Daily Papers

In the era of large language models, creative writing quality lacks a computable theoretical anchor. The dominant approaches are rubric scoring -- decomposing holistic aesthetic judgment into sub-scores -- and RLHF preference signals -- replacing quality with group votes. Both bypass the statistical structure of the text itself. This paper provides an information-theoretic foundation to fill this gap. We propose 'calibrated surprise' as the information-theoretic essence of excellent creative writing. This judgment matches reading intuition and covers its opposite. This literary judgment admits a precise mathematical formulation. Under full-dimensional constraints Y, feasible writing choices are forced into an extremely narrow space. The rare survivors are, from the unconstrained perspective, exactly the least predictable choices. Both are measured precisely by Shannon mutual information I(X;Y) = H(X) - H(X|Y) -- 'calibrated' corresponds to H(X|Y) approaching 0; 'surprising' corresponds to H(X) going high. The subtraction structure of the formula naturally separates 'well-grounded surprise' from 'pure noise'. We use token-level logprobs from Qwen1.5-7B as an operational proxy for the ideal reader's probability distribution. Across 20 pairs (12 Chinese / 8 English) of high-quality vs. systematically degraded literary passages, 20/20 pairs support the core prediction: high-quality passages have systematically higher I(X;Y) than their degraded versions.

We develop a data-driven information-theoretic framework for sharp partial identification of causal effects under unmeasured confounding. Existing approaches often rely on restrictive assumptions, such as bounded or discrete outcomes; require external inputs (for example, instrumental variables, proxies, or user-specified sensitivity parameters); necessitate full structural causal model specifications; or focus solely on population-level averages while neglecting covariate-conditional effects. We overcome all four limitations simultaneously by establishing novel information-theoretic, data-driven divergence bounds. Our key theoretical contribution shows that the f-divergence between the observational distribution P(Y | A = a, X = x) and the interventional distribution P(Y | do(A = a), X = x) is upper bounded by a function of the propensity score alone. This result enables sharp partial identification of conditional causal effects directly from observational data, without requiring external sensitivity parameters, auxiliary variables, full structural specifications, or outcome boundedness assumptions. For practical implementation, we develop a semiparametric estimator satisfying Neyman orthogonality (Chernozhukov et al., 2018), which ensures root-n consistent inference even when nuisance functions are estimated via flexible machine learning methods. Simulation studies and real-world data applications, implemented in the GitHub repository (https://github.com/yonghanjung/Information-Theretic-Bounds), demonstrate that our framework provides tight and valid causal bounds across a wide range of data-generating processes.

Loss Given Default (LGD) modeling faces a fundamental data quality constraint: 90% of available training data consists of proxy estimates based on pre-distress balance sheets rather than actual recovery outcomes from completed bankruptcy proceedings. We demonstrate that this mixture-contaminated training structure causes systematic failure of recursive partitioning methods, with Random Forest achieving negative r-squared (-0.664, worse than predicting the mean) on held-out test data. Information-theoretic approaches based on Shannon entropy and mutual information provide superior generalization, achieving r-squared of 0.191 and RMSE of 0.284 on 1,218 corporate bankruptcies (1980-2023). Analysis reveals that leverage-based features contain 1.510 bits of mutual information while size effects contribute only 0.086 bits, contradicting regulatory assumptions about scale-dependent recovery. These results establish practical guidance for financial institutions deploying LGD models under Basel III requirements when representative outcome data is unavailable at sufficient scale. The findings generalize to medical outcomes research, climate forecasting, and technology reliability-domains where extended observation periods create unavoidable mixture structure in training data.

The design of safety-critical agents based on large language models (LLMs) requires more than simple prompt engineering. This paper presents a comprehensive information-theoretic analysis of how rule encodings in system prompts influence attention mechanisms and compliance behaviour. We demonstrate that rule formats with low syntactic entropy and highly concentrated anchors reduce attention entropy and improve pointer fidelity, but reveal a fundamental trade-off between anchor redundancy and attention entropy that previous work failed to recognize. Through formal analysis of multiple attention architectures including causal, bidirectional, local sparse, kernelized, and cross-attention mechanisms, we establish bounds on pointer fidelity and show how anchor placement strategies must account for competing fidelity and entropy objectives. Combining these insights with a dynamic rule verification architecture, we provide a formal proof that hot reloading of verified rule sets increases the asymptotic probability of compliant outputs. These findings underscore the necessity of principled anchor design and dual enforcement mechanisms to protect LLM-based agents against prompt injection attacks while maintaining compliance in evolving domains.

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 neural networks (DNNs) exhibit an exceptional capacity for generalization in practical applications. This work aims to capture the effect and benefits of depth for supervised learning via information-theoretic generalization bounds. We first derive two hierarchical bounds on the generalization error in terms of the Kullback-Leibler (KL) divergence or the 1-Wasserstein distance between the train and test distributions of the network internal representations. The KL divergence bound shrinks as the layer index increases, while the Wasserstein bound implies the existence of a layer that serves as a generalization funnel, which attains a minimal 1-Wasserstein distance. Analytic expressions for both bounds are derived under the setting of binary Gaussian classification with linear DNNs. To quantify the contraction of the relevant information measures when moving deeper into the network, we analyze the strong data processing inequality (SDPI) coefficient between consecutive layers of three regularized DNN models: Dropout, DropConnect, and Gaussian noise injection. This enables refining our generalization bounds to capture the contraction as a function of the network architecture parameters. Specializing our results to DNNs with a finite parameter space and the Gibbs algorithm reveals that deeper yet narrower network architectures generalize better in those examples, although how broadly this statement applies remains a question.

In order to develop machine learning and deep learning models that take into account the guidelines and principles of trustworthy AI, a novel information theoretic trustworthy AI framework is introduced. A unified approach to "privacy-preserving interpretable and transferable learning" is considered for studying and optimizing the tradeoffs between privacy, interpretability, and transferability aspects. A variational membership-mapping Bayesian model is used for the analytical approximations of the defined information theoretic measures for privacy-leakage, interpretability, and transferability. The approach consists of approximating the information theoretic measures via maximizing a lower-bound using variational optimization. The study presents a unified information theoretic approach to study different aspects of trustworthy AI in a rigorous analytical manner. The approach is demonstrated through numerous experiments on benchmark datasets and a real-world biomedical application concerned with the detection of mental stress on individuals using heart rate variability analysis.

We study image segmentation from an information-theoretic perspective, proposing a novel adversarial method that performs unsupervised segmentation by partitioning images into maximally independent sets. More specifically, we group image pixels into foreground and background, with the goal of minimizing predictability of one set from the other. An easily computed loss drives a greedy search process to maximize inpainting error over these partitions. Our method does not involve training deep networks, is computationally cheap, class-agnostic, and even applicable in isolation to a single unlabeled image. Experiments demonstrate that it achieves a new state-of-the-art in unsupervised segmentation quality, while being substantially faster and more general than competing approaches.

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.

Soft prompt tuning achieves superior performances across a wide range of few-shot tasks. However, the performances of prompt tuning can be highly sensitive to the initialization of the prompts. We also empirically observe that conventional prompt tuning methods cannot encode and learn sufficient task-relevant information from prompt tokens. In this work, we develop an information-theoretic framework that formulates soft prompt tuning as maximizing mutual information between prompts and other model parameters (or encoded representations). This novel view helps us to develop a more efficient, accurate and robust soft prompt tuning method InfoPrompt. With this framework, we develop two novel mutual information based loss functions, to (i) discover proper prompt initialization for the downstream tasks and learn sufficient task-relevant information from prompt tokens and (ii) encourage the output representation from the pretrained language model to be more aware of the task-relevant information captured in the learnt prompt. Extensive experiments validate that InfoPrompt can significantly accelerate the convergence of the prompt tuning and outperform traditional prompt tuning methods. Finally, we provide a formal theoretical result for showing to show that gradient descent type algorithm can be used to train our mutual information loss.

Large language model (LLM) tokenizers act as structured compressors: by mapping text to discrete token sequences, they determine token count (and thus compute and context usage) and the statistical structure seen by downstream models. Despite their central role in LLM pipelines, the link between tokenization, compression efficiency and induced structure is not well understood. We empirically demonstrate that tokenizer training scale redistributes entropy: as training data grows, the token stream becomes more diverse in aggregate (higher unigram entropy) yet markedly more predictable in-context (lower higher-order conditional entropies), indicating that tokenization absorbs substantial short-range regularity although these gains degrade under train-test domain mismatch. To ground these observations, we first benchmark i) pretrained GPT-family tokenizers as black-box compressors across various domains, and ii) learned tokenizers across configurations spanning vocabulary size, training scale, and domain. Next, we study tokenization as a transform for universal compression and introduce a compression-aware BPE variant. Finally, we adopt a channel lens and introduce capacity-utilization metrics to analyze tokenizer behaviour and outline implications for downstream modeling. Put together, our results expose various trade-offs between compression, induced structure, and robustness under domain shift, and motivate principled, compression-aware tokenizer design.

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

Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to best quantify predictive uncertainty. In this work, we revisit core concepts to propose a framework for information-theoretic measures of predictive uncertainty. Our proposed framework categorizes predictive uncertainty measures according to two factors: (I) The predicting model (II) The approximation of the true predictive distribution. Examining all possible combinations of these two factors, we derive a set of predictive uncertainty measures that includes both known and newly introduced ones. We extensively evaluate these measures across a broad set of tasks, identifying conditions under which certain measures excel. Our findings show the importance of aligning the choice of uncertainty measure with the predicting model on in-distribution (ID) data, the limitations of epistemic uncertainty measures for out-of-distribution (OOD) data, and that the disentanglement between measures varies substantially between ID and OOD data. Together, these insights provide a more comprehensive understanding of predictive uncertainty measures, revealing their implicit assumptions and relationships.

Integrating and processing information from various sources or modalities are critical for obtaining a comprehensive and accurate perception of the real world in autonomous systems and cyber-physical systems. Drawing inspiration from neuroscience, we develop the Information-Theoretic Hierarchical Perception (ITHP) model, which utilizes the concept of information bottleneck. Different from most traditional fusion models that incorporate all modalities identically in neural networks, our model designates a prime modality and regards the remaining modalities as detectors in the information pathway, serving to distill the flow of information. Our proposed perception model focuses on constructing an effective and compact information flow by achieving a balance between the minimization of mutual information between the latent state and the input modal state, and the maximization of mutual information between the latent states and the remaining modal states. This approach leads to compact latent state representations that retain relevant information while minimizing redundancy, thereby substantially enhancing the performance of multimodal representation learning. Experimental evaluations on the MUStARD, CMU-MOSI, and CMU-MOSEI datasets demonstrate that our model consistently distills crucial information in multimodal learning scenarios, outperforming state-of-the-art benchmarks. Remarkably, on the CMU-MOSI dataset, ITHP surpasses human-level performance in the multimodal sentiment binary classification task across all evaluation metrics (i.e., Binary Accuracy, F1 Score, Mean Absolute Error, and Pearson Correlation).

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

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.

In nonstationary bandit learning problems, the decision-maker must continually gather information and adapt their action selection as the latent state of the environment evolves. In each time period, some latent optimal action maximizes expected reward under the environment state. We view the optimal action sequence as a stochastic process, and take an information-theoretic approach to analyze attainable performance. We bound limiting per-period regret in terms of the entropy rate of the optimal action process. The bound applies to a wide array of problems studied in the literature and reflects the problem's information structure through its information-ratio.

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

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

In this work, we present an information-theoretic framework that formulates cross-lingual language model pre-training as maximizing mutual information between multilingual-multi-granularity texts. The unified view helps us to better understand the existing methods for learning cross-lingual representations. More importantly, inspired by the framework, we propose a new pre-training task based on contrastive learning. Specifically, we regard a bilingual sentence pair as two views of the same meaning and encourage their encoded representations to be more similar than the negative examples. By leveraging both monolingual and parallel corpora, we jointly train the pretext tasks to improve the cross-lingual transferability of pre-trained models. Experimental results on several benchmarks show that our approach achieves considerably better performance. The code and pre-trained models are available at https://aka.ms/infoxlm.

