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Search papers from 30+ top conferences, including NeurIPS, ICLR, ICML, CVPR, ACL and AAAI. Filter by keyword, then open any paper for its abstract, authors and links.

NeurIPS 2026

Persistent-Transient Policy Evaluation for Markov Chains via Minimal Peripheral Quotients

Yang Xu, Vaneet Aggarwal

We study fixed-policy evaluation for finite Markov chains that may be reducible and periodic. Classical evaluation methods with gain and bias decomposition are not always diagnostic: the gain records only invariant Ces\`aro averages, while persistent phase-dependent behavior is absorbed into the bias together with genuinely transient effects. We identify the real peripheral invariant subspace $\mathcal{K}(P)$ of the transition matrix $P$ as the source of this ambiguity. Quotienting by $\mathcal{K}(P)$ is the minimal exact quotient that removes all non-decaying modes and makes the remaining dynamics strictly stable. After choosing a gauge projection $\Pi$ with kernel $\mathcal{K}(P)$, the reward admits a unique decomposition $r = g_\Pi^\star + (I-P)v_\Pi^\star$, where $g_\Pi^\star$ is a persistent regime profile and $v_\Pi^\star$ is a gauge-fixed transient component. An exact comparison with classical normalized gain and bias shows that the new pair reallocates the same information so that all persistent modes are represented in $g_\Pi^\star$ and $v_\Pi^\star$ is transient. This decomposition reconstructs finite-horizon returns, recovers statewise average reward, admits a transient-cost interpretation, and yields a stable estimator under a generative model.

NeurIPS 2026

Permute-then-Adapt: Weak-to-Strong Contrastive Image--Text Adaptation

Jinhao Li, Sarah Erfani, Lei Feng, Guangrui Li, James Bailey, Feng Liu

Image--text alignment models such as CLIP are typically trained with contrastive learning, where unpaired examples are treated as strict negatives. While this assumption introduces noise by penalising semantically related pairs, existing solutions often rely on heuristic similarity thresholds that lack statistical grounding and sensitivity to dataset-specific noise distributions. In this paper, we propose **Permute-then-Adapt (PTA)**, a framework that leverages efficient *weak models* to identify missed positives, while enforcing *statistical control* to reject random associations. Unlike standard distillation or arbitrary thresholding, PTA estimates the null distribution of the weak teacher's similarities via permutation testing, ensuring selected pairs are *statistically distinguishable from the distribution of random pairings* at level $\alpha$. The calibrated positive set is then trained against by a single multi-positive contrastive objective: each anchor maximises the total probability mass it assigns to its positive set. We further demonstrate that the calibration can be pre-computed offline using the weak model, so training overhead is negligible compared to standard baselines. Extensive experiments show that PTA consistently outperforms heuristic soft-label approaches on object recognition and cross-modal retrieval, while exhibiting superior data efficiency.

NeurIPS 2026

Permutation-Invariant Spectral Learning via Dyson Diffusion

Tassilo Schwarz, Cai Dieball, Constantin Kogler, Renaud Lambiotte, Arnaud Doucet, Aljaz Godec, George Deligiannidis

Diffusion models are central to generative modeling and have been adapted to graphs by diffusing adjacency matrix representations. The challenge of having up to $n!$ such representations for graphs with $n$ nodes is only partially mitigated by using permutation-equivariant learning architectures. Despite their computational efficiency, existing graph diffusion models struggle to distinguish certain graph families and their spectra, unless graph data are augmented with ad hoc features. This shortcoming stems from enforcing the inductive bias within the learning architecture. In this work, we leverage random matrix theory to analytically extract the spectral properties of the diffusion process, allowing us to push most of the inductive bias from the architecture into the dynamics. Building on this, we introduce the Dyson Diffusion Model, which employs Dyson's Brownian motion to capture the spectral dynamics of an Ornstein-Uhlenbeck process on the adjacency matrix. Furthermore, conditioned on the spectral dynamics, we formulate a Lie group diffusion, appropriately modeling the remaining degrees of freedom. Strikingly, the resulting learning problem becomes permutation invariant at the Lie algebra level. We demonstrate that the Dyson Diffusion Model learns graph spectra accurately and outperforms existing graph diffusion models.

