Information Bottleneck

Visual signals require compact yet sufficient representations for robust downstream prediction. Convolutional sparse coding (CSC) provides an explicit mechanism for suppressing redundant components while preserving signal content, but its sparsity coefficient is typically fixed and manually selected. We propose a training-adaptive convolutional sparse coding framework for robust visual signal representation. Specifically, we unfold the CSC optimization with the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) and treat the sparsity coefficient as a differentiable variable jointly learned with the network parameters. From the information bottleneck perspective, this coefficient controls the trade-off between information retention and compression: the sparsity term promotes compact representations, while the reconstruction term together with task loss preserves task-relevant signal content. We further introduce a label-free post-training strategy that adjusts the compression strength for corrupted inputs with the main network parameters fixed. Experiments on CIFAR and ImageNet demonstrate competitive clean-data recognition and greatly improved robustness under different input perturbations.

Semantic and goal-oriented communication is increasingly studied for 6G, but generalization beyond seen data remains a key weakness under tight rate budgets. Many existing systems overfit their training data and degrade sharply at very low bit rates because they attempt to compress the entire signal. We introduce Foundation Model-Guided Semantic and Goal-Oriented Communication (FMSGOC), a framework that uses broad visual-linguistic Foundation Model priors to mitigate overfitting. It further improves rate efficiency by concentrating bits on sparse, goal-aligned anchors and relying on generative foundation-model priors to reconstruct the masked regions. By decoupling what to send from how to reconstruct, a vision-language foundation model selects and transmits a sparse set of semantic anchors, while a pretrained diffusion model, fine-tuned for masked completion, reconstructs the image at the receiver. In our experiments, FMSGOC reaches 0.039 bits per pixel (BPP), maintains high semantic fidelity (cosine similarity 0.87-0.90 on CIFAR-10), remains robust on previously unseen inputs (0.83-0.86 on ImageNet), and shows good perceptual similarity (0.1278/0.1558, CIFAR-10/ImageNet), outperforming strong end-to-end baselines at lower bit rates.

In this work, we study the information bottleneck under perfect privacy, with particular emphasis on the active-rate regime, where the representation-rate constraint is binding and directly limits the achievable utility. The goal is to construct a representation that preserves utility-relevant information while remaining statistically independent of a sensitive variable. This exact independence requirement introduces an additional constraint beyond the classical rate-relevance tradeoff and must be explicitly incorporated into the optimization. To this end, we develop an alternating direction method of multipliers (ADMM)-based method tailored to the resulting problem structure. Under suitable regularity conditions, we establish global convergence of the generated sequence, characterize its convergence rate through the Kurdyka-Lojasiewicz exponent, and extend the analysis to inexact block updates.

As forecasts increasingly drive decisions in fields such as energy, transportation, and healthcare, understanding the historical data behind these predictions has become as crucial as the predictions themselves. Although existing interpretable-by-design forecasters reveal their internal structures, they offer no guarantee that these structures faithfully reflect the underlying evidence driving the predictions. In contrast, while faithfulness-oriented methods explicitly verify model behavior, they are almost exclusively designed for post-hoc classification tasks. To bridge this gap, we propose IB-Forecast, an inherently interpretable multivariate time-series forecasting framework. It decomposes forecasting into a learned periodic component and a residual component computed with explainable masks over input tokens. With a budget-constrained information bottleneck, end-to-end optimization enables users to directly control explanation sparsity. With a rigorous faithfulness evaluation protocol, extensive experiments demonstrate that IB-Forecast matches the forecasting error of leading black-box models while providing faithful explanations at no additional inference cost. Furthermore, under a matched sparsity budget, these native explanations consistently surpass gradient-based, occlusion-based, and optimization-based baselines across all evaluated datasets. Ultimately, whereas the native explanations of existing interpretable forecasters exhibit poor faithfulness, IB-Forecast guarantees high explanation fidelity, requiring only 14-20% of the observations to deliver low-error predictions.

Memory-augmented LLM-based agents are vulnerable to memory injection attacks: Agents may retrieve poisoned memory from attackers, which diverts their behavior from initial user intent and finally causes task failure. However, existing defense mechanisms either incur high computational cost or suffer from information redundancy in multi-turn contexts. To address these challenges, we propose Memory Intent-Aware Neural Denoising(MIND), a lightweight defense framework for memory injection attack. Our preliminary analysis reveals that benign and poisoned trajectories exhibit distinguishable relationships between the initial user intent and subsequent behavior. Building on this observation, MIND employs an intent-aware Information Bottleneck(IB) to extract compact intent--behavior representations from the initial intent and turn-level behavior. The IB preserves intent-relevant cross-turn attack signals while filtering task-irrelevant and repetitive information, and a lightweight detector identifies malicious memories from the resulting representations. As such, MIND mitigates information redundancy in multi-turn contexts while avoiding the overhead of repeated LLM auditing. Extensive experiments show that MIND reduces attack success rates while preserving task accuracy and inference efficiency. Notably, on ReAct-StrategyQA, MIND reduces mean ASR-r and ASR-a by 55.4% and 55.3%, respectively, while matching the undefended agent in average accuracy and latency.

We study information bottlenecks in modern deep-learning architectures -- RNNs, softmax transformers, linear-attention transformers and state-space models -- through the lens of the indexing primitive. In this primitive, the input consists of $n$ bits and one integer $i$ from $1$ to $n$ called the index, and the output equals the value of the $i$-th bit. We introduce causal complexity for masked architectures. We show that architectures with low causal complexity cannot solve the indexing primitive in any constant number of layers when the index appears at the end of the input. In particular, this limitation applies to low-parameter RNNs, SSMs and masked linear-attention transformers. In contrast, small softmax transformers can solve it in one layer, while non-masked linear-attention transformers can solve it in 2, which separates them from their masked counterparts. In turn, when the index appears at the beginning, we show that small RNNs are capable of solving this task in 1 layer, while all the other architectures require 2. All our impossibility results are unconditional and apply even to models that employ infinite-precision real arithmetic. Moreover, experiments for up to $n=64$ qualitatively align with our theory: configurations with low-parameter theoretical solutions learn the indexing task easily, while configurations that do not admit such theoretical solutions struggle to learn as the sequence length grows.