Direct Preference Optimization (DPO) has become a standard technique for aligning language models with human preferences in a supervised manner. Despite its empirical success, the theoretical justification behind its log-ratio reward parameterization remains incomplete. In this work, we address this gap by utilizing the Differential Information Distribution (DID): a distribution over token sequences that captures the information gained during policy updates. First, we show that when preference labels encode the differential information required to transform a reference policy into a target policy, the log-ratio reward in DPO emerges as the uniquely optimal form for learning the target policy via preference optimization. This result naturally yields a closed-form expression for the optimal sampling distribution over rejected responses. Second, we find that the condition for preferences to encode differential information is fundamentally linked to an implicit assumption regarding log-margin ordered policies-an inductive bias widely used in preference optimization yet previously unrecognized. Finally, by analyzing the entropy of the DID, we characterize how learning low-entropy differential information reinforces the policy distribution, while high-entropy differential information induces a smoothing effect, which explains the log-likelihood displacement phenomenon. We validate our theoretical findings in synthetic experiments and extend them to real-world instruction-following datasets. Our results suggest that learning high-entropy differential information is crucial for general instruction-following, while learning low-entropy differential information benefits knowledge-intensive question answering. Overall, our work presents a unifying perspective on the DPO objective, the structure of preference data, and resulting policy behaviors through the lens of differential information.

Modern semantic search and retrieval-augmented generation (RAG) systems rely predominantly on in-memory approximate nearest neighbor (ANN) indexes over high-precision floating-point vectors, resulting in escalating operational cost and inherent trade-offs between latency, throughput, and retrieval accuracy. This paper analyzes the architectural limitations of the dominant "HNSW + float32 + cosine similarity" stack and evaluates existing cost-reduction strategies, including storage disaggregation and lossy vector quantization, which inevitably sacrifice either performance or accuracy. We introduce and empirically evaluate an alternative information-theoretic architecture based on maximally informative binarization (MIB), efficient bitwise distance metrics, and an information-theoretic scoring (ITS) mechanism. Unlike conventional ANN systems, this approach enables exhaustive search over compact binary representations, allowing deterministic retrieval and eliminating accuracy degradation under high query concurrency. Using the MAIR benchmark across 14 datasets and 10,038 queries, we compare this architecture against Elasticsearch, Pinecone, PGVector, and Qdrant. Results demonstrate retrieval quality comparable to full-precision systems, while achieving substantially lower latency and maintaining constant throughput at high request rates. We show that this architectural shift enables a truly serverless, cost-per-query deployment model, challenging the necessity of large in-memory ANN indexes for high-quality semantic search.

Designing learnable information-theoretic objectives for robot exploration remains challenging. Such objectives aim to guide exploration toward data that reduces uncertainty in model parameters, yet it is often unclear what information the collected data can actually reveal. Although reinforcement learning (RL) can optimize a given objective, constructing objectives that reflect parametric learnability is difficult in high-dimensional robotic systems. Many parameter directions are weakly observable or unidentifiable, and even when identifiable directions are selected, omitted directions can still influence exploration and distort information measures. To address this challenge, we propose Quasi-Optimal Experimental Design (Q{\footnotesize OED}), an adaptive information objective grounded in optimal experimental design. Q{\footnotesize OED} (i) performs eigenspace analysis of the Fisher information matrix to identify an observable subspace and select identifiable parameter directions, and (ii) modifies the exploration objective to emphasize these directions while suppressing nuisance effects from non-critical parameters. Under bounded nuisance influence and limited coupling between critical and nuisance directions, Q{\footnotesize OED} provides a constant-factor approximation to the ideal information objective that explores all parameters. We evaluate Q{\footnotesize OED} on simulated and real-world navigation and manipulation tasks, where identifiable-direction selection and nuisance suppression yield performance improvements of 35.23{\percent} and 21.98{\percent}, respectively. When integrated as an exploration objective in model-based policy optimization, Q{\footnotesize OED} further improves policy performance over established RL baselines.

Large-scale land enclosure for speculative mega-development constitutes a non-equilibrium spatial process whose velocity, topology, and irreversibility remain poorly quantified. We study the Pantai Indah Kapuk 2 (PIK2) coastal mega-development north of Jakarta, Indonesia, using eight years (2017--2024) of Sentinel-2 land-use/land-cover (LULC) data at 10-meter resolution. The landscape is projected onto a Marxian probability simplex partitioning terrestrial pixels into Commons, Agrarian, and Capital fractions. Fisher-Rao (FR) geodesic distances on this simplex identify a transformation pulse of 0.405~rad/yr during 2019--2020, coinciding with major construction activity. Absorbing Markov chain analysis yields expected absorption times into the built environment of 46.0~years for cropland and 38.1~years for tree cover, with a pooled built-area self-retention rate of 96.4%. Percolation analysis reveals that a giant connected component containing 89--95% of all built pixels persists at occupation probabilities p in [0.096, 0.162], far below the random percolation threshold p_c approx 0.593, indicating planned rather than stochastic spatial growth. The box-counting fractal dimension of the urban boundary increases from d_f = 1.316 to 1.397, consistent with increasingly irregular frontier expansion. These results suggest that information-geometric and statistical-mechanical tools can characterize the kinematic and topological signatures of capitalist spatial accumulation with quantitative precision.

Retrieval-augmented generation (RAG) relies on retrieved context to guide large language models (LLM), yet treats retrieval as a weak heuristic rather than verifiable evidence -- leading to unsupported answers, hallucinations, and reliance on spurious context. We introduce a novel training framework that treats the RAG pipeline as an interactive proof system by adapting the Merlin-Arthur (M/A) protocol: Arthur (the generator LLM) trains on questions with unknown context provenance and Merlin gives helpful evidence, while Morgana injects adversarial, misleading context. Both use an XAI method to identify and modify evidence most influential to Arthur. This trains Arthur to (1) answer when evidence supports the answer, (2) reject when evidence is insufficient, and (3) rely on the context spans that truly ground the answer. We further introduce a verification framework that disentangles explanation fidelity from model predictive errors, and introduce the Explained Information Fraction (EIF), which normalizes M/A mutual-information guarantees. Across three RAG datasets and multiple LLM families and sizes, M/A training makes LLMs more grounded in evidence, increases information theoretic measures (soundness, completeness) and reject behavior with less hallucinations, without manually annotated unanswerable samples. Finally, the retriever also improves recall and MRR via automatically generated M/A hard positives and negatives. While high accuracy does not guarantee entropy flow from context to answer, our EIF results show that autonomous interactive-proof-style supervision enables RAG systems that treat retrieved documents as verifiable evidence. % rather than suggestions.

Fine-tuned large language models (LLMs) often exhibit overconfidence, particularly when trained on small datasets, resulting in poor calibration and inaccurate uncertainty estimates. Evidential Deep Learning (EDL), an uncertainty-aware approach, enables uncertainty estimation in a single forward pass, making it a promising method for calibrating fine-tuned LLMs. However, despite its computational efficiency, EDL is prone to overfitting, as its training objective can result in overly concentrated probability distributions. To mitigate this, we propose regularizing EDL by incorporating an information bottleneck (IB). Our approach IB-EDL suppresses spurious information in the evidence generated by the model and encourages truly predictive information to influence both the predictions and uncertainty estimates. Extensive experiments across various fine-tuned LLMs and tasks demonstrate that IB-EDL outperforms both existing EDL and non-EDL approaches. By improving the trustworthiness of LLMs, IB-EDL facilitates their broader adoption in domains requiring high levels of confidence calibration. Code is available at https://github.com/sandylaker/ib-edl.

Multimodal large language models (MLLMs) have shown promising capabilities but struggle under distribution shifts, where evaluation data differ from instruction tuning distributions. Although previous works have provided empirical evaluations, we argue that establishing a formal framework that can characterize and quantify the risk of MLLMs is necessary to ensure the safe and reliable application of MLLMs in the real world. By taking an information-theoretic perspective, we propose the first theoretical framework that enables the quantification of the maximum risk of MLLMs under distribution shifts. Central to our framework is the introduction of Effective Mutual Information (EMI), a principled metric that quantifies the relevance between input queries and model responses. We derive an upper bound for the EMI difference between in-distribution (ID) and out-of-distribution (OOD) data, connecting it to visual and textual distributional discrepancies. Extensive experiments on real benchmark datasets, spanning 61 shift scenarios empirically validate our theoretical insights.

Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty. Predictive uncertainty is commonly measured by the entropy of the Bayesian model average (BMA) predictive distribution. Yet, the properness of this current measure of predictive uncertainty was recently questioned. We provide new insights regarding those limitations. Our analyses show that the current measure erroneously assumes that the BMA predictive distribution is equivalent to the predictive distribution of the true model that generated the dataset. Consequently, we introduce a theoretically grounded measure to overcome these limitations. We experimentally verify the benefits of our introduced measure of predictive uncertainty. We find that our introduced measure behaves more reasonably in controlled synthetic tasks. Moreover, our evaluations on ImageNet demonstrate that our introduced measure is advantageous in real-world applications utilizing predictive uncertainty.

Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the uncertainty of model outputs has received relatively little attention. We adapt the popular Shapley value framework to explain various types of predictive uncertainty, quantifying each feature's contribution to the conditional entropy of individual model outputs. We consider games with modified characteristic functions and find deep connections between the resulting Shapley values and fundamental quantities from information theory and conditional independence testing. We outline inference procedures for finite sample error rate control with provable guarantees, and implement efficient algorithms that perform well in a range of experiments on real and simulated data. Our method has applications to covariate shift detection, active learning, feature selection, and active feature-value acquisition.

Diffusion models have emerged as a powerful paradigm for modern generative modeling, demonstrating strong potential for large language models (LLMs). Unlike conventional autoregressive (AR) models that generate tokens sequentially, diffusion models enable parallel token sampling, leading to faster generation and eliminating left-to-right generation constraints. Despite their empirical success, the theoretical understanding of diffusion model approaches remains underdeveloped. In this work, we develop convergence guarantees for diffusion language models from an information-theoretic perspective. Our analysis demonstrates that the sampling error, measured by the Kullback-Leibler (KL) divergence, decays inversely with the number of iterations T and scales linearly with the mutual information between tokens in the target text sequence. In particular, we establish matching upper and lower bounds, up to some constant factor, to demonstrate the tightness of our convergence analysis. These results offer novel theoretical insights into the practical effectiveness of diffusion language models.

The transition from stateless language model inference to persistent, multi session autonomous agents has revealed memory to be a primary architectural bottleneck in the deployment of production grade agentic systems. Existing methodologies largely depend on hybrid semantic graph architectures, which impose substantial computational overhead during both ingestion and retrieval. These systems typically require large language model mediated entity extraction, explicit graph schema maintenance, and multi query retrieval pipelines. This paper introduces Memanto, a universal memory layer for agentic artificial intelligence that challenges the prevailing assumption that knowledge graph complexity is necessary to achieve high fidelity agent memory. Memanto integrates a typed semantic memory schema comprising thirteen predefined memory categories, an automated conflict resolution mechanism, and temporal versioning. These components are enabled by Moorcheh's Information Theoretic Search engine, a no indexing semantic database that provides deterministic retrieval within sub ninety millisecond latency while eliminating ingestion delay. Through systematic benchmarking on the LongMemEval and LoCoMo evaluation suites, Memanto achieves state of the art accuracy scores of 89.8 percent and 87.1 percent respectively. These results surpass all evaluated hybrid graph and vector based systems while requiring only a single retrieval query, incurring no ingestion cost, and maintaining substantially lower operational complexity. A five stage progressive ablation study is presented to quantify the contribution of each architectural component, followed by a discussion of the implications for scalable deployment of agentic memory systems.

