while minimizing activation distortion. Additionally, we introduce vectorized activation quantization, which enables efficient parallel computation and reduces computational overhead while preserving accuracy. GranQ achieves superior performance compared with those of state-of-the-art ZSQ methods that employ quantization-aware training. With these findings, we anticipate that GranQ will inspire novel research directions beyond conventional ZSQ approaches focused on data generation and model training.

Doubly-stochastic matrices (DSM) are increasingly utilized in structure-preserving deep architectures -- such as Optimal Transport layers and Sinkhorn-based attention -- to enforce numerical stability and probabilistic interpretability. In this work, we identify a critical spectral degradation phenomenon inherent to these constraints, termed the Homogeneity Trap. We demonstrate that the maximum-entropy bias, typical of Sinkhorn-based projections, drives the mixing operator towards the uniform barycenter, thereby suppressing the subdominant singular value σ_2 and filtering out high-frequency feature components. We derive a spectral bound linking σ_2 to the network's effective depth, showing that high-entropy constraints restrict feature transformation to a shallow effective receptive field. Furthermore, we formally demonstrate that Layer Normalization fails to mitigate this collapse in noise-dominated regimes; specifically, when spectral filtering degrades the Signal-to-Noise Ratio (SNR) below a critical threshold, geometric structure is irreversibly lost to noise-induced orthogonal collapse. Our findings highlight a fundamental trade-off between entropic stability and spectral expressivity in DSM-constrained networks.

The mechanisms behind the success of multi-view self-supervised learning (MVSSL) are not yet fully understood. Contrastive MVSSL methods have been studied through the lens of InfoNCE, a lower bound of the Mutual Information (MI). However, the relation between other MVSSL methods and MI remains unclear. We consider a different lower bound on the MI consisting of an entropy and a reconstruction term (ER), and analyze the main MVSSL families through its lens. Through this ER bound, we show that clustering-based methods such as DeepCluster and SwAV maximize the MI. We also re-interpret the mechanisms of distillation-based approaches such as BYOL and DINO, showing that they explicitly maximize the reconstruction term and implicitly encourage a stable entropy, and we confirm this empirically. We show that replacing the objectives of common MVSSL methods with this ER bound achieves competitive performance, while making them stable when training with smaller batch sizes or smaller exponential moving average (EMA) coefficients. Github repo: https://github.com/apple/ml-entropy-reconstruction.

As large language models continue to scale, their growing computational and storage demands pose significant challenges for real-world deployment. In this work, we investigate redundancy within Transformer-based models and propose an entropy-based pruning strategy to enhance efficiency while maintaining performance. Empirical analysis reveals that the entropy of hidden representations decreases in the early blocks but progressively increases across most subsequent blocks. This trend suggests that entropy serves as a more effective measure of information richness within computation blocks. Unlike cosine similarity, which primarily captures geometric relationships, entropy directly quantifies uncertainty and information content, making it a more reliable criterion for pruning. Extensive experiments demonstrate that our entropy-based pruning approach surpasses cosine similarity-based methods in reducing model size while preserving accuracy, offering a promising direction for efficient model deployment.

The resurgence of convolutional neural networks (CNNs) in visual recognition tasks, exemplified by ConvNeXt, has demonstrated their capability to rival transformer-based architectures through advanced training methodologies and ViT-inspired design principles. However, both CNNs and transformers exhibit a simplicity bias, favoring straightforward features over complex structural representations. Furthermore, modern CNNs often integrate MLP-like blocks akin to those in transformers, but these blocks suffer from significant information redundancies, necessitating high expansion ratios to sustain competitive performance. To address these limitations, we propose SpaRTAN, a lightweight architectural design that enhances spatial and channel-wise information processing. SpaRTAN employs kernels with varying receptive fields, controlled by kernel size and dilation factor, to capture discriminative multi-order spatial features effectively. A wave-based channel aggregation module further modulates and reinforces pixel interactions, mitigating channel-wise redundancies. Combining the two modules, the proposed network can efficiently gather and dynamically contextualize discriminative features. Experimental results in ImageNet and COCO demonstrate that SpaRTAN achieves remarkable parameter efficiency while maintaining competitive performance. In particular, on the ImageNet-1k benchmark, SpaRTAN achieves 77. 7% accuracy with only 3.8M parameters and approximately 1.0 GFLOPs, demonstrating its ability to deliver strong performance through an efficient design. On the COCO benchmark, it achieves 50.0% AP, surpassing the previous benchmark by 1.2% with only 21.5M parameters. The code is publicly available at [https://github.com/henry-pay/SpaRTAN].