Vision foundation models are increasingly reused as frozen backbones for downstream visual recognition, making parameter-efficient adaptation a central problem. Prompt-based adaptation, including Visual Prompt Tuning (VPT), provides a lightweight way to specialize these models, but its layer-wise behavior remains poorly understood: performance is sensitive to prompt depth, placement, and task distribution, and gains on standard in-domain benchmarks do not always translate into robust generalization. We argue that this limitation is not solely an optimization issue, but a layer-wise information allocation issue: existing prompt-based methods lack principled control over what prompt-conditioned representations should preserve, suppress, and propagate across depth. Inspired by the Information Bottleneck principle, we introduce Prompted Information Bottlenecks (PIB), a framework that regularizes layer-wise compression-sufficiency trade-offs and promotes a more coherent cross-layer information path. The key idea is that effective adaptation should be minimal yet sufficient, retaining task-relevant local evidence in earlier layers while progressively discarding nuisance factors and redundant details in deeper layers. Extensive experiments show that PIB achieves strong performance across 34 datasets, reaching 92.1% on FGVC, 93.01% on HTA, and 77.33% on VTAB-1k, while tuning only 0.35% parameters on average across the main settings. Beyond benchmark accuracy, PIB helps explain the non-monotonic behavior of prompt capacity scaling, reduces shortcut reliance, and improves robustness under distribution shift and fine-grained recognition settings. These results position PIB as both a practical method and an information-allocation perspective for adapting frozen vision foundation models. Our code is available at https://github.com/itsnotacie/MM-26-PIB

Scalar metrics are often used to evaluate clusterings against known classes, but they can obscure a fundamental trade-off: clusterings should be informative about class labels while avoiding unnecessary fragmentation. Here we describe normalized scores of cluster homogeneity and parsimony that quantify this trade-off. These scores build on the information bottleneck principle, modified to not reward lossy compression. We show by example and mathematical proof that our definitions of these scores have the intuitive property of varying monotonically under cluster refinement in contrast to related proposals. Extending the information-theoretic framework beyond Shannon entropies, we furthermore derive set-matching and pair-based counterparts of the homogeneity and parsimony scores. These unify commonly used evaluation criteria and show that, in the pair-based setting, the homogeneity-parsimony trade-off recovers the receiver operating characteristic of binary classifiers. We demonstrate the framework's utility for feature selection and algorithm comparison, illustrating how considering scores jointly can clarify clustering operating points and identify Pareto-optimal solutions.

LLM powered multi-agent systems (MAS) have emerged as a promising paradigm for complex tasks. However, their advantages over single-agent systems (SAS) remain unclear, with performance varying inconsistently across settings. Here, we provide an information bottleneck perspective on elucidating the differences between MAS and SAS. Specifically, our key observation is that a SAS accumulates its full reasoning trace in one shared context, while a MAS uses isolated local contexts connected by bounded relay messages. We show that, under infinite relay bandwidth, any SAS can be simulated by a MAS that transmits the full upstream context. Thus, the nontrivial advantage of MAS arises under bounded relays, where compression introduces a fundamental trade-off: reducing redundant context can improve efficiency, but may also incur loss of task-relevant information. We formalize this trade-off as an information bottleneck controlled by an effective parameter $β$, which captures how the balance shifts with model capability, and shows that MAS gains arise when context reduction outweighs relay information loss. We conduct 18 controlled experiments across five benchmarks and three model scales to validate our theoretical studies. We observe that MAS consistently helps when relays are near-sufficient, especially for weaker models. In contrast, MAS gains shrink or reverse when relays incur information loss, especially for stronger models that can already extract useful information from redundant context and thus gain little from compression. Our study shows that multi-agent design is fundamentally an information-bottleneck optimization problem. This perspective explains when bounded inter-agent communication helps or hurts.

How does the way information reaches a transformer -- as symbolic tokens, a clean per-factor "oracle" code, or an entangled perceptual vector -- shape whether it binds that information compositionally? We study ~6-10K-parameter transformers on finite factored worlds enumerated exhaustively, so every measurement covers the whole input space (zero sampling variance) and the informative routes are information-matched (exact Bayes ceiling 1.0). We report four findings. (1) Endpoint invariance: on held-out binding queries no informative route reaches converged zero-shot composition -- each ends at or below chance despite a ceiling of 1.0, so within a bounded sweep the failure reflects inductive bias under a lookup-sufficient objective, not missing information. (2) A two-factor account of few-shot binding: sample efficiency is best explained by input-pathway parameter sharing and code readability; a dimension-matched control and a graded readability sweep isolate readability from input dimension, and the clean oracle is not the most sample-efficient readable route. (3) A double dissociation: early in training, distributed -- but not index-like -- codes pass through a transient above-chance phase (tracking code format), while few-shot efficiency tracks pathway sharing. (4) Failure anatomy: symbolic routes lose the answer at the readout; index routes mis-bind (the answer stays decodable, yet an input intervention shows the output tracks the wrong slot); entangled routes inherit their input's readability. The central claim is the two-factor account; the endpoint and anatomy results are diagnostic constraints. All code, manifests, and per-seed logs are released for exact reproduction.

Visual recognition models often fail when deployed in new environments. Domain Generalization (DG) addresses this by learning representations that remain invariant to environment-specific variations. Recent approaches increasingly rely on large vision-language models, assuming that preserving their expressive visual representations improves robustness. However, we show that such visual expressiveness can instead propagate spurious cues that tie representations to the training environments, hindering invariant learning. We therefore discard visual guidance and instead treat the language embedding space as the primary source of domain invariance, naturally acting as an information bottleneck that preserves core semantics while suppressing domain-specific variations. Extensive experiments across diverse backbones exhibit state-of-the-art performance and further analyze what makes guidance effective for robust generalization. These findings shift the focus of DG from improving representations to designing supervision that enforces invariance.

Rapid advancements in generative speech technology have compromised the reliability of voice biometrics. While current spoofing detectors excel when assessed under in-domain conditions, generalisation to out-of-domain settings is often poor. We show that this can be due to linguistic bias. A reliance on linguistic cues observed in training data can then compromise robustness to cross-data. We propose a linguistic-invariant spoofing detection framework utilizing teacher-student adversarial learning. The linguistic-aware teacher model, pre-trained on linguistic content of an external dataset, guides the student detector via gradient reversal to minimize the linguistic information. To prevent the inadvertent removal of non-linguistic cues, we incorporate a Variational Information Bottleneck to enable suppression of principal cues. Across nine DF Arena datasets, our method achieves up to a 36.2% relative reduction in the EER compare to the baseline.