Model-based reinforcement learning (MBRL) improves sample efficiency by optimizing policies inside imagined rollouts, but long-horizon planning degrades when model errors compound and imagined trajectories drift off the training manifold. We introduce GIRL (Generative Imagination Reinforcement Learning), a latent world-model framework that addresses this failure mode with two key components. First, a cross-modal grounding signal derived from a frozen foundation model (DINOv2) anchors the latent transition prior to a semantically consistent embedding space, penalizing inconsistent or implausible predictions. Second, an uncertainty-adaptive trust-region bottleneck interprets the KL regularizer as the Lagrange multiplier of a constrained optimization problem, restricting imagination drift within a learned region calibrated by Expected Information Gain and a Relative Performance Loss signal. We re-derive a value-gap bound using the Performance Difference Lemma and Integral Probability Metrics, yielding a bound that remains informative as the discount factor approaches one and connects the objective to real-environment regret. Experiments across three benchmark suites, including DeepMind Control, Adroit Hand Manipulation, and Meta-World with visual distractors, show that GIRL reduces latent rollout drift by 38 to 61 percent across tasks relative to DreamerV3, improves asymptotic return, and requires fewer environment interactions on long-horizon tasks. GIRL also outperforms TD-MPC2 on sparse-reward and high-contact settings under standard evaluation metrics. A distilled-prior variant reduces inference overhead and improves computational efficiency relative to the full model.

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

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.

We consider the problem of designing an artificial agent capable of interacting with humans in collaborative dialogue to produce creative, engaging narratives. In this task, the goal is to establish universe details, and to collaborate on an interesting story in that universe, through a series of natural dialogue exchanges. Our model can augment any probabilistic conversational agent by allowing it to reason about universe information established and what potential next utterances might reveal. Ideally, with each utterance, agents would reveal just enough information to add specificity and reduce ambiguity without limiting the conversation. We empirically show that our model allows control over the rate at which the agent reveals information and that doing so significantly improves accuracy in predicting the next line of dialogues from movies. We close with a case-study with four professional theatre performers, who preferred interactions with our model-augmented agent over an unaugmented agent.

The recent rise of Large Reasoning Models (LRMs) has significantly improved multi-step reasoning performance, but often at the cost of generating excessively long reasoning chains. This paper revisits the efficiency of such reasoning processes through an information-theoretic lens, revealing a fundamental trade-off between reasoning length and semantic efficiency. We propose two metrics, InfoBias and InfoGain, to quantify divergence from ideal reasoning paths and stepwise information contribution, respectively. Empirical analyses show that longer reasoning chains tend to exhibit higher information bias and diminishing information gain, especially for incorrect answers. Motivated by these findings, we introduce an entropy-based Adaptive Think strategy that dynamically halts reasoning once confidence is sufficiently high, improving efficiency while maintaining competitive accuracy. Compared to the Vanilla Think approach (default mode), our strategy yields a 1.10% improvement in average accuracy and a 50.80% reduction in token usage on QwQ-32B across six benchmark tasks spanning diverse reasoning types and difficulty levels, demonstrating superior efficiency and reasoning performance. These results underscore the promise of entropy-based methods for enhancing both accuracy and cost-effiiciency in large language model deployment.

Large language models increasingly rely on long chains of thought to improve accuracy, yet such gains come with substantial inference-time costs. We revisit token-efficient post-training and argue that existing sequence-level reward-shaping methods offer limited control over how reasoning effort is allocated across tokens. To bridge the gap, we propose IAPO, an information-theoretic post-training framework that assigns token-wise advantages based on each token's conditional mutual information (MI) with the final answer. This yields an explicit, principled mechanism for identifying informative reasoning steps and suppressing low-utility exploration. We provide a theoretical analysis showing that our IAPO can induce monotonic reductions in reasoning verbosity without harming correctness. Empirically, IAPO consistently improves reasoning accuracy while reducing reasoning length by up to 36%, outperforming existing token-efficient RL methods across various reasoning datasets. Extensive empirical evaluations demonstrate that information-aware advantage shaping is a powerful and general direction for token-efficient post-training. The code is available at https://github.com/YinhanHe123/IAPO.

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

Behavior Cloning (BC) is a widely adopted visual imitation learning method in robot manipulation. Current BC approaches often enhance generalization by leveraging large datasets and incorporating additional visual and textual modalities to capture more diverse information. However, these methods overlook whether the learned representations contain redundant information and lack a solid theoretical foundation to guide the learning process. To address these limitations, we adopt an information-theoretic perspective and introduce mutual information to quantify and mitigate redundancy in latent representations. Building on this, we incorporate the Information Bottleneck (IB) principle into BC, which extends the idea of reducing redundancy by providing a structured framework for compressing irrelevant information while preserving task-relevant features. This work presents the first comprehensive study on redundancy in latent representations across various methods, backbones, and experimental settings, while extending the generalizability of the IB to BC. Extensive experiments and analyses on the CortexBench and LIBERO benchmarks demonstrate significant performance improvements with IB, underscoring the importance of reducing input data redundancy and highlighting its practical value for more practical applications. Project Page: https://baishuanghao.github.io/BC-IB.github.io.

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

Machine learning interatomic potentials (MLIPs) balance high accuracy and lower costs compared to density functional theory calculations, but their performance often depends on the size and diversity of training datasets. Large datasets improve model accuracy and generalization but are computationally expensive to produce and train on, while smaller datasets risk discarding rare but important atomic environments and compromising MLIP accuracy/reliability. Here, we develop an information-theoretical framework to quantify the efficiency of dataset compression methods and propose an algorithm that maximizes this efficiency. By framing atomistic dataset compression as an instance of the minimum set cover (MSC) problem over atom-centered environments, our method identifies the smallest subset of structures that contains as much information as possible from the original dataset while pruning redundant information. The approach is extensively demonstrated on the GAP-20 and TM23 datasets, and validated on 64 varied datasets from the ColabFit repository. Across all cases, MSC consistently retains outliers, preserves dataset diversity, and reproduces the long-tail distributions of forces even at high compression rates, outperforming other subsampling methods. Furthermore, MLIPs trained on MSC-compressed datasets exhibit reduced error for out-of-distribution data even in low-data regimes. We explain these results using an outlier analysis and show that such quantitative conclusions could not be achieved with conventional dimensionality reduction methods. The algorithm is implemented in the open-source QUESTS package and can be used for several tasks in atomistic modeling, from data subsampling, outlier detection, and training improved MLIPs at a lower cost.

Zero-Input AI (ZIA) introduces a novel framework for human-computer interaction by enabling proactive intent prediction without explicit user commands. It integrates gaze tracking, bio-signals (EEG, heart rate), and contextual data (time, location, usage history) into a multi-modal model for real-time inference, targeting <100 ms latency. The proposed architecture employs a transformer-based model with cross-modal attention, variational Bayesian inference for uncertainty estimation, and reinforcement learning for adaptive optimization. To support deployment on edge devices (CPUs, TPUs, NPUs), ZIA utilizes quantization, weight pruning, and linear attention to reduce complexity from quadratic to linear with sequence length. Theoretical analysis establishes an information-theoretic bound on prediction error and demonstrates how multi-modal fusion improves accuracy over single-modal approaches. Expected performance suggests 85-90% accuracy with EEG integration and 60-100 ms inference latency. ZIA provides a scalable, privacy-preserving framework for accessibility, healthcare, and consumer applications, advancing AI toward anticipatory intelligence.

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.

Tree search has become as a representative framework for test-time reasoning with large language models (LLMs), exemplified by methods such as Tree-of-Thought and Monte Carlo Tree Search that explore multiple reasoning paths. However, it remains difficult to provide instant and reliable quantitative assessments of intermediate reasoning step quality, and extensive path exploration is computationally costly. To address this, we propose Mutual Information Tree Search (MITS), a novel framework that guides reasoning with information-theoretic principles. MITS introduces an effective scoring function based on pointwise mutual information (PMI), which enables step-wise evaluation of reasoning paths and search tree expansion via beam search without expensive look-ahead simulations, achieving superior reasoning performances while maintaining computational efficiency. The framework is complemented by an entropy-based dynamic sampling strategy that adaptively allocates computational resources to uncertain reasoning steps where exploration is most beneficial. For final prediction, MITS employs a weighted voting scheme that combines PMI scores with prediction consensus. Through comprehensive experiments on diverse reasoning benchmarks, MITS consistently surpasses baseline methods, establishing a principled and efficient framework for LLM reasoning.

LLMs often exhibit Aha moments during reasoning, such as apparent self-correction following tokens like "Wait," yet their underlying mechanisms remain unclear. We introduce an information-theoretic framework that decomposes reasoning into procedural information and epistemic verbalization - the explicit externalization of uncertainty that supports downstream control actions. We show that purely procedural reasoning can become informationally stagnant, whereas epistemic verbalization enables continued information acquisition and is critical for achieving information sufficiency. Empirical results demonstrate that strong reasoning performance is driven by uncertainty externalization rather than specific surface tokens. Our framework unifies prior findings on Aha moments and post-training experiments, and offers insights for future reasoning model design.

Large Language Models (LLMs) have shown impressive performance in complex reasoning tasks through Chain-of-Thought (CoT) reasoning, allowing models to break down problems into manageable sub-tasks. However, existing CoT evaluation techniques either require annotated CoT data or fall short in accurately assessing intermediate reasoning steps, leading to high rates of false positives. In this paper, we formalize CoT reasoning in LLMs through an information-theoretic lens. Specifically, our framework quantifies the `information gain' at each reasoning step, enabling the identification of failure modes in LLMs without the need for expensive annotated datasets. We demonstrate the efficacy of our approach through extensive experiments on toy and GSM-8K data, where it significantly outperforms existing outcome-based methods by providing more accurate insights into model performance on individual tasks.

State-of-the-art summarization systems can generate highly fluent summaries. These summaries, however, may contain factual inconsistencies and/or information not present in the source. Hence, an important component of assessing the quality of summaries is to determine whether there is information consistency between the source and the summary. Existing approaches are typically based on lexical matching or representation-based methods. In this work, we introduce an alternative scheme based on standard information-theoretic measures in which the information present in the source and summary is directly compared. We propose a Multiple-choice Question Answering and Generation framework, MQAG, which approximates the information consistency by computing the expected KL-divergence between summary and source answer distributions over automatically generated multiple-choice questions. This approach exploits multiple-choice answer probabilities, as predicted answer distributions can be easily compared. We conduct experiments on four summary evaluation datasets: QAG-CNNDM/XSum, XSum-Faithfulness, Podcast Assessment, and SummEval. Experiments show that MQAG (using models trained on RACE) outperforms existing evaluation methods on the majority of tasks.

Multimodal video captioning condenses dense footage into a structured format of keyframes and natural language. By creating a cohesive multimodal summary, this approach anchors generative AI in rich semantic evidence and serves as a lightweight proxy for high-efficiency retrieval. However, traditional metrics like BLEU or ROUGE fail to quantify information coverage across disparate modalities, such as comparing a paragraph of text to a sequence of keyframes. To address this, we propose the Video Summary Information Loss (ViSIL) score, an information-theoretic framework that quantifies the video information not captured by a summary via vision-language model (VLM) inference. By measuring the information loss, ViSIL is a unified metric that enables direct comparison across multimodal summary formats despite their structural discrepancies. Our results demonstrate that ViSIL scores show a statistically significant correlation with both human and VLM performance on Video Question Answering (VQA) tasks. ViSIL also enables summary selection to optimize the trade-off between information loss and processing speed, establishing a Pareto-optimal frontier that outperforms text summaries by 7% in VQA accuracy without increasing processing load.

Representational spaces learned via language modeling are fundamental to Natural Language Processing (NLP), however there has been limited understanding regarding how and when during training various types of linguistic information emerge and interact. Leveraging a novel information theoretic probing suite, which enables direct comparisons of not just task performance, but their representational subspaces, we analyze nine tasks covering syntax, semantics and reasoning, across 2M pre-training steps and five seeds. We identify critical learning phases across tasks and time, during which subspaces emerge, share information, and later disentangle to specialize. Across these phases, syntactic knowledge is acquired rapidly after 0.5% of full training. Continued performance improvements primarily stem from the acquisition of open-domain knowledge, while semantics and reasoning tasks benefit from later boosts to long-range contextualization and higher specialization. Measuring cross-task similarity further reveals that linguistically related tasks share information throughout training, and do so more during the critical phase of learning than before or after. Our findings have implications for model interpretability, multi-task learning, and learning from limited data.