NeurIPS 2026

Permutation Sensitivity in t-SVD-based Multi-view Clustering

Jintian Ji, Yanjun Zhang, He Zhang, Leo Yu Zhang, Cong Wang, Shirui Pan

Tensor Singular Value Decomposition (t-SVD) has achieved strong empirical performance in multi-view clustering (MVC) and its incomplete setting (IMVC). However, the success of this framework heavily relies on the implicit dependency of its Fourier transform on the sample sequence, which raises serious concerns regarding sample-permutation sensitivity. To address this issue, we first formulate the permutation sensitivity in multi-view clustering by providing rigorous definitions of invariance at both the outcome level and the representation level. Secondly, by revealing the potential structural risks associated with the fixed Fourier basis, we propose two plug-and-play strategies: (1) an Order-Restoration strategy (K-OR), designed to reconstruct a locally smooth signal favored by the Fourier transform; and (2) an equivariant t-SVD framework (Cor-SVD), which fundamentally resolves the sensitivity of the Fourier transform by replacing fixed bases with data-dependent, equivariant transforms. Finally, we design a controlled permutation evaluation protocol to verify the robustness of tensorial clustering models. Extensive experiments demonstrate the significant performance variability of existing t-SVD-based methods under sample permutations, whereas our approaches substantially improve their permutation robustness while maintaining competitive clustering performance. These findings reveal critical vulnerabilities in current tensorial clustering benchmarks and underscore the necessity of the proposed method for achieving robust performance and reliable evaluation.

NeurIPS 2026

PermuQuant: Lowering Per-Group Quantization Error by Reordering Channels for Diffusion Models

Yongsen Cheng, Kai Liu, Kaiwen Tao, Junxian Li, Zhixin Wang, Zhikai Chen, Renjing Pei, Yulun Zhang

Large-scale visual generative models have achieved remarkable performance. However, their high computational and memory costs make deployment challenging in resource-constrained scenarios, such as interactive applications and personal single-GPU usage. Post-training quantization (PTQ) offers a practical solution by compressing pretrained models without expensive retraining. However, existing PTQ methods still suffer from severe quality degradation under extremely low-bit settings. In this paper, we identify channel ordering as an important but underexplored factor in per-group quantization. In this setting, each contiguous group shares one quantization scale. When channels with very different statistics are placed in the same group, the scale can be dominated by outliers and cause large quantization errors. Based on this observation, we propose PermuQuant, a simple and effective PTQ framework for low-bit diffusion models. PermuQuant sorts channels by a joint second-moment criterion before per-group quantization, placing channels with similar activation and weight statistics into the same group. It further uses a calibration-based acceptance rule to apply reordering only when the selected permutation reduces quantization error on calibration data. The selected permutations are absorbed into adjacent modules or applied to weights offline, avoiding explicit runtime permutation operations. Extensive experiments on multiple large diffusion models show that PermuQuant consistently reduces quantization error and outperforms existing PTQ baselines. On FLUX.1-dev with an NVIDIA RTX 5090, PermuQuant achieves up to a 1.8$\times$ single step speedup and reduces the DiT memory footprint by 3.5$\times$ under W4A4 NVFP4 quantization.

NeurIPS 2026

Permit: Permission-Aware Representation Intervention for Controlled Generation in Large Language Models

Pengcheng Sun, Lan Zhang, Zhaopeng Zhang, Jiewei Lai, Chen Tang

Large language models (LLMs) are increasingly deployed in enterprise settings where they handle sensitive documents and user context, raising acute concerns over security and controllability. Conventional access control regulates whether information is accessible to the model, yet leaves how the model uses that information at generation time largely unconstrained: once sensitive content enters the context, outputs may still drift beyond a user's authorized scope. We present Permit, a novel permission-aware representation intervention framework that closes this gap by enforcing fine-grained control directly on the model's hidden states. Through exploratory analysis, we find that permission conditions induce hidden-state shifts that are (i) separable across permissions and (ii) concentrated in a small set of dominant directions. Permit exploits this geometry in two stages: it first identifies a permission-sensitive subspace from activation differences across permission conditions, and then performs lightweight interventions within this subspace to steer generation, with two concrete instantiations (offset-based and gated). Both operate atop a frozen backbone with only a handful of permission-specific parameters, achieving precise control with minimal overhead. Experimental results demonstrate that \textsc{Permit} performs better than the state-of-the-art method across multiple permission settings while driving information leakage to near zero, achieving over \(18\%\) F1-score improvement with \(>98\%\) fewer trainable parameters.