Audio-Visual Speech Recognition takes two input modalities, acoustic and visual streams, where visual information from lip movements aids recognition when audio is noisy. Recently, LLM-based AVSR models have emerged as a promising paradigm by connecting pre-trained audio-visual encoders to an LLM, achieving strong results in clean conditions. However, these models are predominantly optimized for clean acoustic conditions, with limited attention to making the LLM backbone robust to noise. No explicit mechanism is employed to produce stable representations under corrupted audio, leading to performance degradation in noisy environments. To address this, we propose VIB-AVSR, which integrates Variational Information Bottleneck layers at targeted positions within the LLM backbone to regularize representations. VIB-AVSR reduces degradation under noisy conditions across multiple SNR levels and noise types, without requiring architectural modifications or additional training data.

We study the limits of CTC-internal scoring for N-best hypothesis selection and locate the information bottleneck separating acoustic confidence from linguistic plausibility. Eleven CTC-internal and acoustic-feature scoring strategies produce no statistically significant WER improvement over greedy decoding on LibriSpeech dev-other at G=16 (all p > 0.05). The exhaustion is systematic: CTC's Spearman $ρ$ between hypothesis score and per-utterance WER degrades from -0.574 at G=4 to -0.270 at G=128, a 53% loss driven by blank-path proliferation. This establishes that the discriminative capacity of CTC-internal representations is saturated: no recombination of acoustic signals can close the oracle gap. Confirming that the bottleneck is linguistic, not acoustic, external linguistic information introduced via MBR decoding breaks through it. MBR-CER decoding with a RoBERTa pseudo-log-likelihood (PLL) posterior ($τ$=10, G=128) achieves 5.42% WER on held-out LibriSpeech test-other (greedy 5.96%, $Δ$=-0.535 pp, p<0.0001, 9.0% relative). RoBERTa PLL $ρ$ degrades only 21% over the same range, retaining discriminating power where CTC loses it. Applied without retuning across two Zipformer architectures, three domains (LibriSpeech, TED-LIUM 3, VoxPopuli), and four MUSAN noise levels, the recipe gives significant gains in 11 of 13 conditions. On the training side, standard MWER training via the CTC forward-backward algorithm implements Rao-Blackwellized REINFORCE at the output projection (variance about 3x below Viterbi). Yet sequence-level fine-tuning fails at near-converged checkpoints: all four MWER configurations on CR-CTC collapse (+6.18 to +8.90 pp WER), as a training oracle gap of 0.007 pp provides no usable reward signal.

Reasoning-driven universal multimodal embedding has advanced rapidly by introducing Chain-of-Thought (CoT) reasoning into the embedding pipeline. Despite the strong performance across both general and complex tasks, this paradigm suffers from two core limitations: (i) autoregressive CoT reasoning incurs high computational cost, making it impractical for low-latency retrieval; and (ii) embedding performance is heavily coupled with CoT annotation quality, making large-scale training unreliable. These raise fundamental questions: Is textual CoT the optimal form of reasoning for embedding, and can effective embedding reasoning be accomplished in latent space? To this end, we propose LaME (Latent Reasoning Multimodal Embedding), which formulates embedding-oriented latent reasoning as a weakly supervised information bottleneck. LaME employs K learnable reason tokens as a fixed-capacity bottleneck, completing all reasoning within a single forward pass. The two weak supervision signals structurally decouple contrastive from autoregressive objectives and eliminate dependence on CoT annotations, while a two-stage training pipeline ensures stable convergence. Experiments on MMEB-v2 and MRMR show that LaME achieves competitive performance, surpassing some explicit CoT-based models, while delivering 60x faster inference than explicit CoT methods and 2x faster than latent baselines with throughput comparable to discriminative embedding models. Code is available at https://github.com/PeppaWu/LaME.

Large language models (LLMs) provide a powerful reasoning backbone for speech understanding, but integrating continuous acoustic signals into a frozen LLM remains challenging. Existing speech-to-LLM interfaces typically operate at two extremes: either enforcing near-discrete token alignment, which benefits transcription but loses paralinguistic information, or learning unconstrained continuous representations, which can drift away from the LLM's input space and degrade autoregressive decoding. In this work, we propose Convex Gate (C-Gate), a speech-to-LLM bridge that constrains all speech representations to lie within the LLM's input embedding manifold with an architectural convex-hull constraint. Concretely, each frame is represented as a convex combination of token embeddings, ensuring compatibility with the pretrained LLM while preserving continuous expressivity. Across automatic speech recognition (ASR) and emotion recognition, C-Gate achieves strong joint performance, improving LibriSpeech WER by up to 48.7% relative while matching or exceeding single-task emotion accuracy. Beyond performance, our analysis reveals a key insight: information is not carried by discrete token identities, but by time-resolved trajectories in the embedding space. Causal interventions confirm that both the trajectory structure and alignment to the pretrained embedding manifold are critical for performance. These results suggest that geometry, rather than token discreteness, is the fundamental design factor in speech-to-LLM interfaces, and provide a controlled regime for studying multimodal integration in frozen LLMs. We release the checkpoint, per-sample outputs, mechanism dumps, and intervention suite for replication.

Synthetic aperture radar (SAR)-assisted optical cloud removal aims to recover surface information obscured by clouds in optical remote sensing images by exploiting complementary SAR observations. Existing multimodal fusion methods typically rely on direct spatial concatenation and pixel-wise supervision, which can propagate SAR speckle noise into optical reconstruction and lead to over-smoothed results. To address these limitations, we propose an Information Bottleneck-driven High-Fidelity Network (IB-HFN) for SAR-assisted optical cloud removal. IB-HFN employs a dual-stream backbone to preserve modality-specific representations before deep semantic fusion, thereby mitigating premature cross-modal contamination. At the fusion stage, we introduce a Spatial Information Bottleneck Fusion module that compresses SAR features through a channel-wise variational information bottleneck to suppress unstructured speckle noise. In parallel, a local-global gating mechanism predicts clear-sky regions and routes reliable optical details through a Dirac-initialized skip connection, decoupling noise suppression from texture preservation. We further develop a joint optimization strategy that integrates feature-level bottleneck regularization with image-level constraints on reconstruction accuracy, structural consistency, spectral fidelity, and contrastive sharpness. A dynamic weighting schedule balances these objectives to stabilize training and reduce hazy artifacts. Experiments on the SEN12MS-CR dataset under challenging spatio-temporal splits demonstrate that IB-HFN achieves superior structural preservation and spectral fidelity over existing methods.