This work presents an information-theoretic perspective to group fairness trade-offs in federated learning (FL) with respect to sensitive attributes, such as gender, race, etc. Existing works often focus on either global fairness (overall disparity of the model across all clients) or local fairness (disparity of the model at each client), without always considering their trade-offs. There is a lack of understanding regarding the interplay between global and local fairness in FL, particularly under data heterogeneity, and if and when one implies the other. To address this gap, we leverage a body of work in information theory called partial information decomposition (PID), which first identifies three sources of unfairness in FL, namely, Unique Disparity, Redundant Disparity, and Masked Disparity. We demonstrate how these three disparities contribute to global and local fairness using canonical examples. This decomposition helps us derive fundamental limits on the trade-off between global and local fairness, highlighting where they agree or disagree. We introduce the Accuracy and Global-Local Fairness Optimality Problem (AGLFOP), a convex optimization that defines the theoretical limits of accuracy and fairness trade-offs, identifying the best possible performance any FL strategy can attain given a dataset and client distribution. We also present experimental results on synthetic datasets and the ADULT dataset to support our theoretical findings.

Text-to-image diffusion models have made significant progress in generating naturalistic images from textual inputs, and demonstrate the capacity to learn and represent complex visual-semantic relationships. While these diffusion models have achieved remarkable success, the underlying mechanisms driving their performance are not yet fully accounted for, with many unanswered questions surrounding what they learn, how they represent visual-semantic relationships, and why they sometimes fail to generalize. Our work presents Diffusion Partial Information Decomposition (DiffusionPID), a novel technique that applies information-theoretic principles to decompose the input text prompt into its elementary components, enabling a detailed examination of how individual tokens and their interactions shape the generated image. We introduce a formal approach to analyze the uniqueness, redundancy, and synergy terms by applying PID to the denoising model at both the image and pixel level. This approach enables us to characterize how individual tokens and their interactions affect the model output. We first present a fine-grained analysis of characteristics utilized by the model to uniquely localize specific concepts, we then apply our approach in bias analysis and show it can recover gender and ethnicity biases. Finally, we use our method to visually characterize word ambiguity and similarity from the model's perspective and illustrate the efficacy of our method for prompt intervention. Our results show that PID is a potent tool for evaluating and diagnosing text-to-image diffusion models.

It is often advantageous to train models on a subset of the available train examples, because the examples are of variable quality or because one would like to train with fewer examples, without sacrificing performance. We present Gradient Information Optimization (GIO), a scalable, task-agnostic approach to this data selection problem that requires only a small set of (unlabeled) examples representing a target distribution. GIO begins from a natural, information-theoretic objective that is intractable in practice. Our contribution is in showing that it can be made highly scalable through a simple relaxation of the objective and a highly efficient implementation. In experiments with machine translation, spelling correction, and image recognition, we show that GIO delivers outstanding results with very small train sets. These findings are robust to different representation models and hyperparameters for GIO itself. GIO is task- and domain-agnostic and can be applied out-of-the-box to new datasets and domains.

Reasoning capability has advanced rapidly in large language models (LLMs), leading to an increasing size of key-value (KV) cache in both prefilling and decoding stages. Existing KV cache compression methods mainly rely on attention weights to estimate token importance. While attention effectively captures contextual relevance, it overlooks complementary information-theoretic signals related to predictive uncertainty and token informativeness. In this paper, we revisit token importance from a forward-looking perspective and introduce Forward Influence, a metric that measures how compressed tokens affect future contexts. Our analysis reveals that tokens selected by attention scores mainly influence nearby contexts, whereas tokens associated with high predictive uncertainty exhibit substantially stronger influence on distant future contexts. Based on the observation, we propose InfoKV, an entropy-aware KV cache compression framework that incorporates information-theoretic signals. It combines token-level predictive uncertainty with layer-wise representation evolution and integrates the resulting entropy scores with attention scores during reasoning. Experiments on long-context reasoning benchmarks with Llama-3.1, Llama-3.2, and DeepSeek-R1 demonstrate that InfoKV consistently outperforms existing attention-based KV compression methods in both long prefilling and decoding scenarios.

Current multimodal large language models (MLLMs) face a critical challenge in modality alignment, often exhibiting a bias towards textual information at the expense of other modalities like vision. This paper conducts a systematic information-theoretic analysis of the widely used cross-entropy loss in MLLMs, uncovering its implicit alignment objective. Our theoretical investigation reveals that this implicit objective has inherent limitations, leading to a degradation of cross-modal alignment as text sequence length increases, thereby hindering effective multimodal information fusion. To overcome these drawbacks, we propose Vision-Text Alignment (VISTA), a novel approach guided by our theoretical insights. VISTA introduces an explicit alignment objective designed to maximize cross-modal mutual information, preventing the degradation of visual alignment. Notably, VISTA enhances the visual understanding capabilities of existing MLLMs without requiring any additional trainable modules or extra training data, making it both efficient and practical. Our method significantly outperforms baseline models across more than a dozen benchmark datasets, including VQAv2, MMStar, and MME, paving the way for new directions in MLLM modal alignment research.

Dynamic feature selection, where we sequentially query features to make accurate predictions with a minimal budget, is a promising paradigm to reduce feature acquisition costs and provide transparency into a model's predictions. The problem is challenging, however, as it requires both predicting with arbitrary feature sets and learning a policy to identify valuable selections. Here, we take an information-theoretic perspective and prioritize features based on their mutual information with the response variable. The main challenge is implementing this policy, and we design a new approach that estimates the mutual information in a discriminative rather than generative fashion. Building on our approach, we then introduce several further improvements: allowing variable feature budgets across samples, enabling non-uniform feature costs, incorporating prior information, and exploring modern architectures to handle partial inputs. Our experiments show that our method provides consistent gains over recent methods across a variety of datasets.

Large language models (LLMs) have demonstrated significant advancements in reasoning and code generation. However, efficiently creating new benchmarks to evaluate these capabilities remains a challenge. Traditional benchmark creation relies on manual human effort, a process that is both expensive and time-consuming. Furthermore, existing benchmarks often contaminate LLM training data, necessitating novel and diverse benchmarks to accurately assess their genuine capabilities. This work introduces InfoSynth, a novel framework for automatically generating and evaluating reasoning benchmarks guided by information-theoretic principles. We propose metrics based on KL-divergence and entropy to quantify benchmark novelty and diversity without relying on costly model evaluations. Building on this framework, we develop an end-to-end pipeline that synthesizes robust Python coding problems from seed datasets using genetic algorithms and iterative code feedback. Our method generates accurate test cases and solutions to new problems 97% of the time, and the synthesized benchmarks consistently exhibit higher novelty and diversity compared to their seed datasets. Moreover, our algorithm provides a method for controlling the novelty/diversity and difficulty of generated problems. InfoSynth offers a scalable, self-verifying pipeline for constructing high-quality, novel and diverse benchmarks for LLMs. Project Page: https://ishirgarg.github.io/infosynth_web/

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.

Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and cannot integrate new data points. To address these drawbacks, we propose InfoOT, an information-theoretic extension of optimal transport that maximizes the mutual information between domains while minimizing geometric distances. The resulting objective can still be formulated as a (generalized) optimal transport problem, and can be efficiently solved by projected gradient descent. This formulation yields a new projection method that is robust to outliers and generalizes to unseen samples. Empirically, InfoOT improves the quality of alignments across benchmarks in domain adaptation, cross-domain retrieval, and single-cell alignment.

Unified multimodal models (UMMs) were designed to combine the reasoning ability of large language models (LLMs) with the generation capability of vision models. In practice, however, this synergy remains elusive: UMMs fail to transfer LLM-like reasoning to image synthesis and exhibit divergent response behaviors. We term this phenomenon pseudo-unification. Diagnosing its internal causes is important, but existing probing methods either lack model-internal insight or ignore prompt-response dependencies. To address these limitations, we propose an information-theoretic probing framework that jointly analyzes how UMMs encode inputs and generate outputs. Applied to ten representative UMMs, our framework reveals that pseudo-unification stems from a dual divergence: (i) Modality-Asymmetric Encoding, where vision and language follow different entropy trajectories, and (ii) Pattern-Split Response, where text generation exhibits high-entropy creativity while image synthesis enforces low-entropy fidelity. Only models that unify both sides (e.g., via contextual prediction) achieve more genuine unification, enabling stronger reasoning-based text-to-image generation even with fewer parameters. Our work provides the first model-internal probing of unification, demonstrating that real multimodal synergy requires consistency in information flow, not just shared parameters.

Role-playing models (RPMs) are widely used in real-world applications but underperform when deployed in the wild. This degradation can be attributed to distribution shifts, including user, character, and dialogue compositional shifts. Existing methods like LLM-as-a-judge fall short in providing a fine-grained diagnosis of how these shifts affect RPM generalization, and thus there lack formal frameworks to characterize RPM generalization behaviors. To bridge these gaps, we introduce an information-theoretic metric, named reasoning-based effective mutual information difference (R-EMID), to measure RPM performance degradation in an interpretable way. We also derive an upper bound on R-EMID to predict the worst-case generalization performance of RPMs and theoretically reveal how various shifts contribute to the RPM performance degradation. Moreover, we propose a co-evolving reinforcement learning framework to adaptively model the connection among user, character, and dialogue context and thus enhance the estimation of dialogue response generation probability, which is critical for calculating R-EMID. Finally, we evaluate the generalization performance of various RPMs using R-EMID, finding that user shift poses the highest risk among all shifts and reinforcement learning is the most effective approach for enhancing RPM generalization.

In Vision-Language Models (VLMs), high-resolution images produce a large number of visual tokens, resulting in high computational costs and KV-cache overhead during inference. To address this problem, we propose an Extreme Token Compression (ETC) framework that minimizes task loss when reducing the number of input tokens based on the principle of variational information distillation. Specifically, from an information-theoretic perspective, we show that minimizing task loss requires the compact representation to preserve the instruction-aware sufficient statistic of the task-relevant visual information for prediction. In practice, ETC leverages text-to-image cross-attention to weight the original visual features to approximate the latent instruction-aware predictive statistic. Moreover, ETC introduces a variational information distillation, enabling the compact representation to preserve the essential information to recover this predictive statistic. Experiments on LLaVA-1.5-7B and Qwen3-VL-2B show that ETC remains effective even under single-token compression, substantially reducing KV-cache overhead while retaining strong task performance.

Large Language Models (LLMs) are vulnerable to jailbreaksx2013methods to elicit harmful or generally impermissible outputs. Safety measures are developed and assessed on their effectiveness at defending against jailbreak attacks, indicating a belief that safety is equivalent to robustness. We assert that current defense mechanisms, such as output filters and alignment fine-tuning, are, and will remain, fundamentally insufficient for ensuring model safety. These defenses fail to address risks arising from dual-intent queries and the ability to composite innocuous outputs to achieve harmful goals. To address this critical gap, we introduce an information-theoretic threat model called inferential adversaries who exploit impermissible information leakage from model outputs to achieve malicious goals. We distinguish these from commonly studied security adversaries who only seek to force victim models to generate specific impermissible outputs. We demonstrate the feasibility of automating inferential adversaries through question decomposition and response aggregation. To provide safety guarantees, we define an information censorship criterion for censorship mechanisms, bounding the leakage of impermissible information. We propose a defense mechanism which ensures this bound and reveal an intrinsic safety-utility trade-off. Our work provides the first theoretically grounded understanding of the requirements for releasing safe LLMs and the utility costs involved.

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.

We present a complete theoretical characterization of Latent Posterior Factors (LPF), a principled framework for aggregating multiple heterogeneous evidence items in probabilistic prediction tasks. Multi-evidence reasoning arises pervasively in high-stakes domains including healthcare diagnosis, financial risk assessment, legal case analysis, and regulatory compliance, yet existing approaches either lack formal guarantees or fail to handle multi-evidence scenarios architecturally. LPF encodes each evidence item into a Gaussian latent posterior via a variational autoencoder, converting posteriors to soft factors through Monte Carlo marginalization, and aggregating factors via exact Sum-Product Network inference (LPF-SPN) or a learned neural aggregator (LPF-Learned). We prove seven formal guarantees spanning the key desiderata for trustworthy AI: Calibration Preservation (ECE <= epsilon + C/sqrt(K_eff)); Monte Carlo Error decaying as O(1/sqrt(M)); a non-vacuous PAC-Bayes bound with train-test gap of 0.0085 at N=4200; operation within 1.12x of the information-theoretic lower bound; graceful degradation as O(epsilon*delta*sqrt(K)) under corruption, maintaining 88% performance with half of evidence adversarially replaced; O(1/sqrt(K)) calibration decay with R^2=0.849; and exact epistemic-aleatoric uncertainty decomposition with error below 0.002%. All theorems are empirically validated on controlled datasets spanning up to 4,200 training examples. Our theoretical framework establishes LPF as a foundation for trustworthy multi-evidence AI in safety-critical applications.