Large language models (LLMs) have demonstrated remarkable success across diverse artificial intelligence tasks, driven by scaling laws that correlate model size and training data with performance improvements. However, this scaling paradigm incurs substantial memory overhead, creating significant challenges for both training and inference. While existing research has primarily addressed parameter and optimizer state memory reduction, activation memory-particularly from feed-forward networks (FFNs)-has become the critical bottleneck, especially when FlashAttention is implemented. In this work, we conduct a detailed memory profiling of LLMs and identify FFN activations as the predominant source to activation memory overhead. Motivated by this, we introduce Mixture-of-Channels (MoC), a novel FFN architecture that selectively activates only the Top-K most relevant channels per token determined by SwiGLU's native gating mechanism. MoC substantially reduces activation memory during pre-training and improves inference efficiency by reducing memory access through partial weight loading into GPU SRAM. Extensive experiments validate that MoC delivers significant memory savings and throughput gains while maintaining competitive model performance.

Human motion recognition (HMR) based on wireless sensing is a low-cost technique for scene understanding. Current HMR systems adopt support vector machines (SVMs) and convolutional neural networks (CNNs) to classify radar signals. However, whether a deeper learning model could improve the system performance is currently not known. On the other hand, training a machine learning model requires a large dataset, but data gathering from experiment is cost-expensive and time-consuming. Although wireless channel models can be adopted for dataset generation, current channel models are mostly designed for communication rather than sensing. To address the above problems, this paper proposes a deep spectrogram network (DSN) by leveraging the residual mapping technique to enhance the HMR performance. Furthermore, a primitive based autoregressive hybrid (PBAH) channel model is developed, which facilitates efficient training and testing dataset generation for HMR in a virtual environment. Experimental results demonstrate that the proposed PBAH channel model matches the actual experimental data very well and the proposed DSN achieves significantly smaller recognition error than that of CNN.

Learned Image Compression (LIC) has explored various architectures, such as Convolutional Neural Networks (CNNs) and transformers, in modeling image content distributions in order to achieve compression effectiveness. However, achieving high rate-distortion performance while maintaining low computational complexity (\ie, parameters, FLOPs, and latency) remains challenging. In this paper, we propose a hybrid Convolution and State Space Models (SSMs) based image compression framework, termed CMamba, to achieve superior rate-distortion performance with low computational complexity. Specifically, CMamba introduces two key components: a Content-Adaptive SSM (CA-SSM) module and a Context-Aware Entropy (CAE) module. First, we observed that SSMs excel in modeling overall content but tend to lose high-frequency details. In contrast, CNNs are proficient at capturing local details. Motivated by this, we propose the CA-SSM module that can dynamically fuse global content extracted by SSM blocks and local details captured by CNN blocks in both encoding and decoding stages. As a result, important image content is well preserved during compression. Second, our proposed CAE module is designed to reduce spatial and channel redundancies in latent representations after encoding. Specifically, our CAE leverages SSMs to parameterize the spatial content in latent representations. Benefiting from SSMs, CAE significantly improves spatial compression efficiency while reducing spatial content redundancies. Moreover, along the channel dimension, CAE reduces inter-channel redundancies of latent representations via an autoregressive manner, which can fully exploit prior knowledge from previous channels without sacrificing efficiency. Experimental results demonstrate that CMamba achieves superior rate-distortion performance.

The framework of dominant learned video compression methods is usually composed of motion prediction modules as well as motion vector and residual image compression modules, suffering from its complex structure and error propagation problem. Approaches have been proposed to reduce the complexity by replacing motion prediction modules with implicit flow networks. Error propagation aware training strategy is also proposed to alleviate incremental reconstruction errors from previously decoded frames. Although these methods have brought some improvement, little attention has been paid to the framework itself. Inspired by the success of learned image compression through simplifying the framework with a single deep neural network, it is natural to expect a better performance in video compression via a simple yet appropriate framework. Therefore, we propose a framework to directly compress raw-pixel frames (rather than residual images), where no extra motion prediction module is required. Instead, an entropy model is used to estimate the spatiotemporal redundancy in a latent space rather than pixel level, which significantly reduces the complexity of the framework. Specifically, the whole framework is a compression module, consisting of a unified auto-encoder which produces identically distributed latents for all frames, and a spatiotemporal entropy estimation model to minimize the entropy of these latents. Experiments showed that the proposed method outperforms state-of-the-art (SOTA) performance under the metric of multiscale structural similarity (MS-SSIM) and achieves competitive results under the metric of PSNR.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