Sophisticated generative speech technology can undermined the reliability of voice biometrics. While spoofing detection systems excel when assessed under in-domain conditions, generalisation to out-of-domain settings is often poor. In this paper, we show that such issues could be caused by speaker bias, where models learn individual voice traits rather than markers of manipulation or generation. We propose a teacher-student framework for speaker-invariant spoofing detection that disentangles identity without requiring speaker labels. We leverage a pre-trained speaker recognition teacher to guide a student model via a gradient reversal layer. To control the balance between suppressing cues related to voice identity with the preservation of those related to spoofing detection, we integrate a Variational Information Bottleneck. Evaluations across nine datasets show our model achieves a 25.7% relative reduction to the EER compared to the MHFA baseline.

Graph Neural Networks (GNNs) have demonstrated remarkable performance across a range of applications involving graph-structured data, particularly in high-stakes domains. However, the opaque nature of their decision-making processes limits their trustworthiness and broader adoption. Existing post-hoc explanation methods aim to improve explainability by identifying subgraphs that influence GNN predictions and adopt mixup strategies to alleviate the out-of-distribution (OOD) issue caused by using subgraphs for prediction. Yet, these approaches typically rely on soft masks, which are inherently unable to fully eliminate label-irrelevant information, allowing redundant structures to leak into the mixup process and hindering the resolution of the OOD problem, thereby degrading explanation fidelity. In this work, we propose HPME, a Hard-Perturbation Mixup Explanation framework grounded in a generalized Graph Information Bottleneck, which leverages graph pooling to extract discrete explanatory subgraphs and to yield an information-capacity bound to thoroughly compress label-irrelevant components. Furthermore, we introduce a novel mixup strategy built upon structure-level replacement, generating in-distribution explanations to effectively mitigate the distribution shift. Extensive experiments on diverse tasks demonstrate that HPME achieves state-of-the-art performance in generating robust and interpretable explanations across both synthetic and real-world datasets.

Neural audio codecs are a key component of speech processing pipelines, compressing audio into discrete tokens for downstream modeling. However, existing codecs struggle to balance reconstruction quality with token efficiency, often encoding perceptually irrelevant information such as background noise and recording artifacts at the expense of linguistically and acoustically meaningful content. We reframe audio tokenization as a selective information bottleneck problem and propose CleanCodec, a denoising audio codec which learns to encode only perceptually important features and discard imperceptible information. At just 12.5 tokens per second, CleanCodec achieves state-of-the-art tokenization efficiency, substantially outperforming existing codecs in speaker similarity and speech intelligibility. Evaluations on downstream text-to-speech and voice conversion tasks further demonstrate improved performance and up to 17x faster inference, highlighting significant efficiency gains.

Text-to-motion (T2M) generation has broad applications in character animation, virtual avatars, and human-robot interaction. Existing methods typically generate pose trajectories or motion tokens directly from language, forcing a single model to handle semantic interpretation, long-horizon structure, and low-level physical realization. This coupling makes them costly and often unreliable for long, compositional, or semantically dense prompts. We propose Text2BFM, the first framework that aligns natural language with pretrained Behavioral Foundation Models (BFMs) for T2M generation without relying on heavy end-to-end motion generators. Text2BFM operates in the latent policy space of a frozen BFM, using it as an executable motion prior. A text-aligned variational behavioral bottleneck compresses BFM policy-latent sequences into compact motion representations that are compatible with language and preserve long-horizon behavioral structure. Generation is performed in this compact behavioral manifold with a lightweight conditional generator, and the resulting latent encoded behaviors are decoded into policy latents that drive the pretrained frozen BFM. By decoupling semantic planning from motion execution, Text2BFM achieves efficient, robust T2M generation and strong performance on long, compositional textual descriptions.

Contrastive learning is effective for aligning paired views or modalities, but alignment beyond two modalities remains non-trivial and comparatively underexplored. Pairwise CLIP-style losses decompose multi-modal alignment into independent two-way comparisons and therefore do not explicitly model higher-order dependencies among multiple modalities. Recent beyond-pairwise objectives approach this problem from statistical or geometric perspectives, but arbitrary-modality alignment still lacks a principled criterion for defining what each modality should preserve and compress relative to the others. We revisit arbitrary-modality alignment through the Information Bottleneck principle. In multi-modal learning, sufficiency should preserve information predictable from the remaining modalities, while minimality should compress modality-specific information not supported by them. This naturally leads to a One-vs-All view, where each modality is characterized with respect to the remaining modalities. We propose OVA-IB, an Information Bottleneck framework for arbitrary-modality alignment. OVA-IB optimizes a tractable One-vs-All contrastive lower bound for sufficiency connected to a Dual Total Correlation-style objective, uses a parameter-free geometry-aware projection score, and derives a tractable upper-bound regularizer for minimality by bounding each representation's dependence on its own input with representation distributions induced by the remaining modalities. Experiments on classification, regression, modality-agnostic evaluation, and cross-modal retrieval benchmarks demonstrate strong and robust performance.

Recent advances in online reinforcement learning (RL) for large language models (LLMs) have demonstrated promising performance in complex reasoning tasks. However, they often exhibit an imbalanced exploration-exploitation trade-off, resulting in unstable optimization and sub-optimal performance. We introduce IB-Score, a novel metric grounded in Information Bottleneck theory that evaluates policy's exploration-exploitation balance by quantifying the trade-off between step-level reasoning diversity and mutual information shared with the correct answer. Analysis based on IB-Score shows that popular online RL approaches (e.g., GRPO) with common regularizers fail to consistently maintain balance during training with suboptimal results. To address this, we propose Information Bottleneck-driven Tree-based Policy Optimization (IB-TPO), a principled framework that formulates IB-Score as a fine-grained optimization objective and utilizes a novel IB-guided tree sampling strategy that not only improves the efficiency of online sampling with 50% more trajectories under the same token budget, but also reuses the tree structure for effective IB-Score Monte Carlo estimation. Extensive experiments across standard benchmarks show that our method significantly outperforms GRPO baseline by 2.9% to 3.6% and also outperforms other state-of-the-art online RL approaches. Our code is available at https://github.com/alibaba/EfficientRL.