Large reasoning models (LRMs) have demonstrated impressive capabilities in complex problem-solving, yet their internal reasoning mechanisms remain poorly understood. In this paper, we investigate the reasoning trajectories of LRMs from an information-theoretic perspective. By tracking how mutual information (MI) between intermediate representations and the correct answer evolves during LRM reasoning, we observe an interesting MI peaks phenomenon: the MI at specific generative steps exhibits a sudden and significant increase during LRM's reasoning process. We theoretically analyze such phenomenon and show that as MI increases, the probability of model's prediction error decreases. Furthermore, these MI peaks often correspond to tokens expressing reflection or transition, such as ``Hmm'', ``Wait'' and ``Therefore,'' which we term as the thinking tokens. We then demonstrate that these thinking tokens are crucial for LRM's reasoning performance, while other tokens has minimal impacts. Building on these analyses, we propose two simple yet effective methods to improve LRM's reasoning performance, by delicately leveraging these thinking tokens. Overall, our work provides novel insights into the reasoning mechanisms of LRMs and offers practical ways to improve their reasoning capabilities. The code is available at https://github.com/ChnQ/MI-Peaks.

Explaining deep learning models operating on time series data is crucial in various applications of interest which require interpretable and transparent insights from time series signals. In this work, we investigate this problem from an information theoretic perspective and show that most existing measures of explainability may suffer from trivial solutions and distributional shift issues. To address these issues, we introduce a simple yet practical objective function for time series explainable learning. The design of the objective function builds upon the principle of information bottleneck (IB), and modifies the IB objective function to avoid trivial solutions and distributional shift issues. We further present TimeX++, a novel explanation framework that leverages a parametric network to produce explanation-embedded instances that are both in-distributed and label-preserving. We evaluate TimeX++ on both synthetic and real-world datasets comparing its performance against leading baselines, and validate its practical efficacy through case studies in a real-world environmental application. Quantitative and qualitative evaluations show that TimeX++ outperforms baselines across all datasets, demonstrating a substantial improvement in explanation quality for time series data. The source code is available at https://github.com/zichuan-liu/TimeXplusplus.

How can deep neural networks encode information that corresponds to words in human speech into raw acoustic data? This paper proposes two neural network architectures for modeling unsupervised lexical learning from raw acoustic inputs, ciwGAN (Categorical InfoWaveGAN) and fiwGAN (Featural InfoWaveGAN), that combine a Deep Convolutional GAN architecture for audio data (WaveGAN; arXiv:1705.07904) with an information theoretic extension of GAN -- InfoGAN (arXiv:1606.03657), and propose a new latent space structure that can model featural learning simultaneously with a higher level classification and allows for a very low-dimension vector representation of lexical items. Lexical learning is modeled as emergent from an architecture that forces a deep neural network to output data such that unique information is retrievable from its acoustic outputs. The networks trained on lexical items from TIMIT learn to encode unique information corresponding to lexical items in the form of categorical variables in their latent space. By manipulating these variables, the network outputs specific lexical items. The network occasionally outputs innovative lexical items that violate training data, but are linguistically interpretable and highly informative for cognitive modeling and neural network interpretability. Innovative outputs suggest that phonetic and phonological representations learned by the network can be productively recombined and directly paralleled to productivity in human speech: a fiwGAN network trained on `suit' and `dark' outputs innovative `start', even though it never saw `start' or even a [st] sequence in the training data. We also argue that setting latent featural codes to values well beyond training range results in almost categorical generation of prototypical lexical items and reveals underlying values of each latent code.

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

By reducing resolution, coarse-grained models greatly accelerate molecular simulations, unlocking access to long-timescale phenomena, though at the expense of microscopic information. Recovering this fine-grained detail is essential for tasks that depend on atomistic accuracy, making backmapping a central challenge in molecular modeling. We introduce split-flows, a novel flow-based approach that reinterprets backmapping as a continuous-time measure transport across resolutions. Unlike existing generative strategies, split-flows establish a direct probabilistic link between resolutions, enabling expressive conditional sampling of atomistic structures and -- for the first time -- a tractable route to computing mapping entropies, an information-theoretic measure of the irreducible detail lost in coarse-graining. We demonstrate these capabilities on diverse molecular systems, including chignolin, a lipid bilayer, and alanine dipeptide, highlighting split-flows as a principled framework for accurate backmapping and systematic evaluation of coarse-grained models.

We expose a critical limitation in current approaches to machine unlearning in language models: despite the apparent success of unlearning algorithms, information about the forgotten data remains linearly decodable from internal representations. To systematically assess this discrepancy, we introduce an interpretable, information-theoretic framework for auditing unlearning using Partial Information Decomposition (PID). By comparing model representations before and after unlearning, we decompose the mutual information with the forgotten data into distinct components, formalizing the notions of unlearned and residual knowledge. Our analysis reveals that redundant information, shared across both models, constitutes residual knowledge that persists post-unlearning and correlates with susceptibility to known adversarial reconstruction attacks. Leveraging these insights, we propose a representation-based risk score that can guide abstention on sensitive inputs at inference time, providing a practical mechanism to mitigate privacy leakage. Our work introduces a principled, representation-level audit for unlearning, offering theoretical insight and actionable tools for safer deployment of language models.

We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former comes from the lack of knowledge about the ground truth (such as about facts or the language), and the latter comes from irreducible randomness (such as multiple possible answers). In particular, we derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large, in which case the output of the model is unreliable. This condition can be computed based solely on the output of the model obtained simply by some special iterative prompting based on the previous responses. Such quantification, for instance, allows to detect hallucinations (cases when epistemic uncertainty is high) in both single- and multi-answer responses. This is in contrast to many standard uncertainty quantification strategies (such as thresholding the log-likelihood of a response) where hallucinations in the multi-answer case cannot be detected. We conduct a series of experiments which demonstrate the advantage of our formulation. Further, our investigations shed some light on how the probabilities assigned to a given output by an LLM can be amplified by iterative prompting, which might be of independent interest.

The pursuit of out-of-distribution generalization in Vision-Language-Action (VLA) models is often hindered by catastrophic forgetting of the Vision-Language Model (VLM) backbone during fine-tuning. While co-training with external reasoning data helps, it requires experienced tuning and data-related overhead. Beyond such external dependencies, we identify an intrinsic cause within VLA datasets: modality imbalance, where language diversity is much lower than visual and action diversity. This imbalance biases the model toward visual shortcuts and language forgetting. To address this, we introduce BayesVLA, a Bayesian factorization that decomposes the policy into a visual-action prior, supporting seeing-to-act, and a language-conditioned likelihood, enabling prompt-to-specify. This inherently preserves generalization and promotes instruction following. We further incorporate pre- and post-contact phases to better leverage pre-trained foundation models. Information-theoretic analysis formally validates our effectiveness in mitigating shortcut learning. Extensive experiments show superior generalization to unseen instructions, objects, and environments compared to existing methods. Project page is available at: https://xukechun.github.io/papers/BayesVLA.

We introduce rd-spiral, an open-source Python library for simulating 2D reaction-diffusion systems using pseudo-spectral methods. The framework combines FFT-based spatial discretization with adaptive Dormand-Prince time integration, achieving exponential convergence while maintaining pedagogical clarity. We analyze three dynamical regimes: stable spirals, spatiotemporal chaos, and pattern decay, revealing extreme non-Gaussian statistics (kurtosis >96) in stable states. Information-theoretic metrics show 10.7% reduction in activator-inhibitor coupling during turbulence versus 6.5% in stable regimes. The solver handles stiffness ratios >6:1 with features including automated equilibrium classification and checkpointing. Effect sizes (delta=0.37--0.78) distinguish regimes, with asymmetric field sensitivities to perturbations. By balancing computational rigor with educational transparency, rd-spiral bridges theoretical and practical nonlinear dynamics.

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

Biological systems often choose actions without an explicit reward signal, a phenomenon known as intrinsic motivation. The computational principles underlying this behavior remain poorly understood. In this study, we investigate an information-theoretic approach to intrinsic motivation, based on maximizing an agent's empowerment (the mutual information between its past actions and future states). We show that this approach generalizes previous attempts to formalize intrinsic motivation, and we provide a computationally efficient algorithm for computing the necessary quantities. We test our approach on several benchmark control problems, and we explain its success in guiding intrinsically motivated behaviors by relating our information-theoretic control function to fundamental properties of the dynamical system representing the combined agent-environment system. This opens the door for designing practical artificial, intrinsically motivated controllers and for linking animal behaviors to their dynamical properties.

Sparse linear regression is one of the most basic questions in machine learning and statistics. Here, we are given as input a design matrix X in R^{N times d} and measurements or labels {y} in R^N where {y} = {X} {w}^* + {xi}, and {xi} is the noise in the measurements. Importantly, we have the additional constraint that the unknown signal vector {w}^* is sparse: it has k non-zero entries where k is much smaller than the ambient dimension. Our goal is to output a prediction vector {w} that has small prediction error: 1{N}cdot |{X} {w}^* - {X} {w}|^2_2. Information-theoretically, we know what is best possible in terms of measurements: under most natural noise distributions, we can get prediction error at most epsilon with roughly N = O(k log d/epsilon) samples. Computationally, this currently needs d^{Omega(k)} run-time. Alternately, with N = O(d), we can get polynomial-time. Thus, there is an exponential gap (in the dependence on d) between the two and we do not know if it is possible to get d^{o(k)} run-time and o(d) samples. We give the first generic positive result for worst-case design matrices {X}: For any {X}, we show that if the support of {w}^* is chosen at random, we can get prediction error epsilon with N = poly(k, log d, 1/epsilon) samples and run-time poly(d,N). This run-time holds for any design matrix {X} with condition number up to 2^{poly(d)}. Previously, such results were known for worst-case {w}^*, but only for random design matrices from well-behaved families, matrices that have a very low condition number (poly(log d); e.g., as studied in compressed sensing), or those with special structural properties.

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}.

Sparse Autoencoders (SAEs) have emerged as a useful tool for interpreting the internal representations of neural networks. However, naively optimising SAEs for reconstruction loss and sparsity results in a preference for SAEs that are extremely wide and sparse. We present an information-theoretic framework for interpreting SAEs as lossy compression algorithms for communicating explanations of neural activations. We appeal to the Minimal Description Length (MDL) principle to motivate explanations of activations which are both accurate and concise. We further argue that interpretable SAEs require an additional property, "independent additivity": features should be able to be understood separately. We demonstrate an example of applying our MDL-inspired framework by training SAEs on MNIST handwritten digits and find that SAE features representing significant line segments are optimal, as opposed to SAEs with features for memorised digits from the dataset or small digit fragments. We argue that using MDL rather than sparsity may avoid potential pitfalls with naively maximising sparsity such as undesirable feature splitting and that this framework naturally suggests new hierarchical SAE architectures which provide more concise explanations.

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

Existing theoretical studies on offline reinforcement learning (RL) mostly consider a dataset sampled directly from the target task. In practice, however, data often come from several heterogeneous but related sources. Motivated by this gap, this work aims at rigorously understanding offline RL with multiple datasets that are collected from randomly perturbed versions of the target task instead of from itself. An information-theoretic lower bound is derived, which reveals a necessary requirement on the number of involved sources in addition to that on the number of data samples. Then, a novel HetPEVI algorithm is proposed, which simultaneously considers the sample uncertainties from a finite number of data samples per data source and the source uncertainties due to a finite number of available data sources. Theoretical analyses demonstrate that HetPEVI can solve the target task as long as the data sources collectively provide a good data coverage. Moreover, HetPEVI is demonstrated to be optimal up to a polynomial factor of the horizon length. Finally, the study is extended to offline Markov games and offline robust RL, which demonstrates the generality of the proposed designs and theoretical analyses.