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

Research into 6G networks has been initiated to support a variety of critical artificial intelligence (AI) assisted applications such as autonomous driving. In such applications, AI-based decisions should be performed in a real-time manner. These decisions include resource allocation, localization, channel estimation, etc. Considering the black-box nature of existing AI-based models, it is highly challenging to understand and trust the decision-making behavior of such models. Therefore, explaining the logic behind those models through explainable AI (XAI) techniques is essential for their employment in critical applications. This manuscript proposes a novel XAI-based channel estimation (XAI-CHEST) scheme that provides detailed reasonable interpretability of the deep learning (DL) models that are employed in doubly-selective channel estimation. The aim of the proposed XAI-CHEST scheme is to identify the relevant model inputs by inducing high noise on the irrelevant ones. As a result, the behavior of the studied DL-based channel estimators can be further analyzed and evaluated based on the generated interpretations. Simulation results show that the proposed XAI-CHEST scheme provides valid interpretations of the DL-based channel estimators for different scenarios.

Graph Neural Networks (GNNs) are limited in their propagation operators. In many cases, these operators often contain non-negative elements only and are shared across channels, limiting the expressiveness of GNNs. Moreover, some GNNs suffer from over-smoothing, limiting their depth. On the other hand, Convolutional Neural Networks (CNNs) can learn diverse propagation filters, and phenomena like over-smoothing are typically not apparent in CNNs. In this paper, we bridge these gaps by incorporating trainable channel-wise weighting factors omega to learn and mix multiple smoothing and sharpening propagation operators at each layer. Our generic method is called omegaGNN, and is easy to implement. We study two variants: omegaGCN and omegaGAT. For omegaGCN, we theoretically analyse its behaviour and the impact of omega on the obtained node features. Our experiments confirm these findings, demonstrating and explaining how both variants do not over-smooth. Additionally, we experiment with 15 real-world datasets on node- and graph-classification tasks, where our omegaGCN and omegaGAT perform on par with state-of-the-art methods.

This paper addresses the problem of formalizing and quantifying the concept of "intensional inheritance" between two concepts. We begin by conceiving the intensional inheritance of W from F as the amount of information the proposition "x is F " provides about the proposition "x is W. To flesh this out, we consider concepts F and W defined by sets of properties left{F_{1}, F_{2}, ldots, F_{n}right} and left{W_{1}, W_{2}, ldots, W_{m}right} with associated degrees left{d_{1}, d_{2}, ldots, d_{n}right} and left{e_{1}, e_{2}, ldots, e_{m}right}, respectively, where the properties may overlap. We then derive formulas for the intensional inheritance using both Shannon information theory and algorithmic information theory, incorporating interaction information among properties. We examine a special case where all properties are mutually exclusive and calculate the intensional inheritance in this case in both frameworks. We also derive expressions for P(W mid F) based on the mutual information formula. Finally we consider the relationship between intensional inheritance and conventional set-theoretic "extensional" inheritance, concluding that in our information-theoretic framework, extensional inheritance emerges as a special case of intensional inheritance.

Deploying LLMs raises two coupled challenges: (1) monitoring - estimating where a model underperforms as traffic and domains drift - and (2) improvement - prioritizing data acquisition to close the largest performance gaps. We test whether an inference-time signal can estimate slice-level accuracy under domain shift. For each response, we compute an output-entropy profile from final-layer next-token probabilities (from top-k logprobs) and summarize it with eleven statistics. A lightweight classifier predicts instance correctness, and averaging predicted probabilities yields a domain-level accuracy estimate. We evaluate on ten STEM reasoning benchmarks with exhaustive train/test compositions (k in {1,2,3,4}; all "10 choose k" combinations), across nine LLMs from six families (3B-20B). Estimates often track held-out benchmark accuracy, and several models show near-monotonic ordering of domains. Output-entropy profiles are thus an accessible signal for scalable monitoring and for targeting data acquisition.