Message-passing neural networks (MPNNs) often suffer from an information bottleneck when capturing long-range dependencies, leading to the oversquashing (OSQ) phenomenon. Alongside spatial connectivity enrichment (e.g., rewiring), recent studies have shown that spectral filtering can yield strong long-range learning outcomes, as spectral operators enable global information mixing that alleviates OSQ. These approaches achieve this either by stabilizing the Jacobian energies in deep propagation or by guaranteeing OSQ mitigation under strong theoretical assumptions. We revisit these conclusions and show that the associated Jacobian sensitivity lower bound is generally difficult to achieve in practice. We then propose S$^3$GNN, which mitigates OSQ without such restrictive assumptions by lightweightly reintroducing omitted components with substantially lower computational complexity, while standard stability constraints on feature transformations remain effective under our new dynamics. Extensive experiments across diverse domains (e.g., long-range benchmarks, KGQA, and mesh-based fluid dynamics) demonstrate that S$^3$GNN achieves up to an order-of-magnitude error reduction with up to 50% fewer parameters. Our code can be found in https://github.com/EEthanShi/S3-GNN.git.

Multivariate time series (MTS) classification is foundational to pervasive computing and financial analysis, yet existing multi-scale paradigms are often constrained by suboptimal representation fidelity. We identify two critical bottlenecks: temporal non-causality in standard encoders that induces temporal confounding in non-stationary dynamics, and the absence of explicit channel saliency mechanisms that allows noise to contaminate the latent space. To address these challenges, we propose the Causal Attention and Spatio-temporal Encoder Network (CASE-NET), an architecture designed for structural manifold pre-conditioning. CASE-NET synergizes a Causal Temporal Encoder, which enforces physical arrow-of-time constraints via masked self-attention and causal convolutions, with an Adaptive Channel Recalibration module functioning as an information bottleneck to suppress detrimental noise. Comprehensive evaluations across six heterogeneous domains demonstrate that CASE-NET establishes new state-of-the-art benchmarks on four tasks, achieving a peak accuracy of 98.6% on the AWR dataset and superior robustness in non-stationary regimes.

Large Language Models have achieved strong performance on reasoning tasks with objective answers by generating step-by-step solutions, but diagnosing where a multi-step reasoning trace might fail remains difficult. Confidence estimation offers a diagnostic signal, yet existing methods are restricted to final answers or require internal model access. In this paper, we introduce Stepwise Confidence Attribution (SCA), a framework for closed-source LLMs that assigns step-level confidence based only on generated reasoning traces. SCA applies the Information Bottleneck principle: steps aligning with consensus structures across correct solutions receive high confidence, while deviations are flagged as potentially erroneous. We propose two complementary methods: (1) NIBS, a non-parametric IB approach measuring consistency without graph structures, and (2) GIBS, a graph-based IB model that learns subgraphs through a differentiable mask to capture logical variability. Extensive experiments on mathematical reasoning and multi-hop question answering show that SCA reliably identifies low-confidence steps strongly correlated with reasoning errors. Moreover, using step-level confidence to guide self-correction improves the correction success rate by up to 13.5% over answer-level feedback.

It is infeasible to encompass all possible disturbances within the training dataset. This raises a critical question regarding the robustness of Vision-Language-Action (VLA) models when encountering unseen real-world visual disturbances, particularly under imperfect visual conditions. In this work, we conduct a systematic study based on recent state-of-the-art VLA models and reveal a significant performance drop when visual disturbances absent from the training data are introduced. To mitigate this issue, we propose a lightweight adapter module grounded in information theory, termed the Information Bottleneck Adapter (IB-Adapter), which selectively filters potential noise from visual inputs. Without requiring any extra data or augmentation strategies, IB-Adapter consistently improves over the baseline by an average of 30%, while adding fewer than 10M parameters, demonstrating notable efficiency and effectiveness. Furthermore, even with a 14x smaller backbone (0.5B parameters) and no pre-training on the Open X-Embodiment dataset, our model StableVLA achieves robustness competitive with 7B-scale state-of-the-art VLAs. With negligible parameter overhead (<10M), our approach maintains accuracy on long-horizon tasks and surpasses OpenPi under both synthetic and physical visual corruptions.

Coordination graphs are a central abstraction in cooperative multi-agent reinforcement learning (MARL), yet existing sparse-graph learners lack a theoretically grounded mechanism to decide which edges should exist and how much information each edge should carry. Current methods rely on heuristic criteria that offer no formal guarantee on the learned topology, and no principled way to allocate different communication capacities to structurally different agent relationships. To address this, we propose Heterogeneous Information-Bottleneck Coordination Graphs (HIBCG), which learns a group-aware sparse graph in which both edge existence and message capacity are theoretically justified. With the graph information bottleneck (GIB) serving as the underlying tool, HIBCG first constructs a group-aligned block-diagonal prior that provides a closed-form criterion for edge retention -- determining which edges should exist and at what density per group block -- and then controls per-agent feature bandwidth on the resulting topology, compressing messages to retain only task-relevant content. We prove that the group-aligned prior strictly tightens the variational bound on topology learning, that the objective decomposes per group block, enabling differential edge control, and that capacity allocation follows a water-filling principle.