Due to privacy, storage, and other constraints, there is a growing need for unsupervised domain adaptation techniques in machine learning that do not require access to the data used to train a collection of source models. Existing methods for multi-source-free domain adaptation (MSFDA) typically train a target model using pseudo-labeled data produced by the source models, which focus on improving the pseudo-labeling techniques or proposing new training objectives. Instead, we aim to analyze the fundamental limits of MSFDA. In particular, we develop an information-theoretic bound on the generalization error of the resulting target model, which illustrates an inherent bias-variance trade-off. We then provide insights on how to balance this trade-off from three perspectives, including domain aggregation, selective pseudo-labeling, and joint feature alignment, which leads to the design of novel algorithms. Experiments on multiple datasets validate our theoretical analysis and demonstrate the state-of-art performance of the proposed algorithm, especially on some of the most challenging datasets, including Office-Home and DomainNet.

The emergence of multi-agent systems built from large language models (LLMs) offers a promising paradigm for scalable collective intelligence and self-evolution. Ideally, such systems would achieve continuous self-improvement in a fully closed loop while maintaining robust safety alignment--a combination we term the self-evolution trilemma. However, we demonstrate both theoretically and empirically that an agent society satisfying continuous self-evolution, complete isolation, and safety invariance is impossible. Drawing on an information-theoretic framework, we formalize safety as the divergence degree from anthropic value distributions. We theoretically demonstrate that isolated self-evolution induces statistical blind spots, leading to the irreversible degradation of the system's safety alignment. Empirical and qualitative results from an open-ended agent community (Moltbook) and two closed self-evolving systems reveal phenomena that align with our theoretical prediction of inevitable safety erosion. We further propose several solution directions to alleviate the identified safety concern. Our work establishes a fundamental limit on the self-evolving AI societies and shifts the discourse from symptom-driven safety patches to a principled understanding of intrinsic dynamical risks, highlighting the need for external oversight or novel safety-preserving mechanisms.

As the field of representation learning grows, there has been a proliferation of different loss functions to solve different classes of problems. We introduce a single information-theoretic equation that generalizes a large collection of modern loss functions in machine learning. In particular, we introduce a framework that shows that several broad classes of machine learning methods are precisely minimizing an integrated KL divergence between two conditional distributions: the supervisory and learned representations. This viewpoint exposes a hidden information geometry underlying clustering, spectral methods, dimensionality reduction, contrastive learning, and supervised learning. This framework enables the development of new loss functions by combining successful techniques from across the literature. We not only present a wide array of proofs, connecting over 23 different approaches, but we also leverage these theoretical results to create state-of-the-art unsupervised image classifiers that achieve a +8% improvement over the prior state-of-the-art on unsupervised classification on ImageNet-1K. We also demonstrate that I-Con can be used to derive principled debiasing methods which improve contrastive representation learners.

The rapid proliferation of Vision-Language Models (VLMs) is often framed as enabling unified multimodal knowledge discovery but rests on an under-examined assumption: that current VLMs faithfully synthesise multimodal data. We argue they often do not, and this gap reflects a trustworthiness problem in the dominant Vision Encoder-Projector-LLM paradigm. Rather than extracting grounded knowledge from visual inputs, state-of-the-art models frequently exhibit functional blindness, i.e., exploiting strong language priors to bypass severe visual representation bottlenecks. In this work, we challenge the conventional methodology of multimodal evaluation, which relies on data ablation or new dataset creation and therefore conflates dataset biases with architectural incapacity. We propose an information-theoretic departure: the Modality Translation Protocol, designed to quantify what we call the Expense of Seeing. By translating semantic payloads rather than ablating them, we formulate three novel metrics -- the Toll (ToS), Curse (CoS), and Fallacy (FoS) of Seeing -- culminating in the Semantic Sufficiency Criterion (SSC). Furthermore, we hypothesise a Divergence Law of Multimodal Scaling: as the underlying language engines scale to unprecedented reasoning capabilities, the penalty of the visual knowledge bottleneck may increase rather than diminish. We argue the community should move beyond "multimodal gain" as a primary evaluation target. By elevating the SSC from a passive diagnostic constraint to an active architectural blueprint, we provide a foundation for guiding the next generation of AI systems toward genuine multimodal reasoning.

A variety of Auto-Regressive Video Diffusion Models (ARVDM) have achieved remarkable successes in generating realistic long-form videos. However, theoretical analyses of these models remain scant. In this work, we develop theoretical underpinnings for these models and use our insights to improve the performance of existing models. We first develop Meta-ARVDM, a unified framework of ARVDMs that subsumes most existing methods. Using Meta-ARVDM, we analyze the KL-divergence between the videos generated by Meta-ARVDM and the true videos. Our analysis uncovers two important phenomena inherent to ARVDM -- error accumulation and memory bottleneck. By deriving an information-theoretic impossibility result, we show that the memory bottleneck phenomenon cannot be avoided. To mitigate the memory bottleneck, we design various network structures to explicitly use more past frames. We also achieve a significantly improved trade-off between the mitigation of the memory bottleneck and the inference efficiency by compressing the frames. Experimental results on DMLab and Minecraft validate the efficacy of our methods. Our experiments also demonstrate a Pareto-frontier between the error accumulation and memory bottleneck across different methods.

Speculative decoding has emerged as a popular method to accelerate the inference of Large Language Models (LLMs) while retaining their superior text generation performance. Previous methods either adopt a fixed speculative decoding configuration regardless of the prefix tokens, or train draft models in an offline or online manner to align them with the context. This paper proposes a training-free online learning framework to adaptively choose the configuration of the hyperparameters for speculative decoding as text is being generated. We first formulate this hyperparameter selection problem as a Multi-Armed Bandit problem and provide a general speculative decoding framework BanditSpec. Furthermore, two bandit-based hyperparameter selection algorithms, UCBSpec and EXP3Spec, are designed and analyzed in terms of a novel quantity, the stopping time regret. We upper bound this regret under both stochastic and adversarial reward settings. By deriving an information-theoretic impossibility result, it is shown that the regret performance of UCBSpec is optimal up to universal constants. Finally, extensive empirical experiments with LLaMA3 and Qwen2 demonstrate that our algorithms are effective compared to existing methods, and the throughput is close to the oracle best hyperparameter in simulated real-life LLM serving scenarios with diverse input prompts.

This paper presents a novel syllable-based tokenization approach for Indonesian large language models, inspired by the Gasing Literacy Learning System's pedagogical methodology. Drawing on information-theoretic principles, we develop a tokenization framework that segments Indonesian text at syllable boundaries before applying byte-pair encoding, creating a vocabulary that aligns with the language's morphophonological structure. Our approach first identifies high-frequency syllables through rule-based segmentation, then constructs a compact vocabulary of 3,500 tokens that preserves meaningful linguistic units while maintaining coverage through character-level fallback. Empirical evaluation on Indonesian Wikipedia and folklore corpora from Indonesian Culture Digital Library (PDBI) demonstrates substantial improvements over conventional tokenization methods: the syllable-based approach achieves Rényi efficiency of 0.74 compared to 0.50-0.64 for pretrained multilingual tokenizers, while maintaining higher average token lengths (3.67 characters versus 2.72 for GPT-2) despite using a vocabulary an order of magnitude smaller. These gains emerge from the method's ability to internalize character-level dependencies within syllable units, reducing the computational burden on language models while respecting Indonesian's agglutinative morphology. We call the LLM built upon this principle, TOBA LLM (Tokenisasi Optimum Berbasis Aglutinasi), the convergence of human literacy pedagogy with computational optimization principles offers a promising paradigm for developing linguistically-informed tokenization strategies, particularly for morphologically rich and underrepresented languages in natural language processing.

Small Language Models (SLMs) offer efficient alternatives to LLMs for specific domains. The 2023 TinyStories study developed an English dataset that allows SLMs with 1 to 10 million parameters to produce coherent outputs. Our research expands this framework by translating the original dataset into Indian languages and creating synthetic data using LLMs. We focus on Hindi, Marathi, and Bengali, evaluating SLMs for regional language processing and understanding linguistic complexity. We show that SLMs efficiently process regional languages with significantly fewer parameters than LLMs, providing a complementary framework for ``inference based evaluation" of tokenization strategies and linguistic complexity. Our analysis shows that language-specific tokenizers outperform general-purpose ones for Indian languages. Empirical validations, supported by information-theoretic and morphological analyses, provides fundamental understanding behind the better performance of Hindi models over Marathi and Bengali. Additionally, we show that synthetic datasets outperform translated content for training SLMs. Correlation analyses reveal cross-linguistic patterns and language-specific relationships between creativity, grammatical precision, and narrative completeness. These findings advance both the practical application of SLMs to underserved languages and our theoretical understanding of neural language development.

Parameter-efficient fine-tuning optimizes large, pre-trained foundation models by updating a subset of parameters; in this class, Low-Rank Adaptation (LoRA) is particularly effective. Inspired by an effort to investigate the different roles of LoRA matrices during fine-tuning, this paper characterizes and leverages unexpected asymmetry in the importance of low-rank adapter matrices. Specifically, when updating the parameter matrices of a neural network by adding a product BA, we observe that the B and A matrices have distinct functions: A extracts features from the input, while B uses these features to create the desired output. Based on this observation, we demonstrate that fine-tuning B is inherently more effective than fine-tuning A, and that a random untrained A should perform nearly as well as a fine-tuned one. Using an information-theoretic lens, we also bound the generalization of low-rank adapters, showing that the parameter savings of exclusively training B improves the bound. We support our conclusions with experiments on RoBERTa, BART-Large, LLaMA-2, and ViTs.

Despite the rapid evolution of training paradigms, the decoder backbone of large vision--language models (LVLMs) remains fundamentally rooted in the residual-connection Transformer architecture. Therefore, deciphering the distinct roles of internal modules is critical for understanding model mechanics and guiding architectural optimization. While prior statistical approaches have provided valuable attribution-based insights, they often lack a unified theoretical basis. To bridge this gap, we propose a unified framework grounded in information theory and geometry to quantify the geometric and entropic nature of residual updates. Applying this unified framework reveals a fundamental functional decoupling: Attention acts as a subspace-preserving operator focused on reconfiguration, whereas FFNs serve as subspace-expanding operators driving semantic innovation. Strikingly, further experiments demonstrate that replacing learned attention weights with predefined values (e.g., Gaussian noise) yields comparable or even superior performance across a majority of datasets relative to vanilla models. These results expose severe misallocation and redundancy in current mechanisms, suggesting that state-of-the-art LVLMs effectively ``get lost in attention'' rather than efficiently leveraging visual context.

Multi-agent language systems can exhibit a failure mode where a shared dominant context progressively absorbs individual semantics, yielding near-uniform behavior across agents. We study this effect under the name Asymptotic Semantic Collapse in Hierarchical Optimization. In a closed linguistic setting with a Dominant Anchor Node whose semantic state has effectively infinite inertia, we show that repeated interactions with Peripheral Agent Nodes drive an asymptotic alignment that minimizes a global loss. We model semantic states as points on a Riemannian manifold and analyze the induced projection dynamics. Two consequences follow. First, the limiting semantic configuration is insensitive to the optimization history: both smooth gradient-style updates and stochastic noisy updates converge to the same topological endpoint, establishing path independence at convergence. Second, the degree of context dependence controls information content: moving from atomic (independent) representations to fully entangled (context-bound) representations forces the node entropy, interpreted as available degrees of freedom, to vanish in the limit. The theory connects information-theoretic quantities with differential-geometric structure and suggests an interpretation as an immutable consensus rule that constrains agents to a shared semantic grammar. A lightweight dataset-free benchmark on an RWKV-7 13B GGUF checkpoint complements the analysis, reporting zero hash collisions, mean compliance of 0.50 under greedy decoding and 0.531 under stochastic decoding, and final Jaccard-to-anchor similarity values of 0.295 and 0.224, respectively.

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.