Generative Recommendation (GenRec) models reformulate recommendation as a sequence generation task, representing items as discrete Semantic IDs used symmetrically as both inputs and prediction targets. We identify a critical dual-stage information bottleneck in this design: (1) the Input Bottleneck, where lossy quantization degrades fine-grained semantics, while popularity bias skews the learned representations toward frequent items, and (2) the Output Bottleneck, where imprecise discrete targets limit supervision quality. To address these issues, we propose AsymRec, an asymmetric continuous-discrete framework that decouples input and output representations. Specifically, Multi-expert Semantic Projection (MSP) maps continuous embeddings into the Transformer's hidden space via expert-specialized projections, preserving semantic richness and improving generalization to infrequent items. Multi-faceted Hierarchical Quantization (MHQ) constructs high-capacity, structured discrete targets through multi-view and multi-level quantization with semantic regularization, preventing dimensional collapse while retaining fine-grained distinctions. Extensive experiments demonstrate that AsymRec consistently outperforms state-of-the-art generative recommenders by an average of 15.8 %. The code will be released.

A central objective in multimodal learning is to capture synergy: task-relevant information that arises only from the joint use of multiple modalities, and is not available from any single modality alone. While most approaches operate at the architectural level through larger or more complex fusion models, we propose a complementary axis: shaping the training objective itself. Standard training often emphasizes unimodal or redundant information, falling short on examples that require cross-modal reasoning. We formalize multimodal synergy through information theory and introduce the Synergistic Information Bottleneck (SynIB), a scalable objective that targets synergy directly. To prioritize learning synergy, SynIB motivates the model to predict accurately from all modalities while penalizing confidence when information from any modality is withheld. Alongside the standard task loss, the model runs forward passes with one modality masked at a time and is penalized for remaining confident, which would indicate reliance on unimodal cues rather than cross-modal interactions. We validate SynIB in two regimes. On synthetic XOR tasks where the ground-truth synergy is known by construction, standard training fails to recover it while SynIB does. On five real-world benchmarks, including three MultiBench affective tasks, Hateful Memes with CLIP-ViT and DeBERTa backbones, and a controllable irony extension of CREMA-D we introduce, SynIB improves accuracy on synergy-dependent examples by up to 7.8% and overall accuracy by up to 3.8%.

Detecting out-of-distribution (OOD) samples is critical for safe deployment of neural networks in safety-critical applications. While maximum softmax probability (MSP) provides a simple baseline, it lacks theoretical grounding and suffers from miscalibration. We propose VNDUQE (VIB-based Novelty Detection and Uncertainty Quantification for Nondestructive Evaluation), which investigates novelty detection through the Deep Variational Information Bottleneck (VIB), which explicitly constrains information flow through learned representations. We train VIB models on MNIST with held-out digit classes and evaluate OOD detection using information-theoretic metrics: KL divergence and prediction entropy. Our results reveal complementary detection signals: KL divergence achieves perfect detection (100% AUROC on noise) on far-OOD samples (noise, domain shift), while prediction entropy excels at near-OOD detection (94.7% AUROC on novel digit classes). A parallel detection strategy combining both metrics achieves 95.3% average AUROC and 92% true positive rate at 5% false positive rate, which is a 32 percentage point improvement over baseline MSP (85.0% AUROC, 60.1% TPR). Compression via the information bottleneck principle ($β=10^{-3}$) reduces Expected Calibration Error by 38%, demonstrating that information-theoretic constraints produce fundamentally more reliable uncertainty estimates. These findings directly support active learning with expensive computational oracles, where well-calibrated novelty detection enables principled threshold selection for oracle queries.

Synthetic data becomes crucial for large language model training, but its effectiveness is highly inconsistent. We provide an information-theoretic account of this inconsistency: synthetic data improves a model only when the generation-training loop is information-open, i.e., shaped by external signals (verifiers, environments, or rubrics) that inject task-relevant information beyond the model's current distribution. When the loop is information-closed (relying on the model's own outputs without such signals), the data processing inequality ensures that task-relevant information can only decrease, making collapse a predicted outcome. Among information-open pipelines, both efficiency and generalization hinge on the meta-level of supervision: a coarser signal such as binary correctness treats all acceptable outputs as equivalent, so the behavior it teaches is not tied to any particular domain or surface form and generalizes naturally across tasks and domains. These observations lead to a guiding thesis: learning preferentially converges to the most information-efficient signal component available, which accelerates learning when that component is the intended one, but causes reward hacking when a spurious pattern happens to be simpler.

The evolution of 6G networking toward agentic AI networking (AgentNet) systems requires a shift from traditional data pipelines to task-aware, agentic AI-native communication solutions. Emergent communication, a novel communication paradigm in which autonomous agents learn their own signaling protocols through interaction, is increasingly viewed as a promising solution to address the challenges posed by existing rigid, predefined protocol-based networking architecture. However, most existing emergent communication frameworks fail to account for physical networking constraints, such as bandwidth and computational complexity, and often lack a rigorous information-theoretical foundation. To address these challenges, this paper introduces a novel emergent communication framework that facilitates collaborative task-solving among heterogeneous agents through an information-theoretic lens. We propose a novel joint loss function that unifies the optimization of decision-making functions and the learning of communication signaling. Our proposed solution is grounded on the multi-agent and multi-task distributed information bottleneck (DIB) theory, which allows the quantification of the fundamental trade-off between task-relevant information representation and computational complexity. We further provide theoretical generalization bounds of the emergent communication protocol during decentralized inference across unseen environmental states. Experimental validation on a real-world hardware prototype confirms that our proposed framework significantly improves generalization performance, compared to the state-of-the-art solutions.

Cooperative multi-agent reinforcement learning agents that act on partial local observations face a fundamental information bottleneck: the knowledge needed to select jointly optimal actions is scattered across the team, yet each agent must commit to a decision without access to its teammates' observations, intentions, or chosen actions. Existing methods either ignore this bottleneck, compress it into a scalar mixing signal, or route around it with learned communication channels. Framing action coordination as a problem of structured information integration among agents, we propose \textit{structured agent coordination via holistic information integration}, or SACHI, in which graph transformer convolutions over an inter-agent coordination graph enrich each agent's representation with receiver-sensitive, content-dependent signals from teammates prior to action selection. We evaluate SACHI across five cooperative tasks spanning spatial, communicative, and adversarial coordination challenges against twelve baselines. SACHI consistently matches or outperforms the best baseline on every task, and rigorous aggregate statistical analyses, including normalized metrics with bootstrap confidence intervals, Friedman ranking, and performance profiling, confirm that this advantage is statistically significant, robust across environments, and not attributable to increased model capacity. Parameter-matched ablations further trace the source of the gains to a single architectural property: the degree of content-dependence in the message-passing operator.

Large language models (LLMs) are reshaping how knowledge is produced, with increasing reliance on AI systems for generation, summarization, and reasoning. While prior work has studied cognitive offloading in humans and model collapse in recursive training, these effects are typically considered in isolation. We propose a unified perspective: humans and language models form a coupled dynamical system linked by a feedback loop of usage, generation, and retraining. We introduce a minimal model with three variables -- human cognition, data quality, and model capability -- and show that this feedback can give rise to distinct dynamical regimes. Our analysis identifies three regimes: co-evolutionary enhancement, fragile equilibrium, and degenerative convergence. Through a simple simulation, we demonstrate that increasing reliance on AI can induce a transition toward a low-diversity, suboptimal equilibrium. From an information-theoretic perspective, this transition corresponds to an emergent information bottleneck in the human-AI loop, where entropy reduction reflects loss of diversity and support under closed-loop feedback rather than beneficial compression. These results suggest that the trajectory of AI systems is shaped not only by model design, but by the dynamics of human-AI co-evolution.

Black-box optimization in science and engineering often comes with side information: experts, simulators, pretrained predictors, or heuristics can suggest which candidates look promising. This information can accelerate search, but it can also be biased, input-dependent, or misleading. Feedback-aware BO methods typically handle one task at a time, limiting their ability to generalize over multiple sources of feedback. In-context optimizers address cross-task adaptation, but usually assume that optimization history is the only available signal at test time. We study feedback-informed in-context black-box optimization (FICBO), where a pretrained optimizer conditions on both the observed history and cheap auxiliary feedback for the current candidate set. We introduce a structured feedback prior that models how feedback sources vary in their access, relevance, and distortion relative to the true objective, and use it to pretrain a feedback-aware transformer. At test time, the model estimates source reliability in context by comparing observed objective values with auxiliary signals, improving query selection. On synthetic and real-world tasks, FICBO effectively exploits informative feedback while remaining robust to weak or misleading sources, improving over other baselines. Empirical investigations further illustrate how the model perceives test-time sources, offering insights into its interpretability and decision-making process.

Optimizing the communication structure of large language model based multi-agent systems (LLM-MAS) has been shown to improve downstream performance and reduce token usage. Existing methods typically rely on randomly sampled training tasks. However, tasks may differ substantially in difficulty and domain, and thus they are not equally informative for updating communication structure, making optimization under limited training budgets often unstable and highly sensitive to the particular training set. To actively identify the most valuable tasks for communication-structure optimization, we propose an ensemble-based information-theoretic task selection framework. The proposed method estimates task informativeness by how much a candidate task changes the distribution over graph parameters, using ensemble Kalman inversion as an efficient and derivative-free approximation of the corresponding Bayesian update. The resulting estimator is especially suitable for black-box and noisy multi-agent systems. To enhance scalability, we construct a compact candidate pool through embedding-based representative selection and combine the informative selection with surrogate modeling and batch Thompson sampling. We validate our method in both benign settings and settings with agent attacks, demonstrating its effectiveness for communication-structure optimization under constrained computational budgets.

Self-supervised learning has achieved remarkable empirical success in learning robust representations without explicit labels, most recently demonstrated within the framework of Joint-Embedding Predictive Architectures (JEPA). However, a fundamental question remains: what analytical principles drive these encoders toward specific distributional states? In this paper, we demonstrate that the preference for normal distributions in self-supervised encoders is a direct consequence of the Information Bottleneck (IB) principle. By recasting the IB objective as a rate-distortion problem over the predictive manifold, we provide a theoretical basis for why optimal, target-neutral, latent representations should tend towards isotropic Gaussian states. Under this framework, we show that latent representations correspond to soft clustering of inputs sharing similar predictive distributions, organized within a natural simplex structure. This perspective unifies a wide range of existing supervised and less-supervised objectives and provides a principled explanation for commonly used regularization schemes. Furthermore, we derive practical loss objectives that approximate this structure and demonstrate their effectiveness on standard benchmarks. Ultimately, our framework offers a geometric lens to understanding representation collapse and it establishes a mathematical system for regularization strategies to be used to ensure high-entropy, informative embeddings in modern self-supervised models.

Key-value (KV) caching is essential for large language model inference, yet its memory overhead poses a critical bottleneck for long-context generation. Existing eviction policies predominantly rely on empirical heuristics, lacking a rigorous theoretical foundation. This work rethinks KV cache eviction through the lens of the Information Bottleneck principle. Under a linear-Gaussian surrogate of attention, we derive a closed-form mutual information objective that characterizes the effective information capacity of a retained KV cache subset. This formulation reveals that a wide range of existing eviction strategies can be interpreted as different approximations of the same capacity-maximization principle. Guided by this insight, we introduce CapKV, a capacity-aware eviction method that directly targets information preservation via a log-determinant approximation using statistical leverage scores. This approach replaces heuristic selection with a theoretically grounded mechanism that preserves the maximum predictive signal. Extensive experiments across multiple models and long-context benchmarks show that CapKV consistently outperforms prior methods, achieving a better trade-off between memory efficiency and generational fidelity.

Identifying the dynamical state variables of a system from high-dimensional observations is a central problem across physical sciences. The challenge is that the state variables are not directly observable and must be inferred from raw high-dimensional data without supervision. Here we introduce DySIB (Dynamical Symmetric Information Bottleneck) as a method to learn low-dimensional representations of time-series data by maximizing predictive mutual information between past and future observation windows while penalizing representation complexity. This objective operates entirely in latent space and avoids reconstruction of the observations. We apply DySIB to an experimental video dataset of a physical pendulum, where the underlying state space is known. The method, with hyperparameters of the learning architecture set self-consistently by the data, recovers a two-dimensional representation that matches the dimensionality, topology, and geometry of the pendulum phase space, with the learned coordinates aligning smoothly with the canonical angle and angular velocity. These results demonstrate, on a well-characterized experimental system, that predictive information in latent space can be used to recover interpretable dynamical coordinates directly from high-dimensional data.