The choice of representation for geographic location significantly impacts the accuracy of models for a broad range of geospatial tasks, including fine-grained species classification, population density estimation, and biome classification. Recent works like SatCLIP and GeoCLIP learn such representations by contrastively aligning geolocation with co-located images. While these methods work exceptionally well, in this paper, we posit that the current training strategies fail to fully capture the important visual features. We provide an information-theoretic perspective on why the resulting embeddings from these methods discard crucial visual information that is important for many downstream tasks. To solve this problem, we propose a novel retrieval-augmented strategy called RANGE. We build our method on the intuition that the visual features of a location can be estimated by combining the visual features from multiple similar-looking locations. We evaluate our method across a wide variety of tasks. Our results show that RANGE outperforms the existing state-of-the-art models with significant margins in most tasks. We show gains of up to 13.1% on classification tasks and 0.145 R^2 on regression tasks. All our code and models will be made available at: https://github.com/mvrl/RANGE.

Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of 2-outcome POVMs. However, these shadow tomography procedures yield poor bounds if there are more than 2 outcomes per measurement. In this paper, we consider a general problem of learning properties from unknown quantum states: given an unknown d-dimensional quantum state rho and M unknown quantum measurements M_1,...,M_M with Kgeq 2 outcomes, estimating the probability distribution for applying M_i on rho to within total variation distance epsilon. Compared to the special case when K=2, we need to learn unknown distributions instead of values. We develop an online shadow tomography procedure that solves this problem with high success probability requiring O(Klog^2Mlog d/epsilon^4) copies of rho. We further prove an information-theoretic lower bound that at least Omega(min{d^2,K+log M}/epsilon^2) copies of rho are required to solve this problem with high success probability. Our shadow tomography procedure requires sample complexity with only logarithmic dependence on M and d and is sample-optimal for the dependence on K.

Measuring the diversity of creative outputs is central to evaluating post-training mode collapse, comparing decoding strategies, and quantifying creative behavior in both AI and human writing. We propose a new approach to measuring diversity using in-context learning, of which the ``Decan'' metric, D_{Ca_n} = C times a_n, is the working instance we evaluate: a per-byte score read off the per-token log-probabilities of a base model θ in a single forward pass per permutation, with no embedding model, no reference corpus, and no human labels. This approach is grounded in information theory, makes use of language model in-context learning to detect a wide range of similarities between any number of inputs, and obviates the need to train a special-purpose model. The same pipeline scores AI samples and human-written response sets, with diversity treated as a property of (responses, prompt, scoring model). On Tevet and Berant's human-grounded McDiv benchmark, D_{Ca_n} reaches OCA 0.846 on the McDiv prompt\_gen set where it performs best, behind the strongest neural baseline reported in Tevet and Berant (SentBERT, 0.897). On the OLMo-2-7B post-training pipeline, D_{Ca_n} drops monotonically across the base to SFT to DPO to RLVR stages, detecting the type of diversity loss that creative-writing applications care about.

Cortical neurons are complex, multi-timescale processors wired into recurrent circuits, shaped by long evolutionary pressure under stringent biological constraints. Mainstream machine learning, by contrast, predominantly builds models from extremely simple units, a default inherited from early neural-network theory. We treat this as a normative architectural question. How should one split a fixed parameter budget P between the number of units N, per-unit effective complexity k_e, and per-unit connectivity k_c? What controls the optimal allocation? This calls for a model in which per-unit complexity can be tuned independently of width and connectivity. Accordingly, we introduce the ELM Network, whose recurrent layer is built from Expressive Leaky Memory (ELM) neurons, chosen to mirror functional components of cortical neurons. The architecture allows for individually adjusting N, k_e, and k_c and trains stably across orders of magnitude in scale. We evaluate the model on two qualitatively different sequence benchmarks: the neuromorphic SHD-Adding task and Enwik8 character-level language modeling. Performance improves monotonically along each of the three axes individually. Under a fixed budget, a clear non-trivial optimum emerges in their tradeoff, and larger budgets favor both more and more complex neurons. A closed-form information-theoretic model captures these tradeoffs and attributes the diminishing returns at two ends to: per-neuron signal-to-noise saturation and across-neuron redundancy. A hyperparameter sweep spanning three orders of magnitude in trainable parameters traces a near-Pareto-frontier scaling law consistent with the framework. This suggests that the simple-unit default in ML is not obviously optimal once this tradeoff surface is probed, and offers a normative lens on cortex's reliance on complex spatio-temporal integrators.

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.

In robotic manipulation, vision-language-action (VLA) models have emerged as a promising paradigm for learning generalizable and scalable robot policies. Most existing VLA frameworks rely on standard supervised objectives, typically cross-entropy for discrete actions and mean squared error (MSE) for continuous action regression, which impose strong pointwise constraints on individual predictions. In this work, we focus on continuous-action VLA models and move beyond conventional MSE-based regression by reshaping action error distributions during training. Drawing on information-theoretic principles, we introduce Minimum Error Entropy (MEE) into modern VLA architectures and propose a trajectory-level MEE objective, together with two weighted variants, combined with MSE for continuous-action VLA training. We evaluate our approaches across standard, few-shot, and noisy settings on multiple representative VLA architectures, using simulation benchmarks such as LIBERO and SimplerEnv as well as real-world robotic manipulation tasks. Experimental results demonstrate consistent improvements in success rates and robustness across these settings. Under imbalanced data regimes, the gains persist within a well-characterized operating range, while incurring negligible additional training cost and no impact on inference efficiency. We further provide theoretical analyses that explain why MEE-based supervision is effective and characterize its practical range. Project Page: https://cognition2actionlab.github.io/VLA-TMEE.github.io/

LLM-based multi-agent systems (MAS) have emerged as a promising approach to tackle complex tasks that are difficult for individual LLMs. A natural strategy is to scale performance by increasing the number of agents; however, we find that such scaling exhibits strong diminishing returns in homogeneous settings, while introducing heterogeneity (e.g., different models, prompts, or tools) continues to yield substantial gains. This raises a fundamental question: what limits scaling, and why does diversity help? We present an information-theoretic framework showing that MAS performance is bounded by the intrinsic task uncertainty, not by agent count. We derive architecture-agnostic bounds demonstrating that improvements depend on how many effective channels the system accesses. Homogeneous agents saturate early because their outputs are strongly correlated, whereas heterogeneous agents contribute complementary evidence. We further introduce K^*, an effective channel count that quantifies the number of effective channels without ground-truth labels. Empirically, we show that heterogeneous configurations consistently outperform homogeneous scaling: 2 diverse agents can match or exceed the performance of 16 homogeneous agents. Our results provide principled guidelines for building efficient and robust MAS through diversity-aware design. Code and Dataset are available at the link: https://github.com/SafeRL-Lab/Agent-Scaling.

We present 1d-qt-ideal-solver, an open-source Python library for simulating one-dimensional quantum tunneling dynamics under idealized coherent conditions. The solver implements the split-operator method with second-order Trotter-Suzuki factorization, utilizing FFT-based spectral differentiation for the kinetic operator and complex absorbing potentials to eliminate boundary reflections. Numba just-in-time compilation achieves performance comparable to compiled languages while maintaining code accessibility. We validate the implementation through two canonical test cases: rectangular barriers modeling field emission through oxide layers and Gaussian barriers approximating scanning tunneling microscopy interactions. Both simulations achieve exceptional numerical fidelity with machine-precision energy conservation over femtosecond-scale propagation. Comparative analysis employing information-theoretic measures and nonparametric hypothesis tests reveals that rectangular barriers exhibit moderately higher transmission coefficients than Gaussian barriers in the over-barrier regime, though Jensen-Shannon divergence analysis indicates modest practical differences between geometries. Phase space analysis confirms complete decoherence when averaged over spatial-temporal domains. The library name reflects its scope: idealized signifies deliberate exclusion of dissipation, environmental coupling, and many-body interactions, limiting applicability to qualitative insights and pedagogical purposes rather than quantitative experimental predictions. Distributed under the MIT License, the library provides a deployable tool for teaching quantum mechanics and preliminary exploration of tunneling dynamics.

Motivated by the need to efficiently identify multiple candidates in high trial-and-error cost tasks such as drug discovery, we propose a near-optimal algorithm to identify all ε-best arms (i.e., those at most ε worse than the optimum). Specifically, we introduce LinFACT, an algorithm designed to optimize the identification of all ε-best arms in linear bandits. We establish a novel information-theoretic lower bound on the sample complexity of this problem and demonstrate that LinFACT achieves instance optimality by matching this lower bound up to a logarithmic factor. A key ingredient of our proof is to integrate the lower bound directly into the scaling process for upper bound derivation, determining the termination round and thus the sample complexity. We also extend our analysis to settings with model misspecification and generalized linear models. Numerical experiments, including synthetic and real drug discovery data, demonstrate that LinFACT identifies more promising candidates with reduced sample complexity, offering significant computational efficiency and accelerating early-stage exploratory experiments.

This paper introduces the first two-dimensional XOR-based secret sharing scheme for layered multipath communication networks. We present a construction that guarantees successful message recovery and perfect privacy when an adversary observes and disrupts any single path at each transmission layer. The scheme achieves information-theoretic security using only bitwise XOR operations with linear O(|S|) complexity, where |S| is the message length. We provide mathematical proofs demonstrating that the scheme maintains unconditional security regardless of computational resources available to adversaries. Unlike encryption-based approaches vulnerable to quantum computing advances, our construction offers provable security suitable for resource-constrained military environments where computational assumptions may fail.

We introduce a formal information-theoretic framework for image captioning by regarding it as a representation learning task. Our framework defines three key objectives: task sufficiency, minimal redundancy, and human interpretability. Building upon this foundation, we propose a novel Pyramid of Captions (PoCa) method, which constructs caption pyramids by generating localized captions for zoomed-in image patches and integrating them with global caption information using large language models. This approach leverages intuition that the detailed examination of local patches can reduce error risks and address inaccuracies in global captions, either by correcting the hallucination or adding missing details. Based on our theoretical framework, we formalize this intuition and provide formal proof demonstrating the effectiveness of PoCa under certain assumptions. Empirical tests with various image captioning models and large language models show that PoCa consistently yields more informative and semantically aligned captions, maintaining brevity and interpretability.

In many machine learning systems that jointly learn from multiple modalities, a core research question is to understand the nature of multimodal interactions: the emergence of new task-relevant information during learning from both modalities that was not present in either alone. We study this challenge of interaction quantification in a semi-supervised setting with only labeled unimodal data and naturally co-occurring multimodal data (e.g., unlabeled images and captions, video and corresponding audio) but when labeling them is time-consuming. Using a precise information-theoretic definition of interactions, our key contributions are the derivations of lower and upper bounds to quantify the amount of multimodal interactions in this semi-supervised setting. We propose two lower bounds based on the amount of shared information between modalities and the disagreement between separately trained unimodal classifiers, and derive an upper bound through connections to approximate algorithms for min-entropy couplings. We validate these estimated bounds and show how they accurately track true interactions. Finally, two semi-supervised multimodal applications are explored based on these theoretical results: (1) analyzing the relationship between multimodal performance and estimated interactions, and (2) self-supervised learning that embraces disagreement between modalities beyond agreement as is typically done.

When two different parties use the same learning rule on their own data, how can we test whether the distributions of the two outcomes are similar? In this paper, we study the similarity of outcomes of learning rules through the lens of the Total Variation (TV) distance of distributions. We say that a learning rule is TV indistinguishable if the expected TV distance between the posterior distributions of its outputs, executed on two training data sets drawn independently from the same distribution, is small. We first investigate the learnability of hypothesis classes using TV indistinguishable learners. Our main results are information-theoretic equivalences between TV indistinguishability and existing algorithmic stability notions such as replicability and approximate differential privacy. Then, we provide statistical amplification and boosting algorithms for TV indistinguishable learners.