Resting-state functional magnetic resonance imaging (fMRI) has emerged as a cornerstone for psychiatric diagnosis, yet most approaches rely on pairwise brain cortical or sub-cortical connectivities that overlooks higher-order interactions (HOIs) central to complex brain dynamics. While hypergraph methods encode HOIs through predefined hyperedges, their construction typically relies on heuristic similarity metrics and does not explicitly characterize whether interactions are synergy- or redundancy-dominated. In this paper, we introduce $O$-information, a signed measure that characterizes the informational nature of HOIs, and integrate third- and fourth-order $O$-information into a unified multi-view information bottleneck framework for fMRI-based psychiatric diagnosis. To enable scalable $O$-information estimation, we further develop two independent acceleration strategies: a Gaussian analytical approximation and a randomized matrix-based Rényi entropy estimator, achieving over a 30-fold computational speedup compared with conventional estimators. Our tri-view architecture systematically fuses pairwise, triadic, and tetradic brain interactions, capturing comprehensive brain connectivity while explicitly penalizing redundancy. Extensive evaluation across four benchmark datasets (REST-meta-MDD, ABIDE, UCLA, ADNI) demonstrates consistent improvements, outperforming 11 baseline methods including state-of-the-art graph neural network (GNN) and hypergraph based approaches. Moreover, our method reveals interpretable region-level synergy-redundancy patterns which are not explicitly characterized by conventional hypergraph formulations.

Vision-Language Models (VLMs) achieve strong multimodal performance but are costly to deploy, and post-training quantization often causes significant accuracy loss. Despite its potential, quantization-aware training for VLMs remains underexplored. We propose GRACE, a framework unifying knowledge distillation and QAT under the Information Bottleneck principle: quantization constrains information capacity while distillation guides what to preserve within this budget. Treating the teacher as a proxy for task-relevant information, we introduce confidence-gated decoupled distillation to filter unreliable supervision, relational centered kernel alignment to transfer visual token structures, and an adaptive controller via Lagrangian relaxation to balance fidelity against capacity constraints. Across extensive benchmarks on LLaVA and Qwen families, our INT4 models consistently outperform FP16 baselines (e.g., LLaVA-1.5-7B: 70.1 vs. 66.8 on SQA; Qwen2-VL-2B: 76.9 vs. 72.6 on MMBench), nearly matching teacher performance. Using real INT4 kernel, we achieve 3$\times$ throughput with 54% memory reduction. This principled framework significantly outperforms existing quantization methods, making GRACE a compelling solution for resource-constrained deployment. Code and data are available at: https://github.com/ForeverBlue816/GRACE.

Disentangled representation learning aims to map independent factors of variation to independent representation components. On one hand, purely unsupervised approaches have proven successful on fully disentangled synthetic data, but fail to recover semantic factors from real data without strong inductive biases. On the other hand, supervised approaches are unstable and hard to scale to large attribute sets because they rely on adversarial objectives or auxiliary classifiers. We introduce \textsc{XFactors}, a weakly-supervised VAE framework that disentangles and provides explicit control over a chosen set of factors. Building on the Disentangled Information Bottleneck perspective, we decompose the representation into a residual subspace $\mathcal{S}$ and factor-specific subspaces $\mathcal{T}_1,\ldots,\mathcal{T}_K$ and a residual subspace $\mathcal{S}$. Each target factor is encoded in its assigned $\mathcal{T}_i$ through contrastive supervision: an InfoNCE loss pulls together latents sharing the same factor value and pushes apart mismatched pairs. In parallel, KL regularization imposes a Gaussian structure on both $\mathcal{S}$ and the aggregated factor subspaces, organizing the geometry without additional supervision for non-targeted factors and avoiding adversarial training and classifiers. Across multiple datasets, with constant hyperparameters, \textsc{XFactors} achieves state-of-the-art disentanglement scores and yields consistent qualitative factor alignment in the corresponding subspaces, enabling controlled factor swapping via latent replacement. We further demonstrate that our method scales correctly with increasing latent capacity and evaluate it on the real-world dataset CelebA. Our code is available at \href{https://github.com/ICML26-anon/XFactors}{github.com/ICML26-anon/XFactors}.

We study latent geometry as an explicit component of representation quality in data-scarce learning. For an encoder (φ), we define (Q_{β,γ}(φ)=I(φ(X);Y)-β\mathcal C(φ)-γd_{\mathrm{int}}(φ)), combining task-relevant information with penalties for curvature and intrinsic latent dimension. Thus geometry becomes part of the bottleneck criterion, not only a post hoc diagnostic. Under smooth-manifold, loss-transfer, and estimator-concentration assumptions, we derive non-asymptotic low-label generalization bounds where intrinsic dimension and covering complexity enter explicitly. We characterize the information--geometry frontier and prove empirical-surrogate consistency. The analysis links encoder geometry to learning through latent covering numbers, loss-class entropy, and uniform deviation. We instantiate the theory as \texttt{V-GIB}, adding curvature and dimension penalties to variational bottleneck training. Real low-label benchmarks compare \texttt{V-GIB} with ERM, VIB, and ablations across (1%)--(20%) label fractions. Results show improved performance and reduced geometric complexity in several regimes, especially FashionMNIST and CIFAR-10, while confirming that no fixed regularizer is universally dominant.

Knowledge distillation transfers knowledge from large teacher models to more compact student networks. The standard approach minimizes the Kullback-Leibler (KL) divergence between the probabilistic outputs of the teacher and student, aligning predictions but neglecting the structural relationships encoded within the teacher's internal representations. Recent advances have adopted contrastive learning objectives to address this limitation; however, such instance-discrimination-based methods induce a "class collision problem", in which semantically related samples are inappropriately pushed apart despite belonging to similar classes. To overcome this, we propose Relational Representation Distillation (RRD) that preserves the relative relationships among instances rather than enforcing absolute separation. Our method introduces separate temperature parameters for teacher and student distributions, with a sharper teacher (low $τ_t$) emphasizing primary relationships and a softer student (high $τ_s$) maintaining secondary similarities. This dual-temperature formulation creates an implicit information bottleneck that preserves fine-grained relational structure while avoiding the over-separation characteristic of contrastive losses. We establish theoretical connections showing that InfoNCE emerges as a limiting case of our objective when $τ_t \rightarrow 0$, and empirically demonstrate that this relaxed formulation yields superior relational alignment and generalization across classification and detection tasks.