Motivated by concerns about making online decisions that incur undue amount of risk at each time step, in this paper, we formulate the probably anytime-safe stochastic combinatorial semi-bandits problem. In this problem, the agent is given the option to select a subset of size at most K from a set of L ground items. Each item is associated to a certain mean reward as well as a variance that represents its risk. To mitigate the risk that the agent incurs, we require that with probability at least 1-delta, over the entire horizon of time T, each of the choices that the agent makes should contain items whose sum of variances does not exceed a certain variance budget. We call this probably anytime-safe constraint. Under this constraint, we design and analyze an algorithm {\sc PASCombUCB} that minimizes the regret over the horizon of time T. By developing accompanying information-theoretic lower bounds, we show that under both the problem-dependent and problem-independent paradigms, {\sc PASCombUCB} is almost asymptotically optimal. Experiments are conducted to corroborate our theoretical findings. Our problem setup, the proposed {\sc PASCombUCB} algorithm, and novel analyses are applicable to domains such as recommendation systems and transportation in which an agent is allowed to choose multiple items at a single time step and wishes to control the risk over the whole time horizon.

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.

Existing few-shot learning (FSL) methods rely on training with a large labeled dataset, which prevents them from leveraging abundant unlabeled data. From an information-theoretic perspective, we propose an effective unsupervised FSL method, learning representations with self-supervision. Following the InfoMax principle, our method learns comprehensive representations by capturing the intrinsic structure of the data. Specifically, we maximize the mutual information (MI) of instances and their representations with a low-bias MI estimator to perform self-supervised pre-training. Rather than supervised pre-training focusing on the discriminable features of the seen classes, our self-supervised model has less bias toward the seen classes, resulting in better generalization for unseen classes. We explain that supervised pre-training and self-supervised pre-training are actually maximizing different MI objectives. Extensive experiments are further conducted to analyze their FSL performance with various training settings. Surprisingly, the results show that self-supervised pre-training can outperform supervised pre-training under the appropriate conditions. Compared with state-of-the-art FSL methods, our approach achieves comparable performance on widely used FSL benchmarks without any labels of the base classes.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

Recently, the study of linear misspecified bandits has generated intriguing implications of the hardness of learning in bandits and reinforcement learning (RL). In particular, Du et al. (2020) show that even if a learner is given linear features in R^d that approximate the rewards in a bandit or RL with a uniform error of varepsilon, searching for an O(varepsilon)-optimal action requires pulling at least Omega(exp(d)) queries. Furthermore, Lattimore et al. (2020) show that a degraded O(varepsilond)-optimal solution can be learned within poly(d/varepsilon) queries. Yet it is unknown whether a structural assumption on the ground-truth parameter, such as sparsity, could break the varepsilond barrier. In this paper, we address this question by showing that algorithms can obtain O(varepsilon)-optimal actions by querying O(varepsilon^{-s}d^s) actions, where s is the sparsity parameter, removing the exp(d)-dependence. We then establish information-theoretical lower bounds, i.e., Omega(exp(s)), to show that our upper bound on sample complexity is nearly tight if one demands an error O(s^{delta}varepsilon) for 0<delta<1. For deltageq 1, we further show that poly(s/varepsilon) queries are possible when the linear features are "good" and even in general settings. These results provide a nearly complete picture of how sparsity can help in misspecified bandit learning and provide a deeper understanding of when linear features are "useful" for bandit and reinforcement learning with misspecification.

Diffusion models (DMs) excel in image generation, but suffer from slow inference and the training-inference discrepancies. Although gradient-based solvers like DPM-Solver accelerate the denoising inference, they lack theoretical foundations in information transmission efficiency. In this work, we introduce an information-theoretic perspective on the inference processes of DMs, revealing that successful denoising fundamentally reduces conditional entropy in reverse transitions. This principle leads to our key insights into the inference processes: (1) data prediction parameterization outperforms its noise counterpart, and (2) optimizing conditional variance offers a reference-free way to minimize both transition and reconstruction errors. Based on these insights, we propose an entropy-aware variance optimized method for the generative process of DMs, called EVODiff, which systematically reduces uncertainty by optimizing conditional entropy during denoising. Extensive experiments on DMs validate our insights and demonstrate that our method significantly and consistently outperforms state-of-the-art (SOTA) gradient-based solvers. For example, compared to the DPM-Solver++, EVODiff reduces the reconstruction error by up to 45.5\% (FID improves from 5.10 to 2.78) at 10 function evaluations (NFE) on CIFAR-10, cuts the NFE cost by 25\% (from 20 to 15 NFE) for high-quality samples on ImageNet-256, and improves text-to-image generation while reducing artifacts. Code is available at https://github.com/ShiguiLi/EVODiff.

We introduce Psi-Turing Machines (Psi-TM): classical Turing machines equipped with a constant-depth introspection interface iota and an explicit per-step information budget B(d,n)=c,dlog_2 n . With the interface frozen, we develop an information-theoretic lower-bound toolkit: Budget counting, Psi -Fooling, and Psi -Fano, with worked examples L_k and L_k^{phase} . We prove an oracle-relative separation P^{Psi} neq NP^{Psi} and a strict depth hierarchy, reinforced by an Anti-Simulation Hook that rules out polynomial emulation of iota_k using many calls to iota_{k-1} under the budget regime. We also present two independent platforms (Psi-decision trees and interface-constrained circuits IC-AC^{0}/IC-NC^{1}) and bridges that transfer bounds among machine, tree, and circuit with explicit poly/log losses. The model preserves classical computational power outside iota yet enables precise oracle-aware statements about barriers (relativization; partial/conditional progress on natural proofs and proof complexity). The aim is a standardized minimal introspection interface with clearly accounted information budgets.

We identify empirical scaling laws for the cross-entropy loss in four domains: generative image modeling, video modeling, multimodal imageleftrightarrowtext models, and mathematical problem solving. In all cases autoregressive Transformers smoothly improve in performance as model size and compute budgets increase, following a power-law plus constant scaling law. The optimal model size also depends on the compute budget through a power-law, with exponents that are nearly universal across all data domains. The cross-entropy loss has an information theoretic interpretation as S(True) + D_{KL}(True||Model), and the empirical scaling laws suggest a prediction for both the true data distribution's entropy and the KL divergence between the true and model distributions. With this interpretation, billion-parameter Transformers are nearly perfect models of the YFCC100M image distribution downsampled to an 8times 8 resolution, and we can forecast the model size needed to achieve any given reducible loss (ie D_{KL}) in nats/image for other resolutions. We find a number of additional scaling laws in specific domains: (a) we identify a scaling relation for the mutual information between captions and images in multimodal models, and show how to answer the question "Is a picture worth a thousand words?"; (b) in the case of mathematical problem solving, we identify scaling laws for model performance when extrapolating beyond the training distribution; (c) we finetune generative image models for ImageNet classification and find smooth scaling of the classification loss and error rate, even as the generative loss levels off. Taken together, these results strengthen the case that scaling laws have important implications for neural network performance, including on downstream tasks.

Language exhibits a fractal structure in its information-theoretic complexity (i.e. bits per token), with self-similarity across scales and long-range dependence (LRD). In this work, we investigate whether large language models (LLMs) can replicate such fractal characteristics and identify conditions-such as temperature setting and prompting method-under which they may fail. Moreover, we find that the fractal parameters observed in natural language are contained within a narrow range, whereas those of LLMs' output vary widely, suggesting that fractal parameters might prove helpful in detecting a non-trivial portion of LLM-generated texts. Notably, these findings, and many others reported in this work, are robust to the choice of the architecture; e.g. Gemini 1.0 Pro, Mistral-7B and Gemma-2B. We also release a dataset comprising of over 240,000 articles generated by various LLMs (both pretrained and instruction-tuned) with different decoding temperatures and prompting methods, along with their corresponding human-generated texts. We hope that this work highlights the complex interplay between fractal properties, prompting, and statistical mimicry in LLMs, offering insights for generating, evaluating and detecting synthetic texts.

Malware authors often employ code obfuscations to make their malware harder to detect. Existing tools for generating obfuscated code often require access to the original source code (e.g., C++ or Java), and adding new obfuscations is a non-trivial, labor-intensive process. In this study, we ask the following question: Can Large Language Models (LLMs) potentially generate a new obfuscated assembly code? If so, this poses a risk to anti-virus engines and potentially increases the flexibility of attackers to create new obfuscation patterns. We answer this in the affirmative by developing the MetamorphASM benchmark comprising MetamorphASM Dataset (MAD) along with three code obfuscation techniques: dead code, register substitution, and control flow change. The MetamorphASM systematically evaluates the ability of LLMs to generate and analyze obfuscated code using MAD, which contains 328,200 obfuscated assembly code samples. We release this dataset and analyze the success rate of various LLMs (e.g., GPT-3.5/4, GPT-4o-mini, Starcoder, CodeGemma, CodeLlama, CodeT5, and LLaMA 3.1) in generating obfuscated assembly code. The evaluation was performed using established information-theoretic metrics and manual human review to ensure correctness and provide the foundation for researchers to study and develop remediations to this risk. The source code can be found at the following GitHub link: https://github.com/mohammadi-ali/MetamorphASM.

Much research in machine learning involves finding appropriate inductive biases (e.g. convolutional neural networks, momentum-based optimizers, transformers) to promote generalization on tasks. However, quantification of the amount of inductive bias associated with these architectures and hyperparameters has been limited. We propose a novel method for efficiently computing the inductive bias required for generalization on a task with a fixed training data budget; formally, this corresponds to the amount of information required to specify well-generalizing models within a specific hypothesis space of models. Our approach involves modeling the loss distribution of random hypotheses drawn from a hypothesis space to estimate the required inductive bias for a task relative to these hypotheses. Unlike prior work, our method provides a direct estimate of inductive bias without using bounds and is applicable to diverse hypothesis spaces. Moreover, we derive approximation error bounds for our estimation approach in terms of the number of sampled hypotheses. Consistent with prior results, our empirical results demonstrate that higher dimensional tasks require greater inductive bias. We show that relative to other expressive model classes, neural networks as a model class encode large amounts of inductive bias. Furthermore, our measure quantifies the relative difference in inductive bias between different neural network architectures. Our proposed inductive bias metric provides an information-theoretic interpretation of the benefits of specific model architectures for certain tasks and provides a quantitative guide to developing tasks requiring greater inductive bias, thereby encouraging the development of more powerful inductive biases.

Machine learning models trained with differentially-private (DP) algorithms such as DP-SGD enjoy resilience against a wide range of privacy attacks. Although it is possible to derive bounds for some attacks based solely on an (varepsilon,delta)-DP guarantee, meaningful bounds require a small enough privacy budget (i.e., injecting a large amount of noise), which results in a large loss in utility. This paper presents a new approach to evaluate the privacy of machine learning models against specific record-level threats, such as membership and attribute inference, without the indirection through DP. We focus on the popular DP-SGD algorithm, and derive simple closed-form bounds. Our proofs model DP-SGD as an information theoretic channel whose inputs are the secrets that an attacker wants to infer (e.g., membership of a data record) and whose outputs are the intermediate model parameters produced by iterative optimization. We obtain bounds for membership inference that match state-of-the-art techniques, whilst being orders of magnitude faster to compute. Additionally, we present a novel data-dependent bound against attribute inference. Our results provide a direct, interpretable, and practical way to evaluate the privacy of trained models against specific inference threats without sacrificing utility.

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.

We study the probabilistic modeling performed by Autoregressive Large Language Models (LLMs) through the angle of time directionality, addressing a question first raised in (Shannon, 1951). For large enough models, we empirically find a time asymmetry in their ability to learn natural language: a difference in the average log-perplexity when trying to predict the next token versus when trying to predict the previous one. This difference is at the same time subtle and very consistent across various modalities (language, model size, training time, ...). Theoretically, this is surprising: from an information-theoretic point of view, there should be no such difference. We provide a theoretical framework to explain how such an asymmetry can appear from sparsity and computational complexity considerations, and outline a number of perspectives opened by our results.

Causal structures for observational survival data provide crucial information regarding the relationships between covariates and time-to-event. We derive motivation from the information theoretic source coding argument, and show that incorporating the knowledge of the directed acyclic graph (DAG) can be beneficial if suitable source encoders are employed. As a possible source encoder in this context, we derive a variational inference based conditional variational autoencoder for causal structured survival prediction, which we refer to as DAGSurv. We illustrate the performance of DAGSurv on low and high-dimensional synthetic datasets, and real-world datasets such as METABRIC and GBSG. We demonstrate that the proposed method outperforms other survival analysis baselines such as Cox Proportional Hazards, DeepSurv and Deephit, which are oblivious to the underlying causal relationship between data entities.