NeurIPS 2026

PermaVid: Consistent Video Generation Across Edits via Disentangled Context Memory

Shuai Yang, Bingjie Gao, Ziwei Liu, Jiaqi Wang, Dahua Lin, Tong Wu

Consistent video generation under editing operations requires persistence: when edits modify scene appearance or layout, subsequent generations should remain coherent across time and viewpoints. However, existing memory designs struggle to maintain long-term consistency after such modifications, as stored contexts may become outdated or invalid. To address this, we propose PermaVid, a novel framework built upon a multi-modal context memory that disentangles spatial context into semantic appearance and geometric structure, together with an edit-aware memory update and retrieval strategy that keeps memory evolution aligned with subsequent observations. Specifically, we develop two complementary memory banks: an RGB context memory that captures appearance-aware observations while implicitly encoding geometry, and a depth context memory that preserves geometry-only structure disentangled from semantics. Building on this design, we introduce a memory-guided video generation model that performs multi-modal feature fusion under reference conditions drawn from mixed-modality memory contexts. Experiments demonstrate that our method maintains strong long-term semantic and structural consistency after edits, significantly outperforming state-of-the-art methods.

NeurIPS 2026

Periodic Complex Stochastic Processes for Retrieving Atomic Structures of Unknown Matters

Gyoung S. Na, Chanyoung Park

Retrieving unknown atomic structures from observable analytical spectra or images remains a long-standing challenge across natural sciences. However, retrieval accuracy of existing retrieval methods on analytical data remains suboptimal because they have overlooked the underlying periodic quantum mechanical perturbations of non-equilibrium atomic structures behind analytical data. This paper proposes a periodic complex stochastic process (PCSP) that models such periodic perturbations and establishes theoretical backgrounds of periodic stochastic process in the complex-valued domain, including its sample diversity, process length, and periodicity. Finally, we develop a complex-valued cross-modal retrieval (CVCR) by integrating PCSP with cross-modal retrieval frameworks. CVCR outperformed existing cross-modal retrieval methods in cross-modal retrieval tasks of real-world analytical chemistry. Moreover, CVCR achieved state-of-the-art retrieval accuracy in zero-shot settings on 40 million of molecules.

NeurIPS 2026

Perfect Parallelization in Mini-Batch SGD with Classical Momentum Acceleration

Sachin Garg, Michal Derezinski

Accelerating stochastic gradient methods with classical momentum schemes, such as Polyak's heavy ball, has proven highly successful in training large-scale machine learning models, particularly when combined with the hardware acceleration of large mini-batch computations. Yet, the effect of classical momentum on stochastic mini-batch optimization has been poorly understood theoretically, with prior works requiring strong noise assumptions and extremely large mini-batches. In this work, we develop a general theory of stochastic momentum acceleration for optimizing over quadratics in the interpolation regime, a popular abstraction for studying deep learning dynamics which also includes classical methods such as randomized Kaczmarz and coordinate descent. Our framework encompasses both heavy ball and Nesterov-style momentum, allows for arbitrary mini-batch sizes, and makes minimal assumptions on the stochastic noise. In particular, we show that acceleration from classical momentum is directly proportional to the gradient mini-batch size (up to a natural saturation point), thereby enabling perfect parallelization of mini-batch computations. Our theory also provides a simple choice for the momentum parameter, which is shown to be effective empirically.

NeurIPS 2026

Perception for Action in Latent World Models

Petr Ivashkov, Randall Balestriero, Bernhard Scholkopf

Perception for action suggests that representations of the world should be shaped not by visual fidelity alone, but by their relevance for actions. At the same time, latent JEPA-style world models advocate learning compact predictive states from high-dimensional observations to facilitate the prediction of future states, but end-to-end training of these models is nontrivial because representations may collapse if our only goal is to construct a latent state that is easy to predict. We show that a suitable inverse dynamics regularization addresses both issues: it is an effective anti-collapse mechanism that induces action-aligned representations. By forcing latent states to preserve information about the action underlying a transition, it biases the model toward the controllable degrees of freedom of the environment while discarding uncontrollable distractors. This yields stable latent world models trained end-to-end from offline, reward-free trajectories, without frozen encoders, exponential moving averages, or complex latent regularizers. Empirically, the learned latent spaces are compact, interpretable, and enable competitive planning performance across simple 2D and 3D control tasks.

NeurIPS 2026

Perception Without Engagement: Dissecting the Causal Discovery Deficit in LMMs

Jiafeng Liang, Zhihao Zhu, Zihan Zhang, Baoqi Ren, Tao Ren, Shixin Jiang, Runxuan Liu, Ming Liu, See-Kiong Ng, Bing Qin

Although Large Multimodal Models (LMMs) have achieved strong performance on general video understanding, their susceptibility to textual prior shortcuts during causal discovery has been recognized as a critical deficit. The underlying mechanisms of this phenomenon remain incompletely understood, as existing benchmarks only measure response accuracy without revealing the sources and extent of the deficit. We introduce ProCauEval, a perturbation-based evaluation protocol that shifts from outcome assessment to mechanism diagnosis, probing causal discovery through five controlled configurations that systematically manipulate visual and textual modalities to decompose their respective contributions to model behavior and dissect the failure modes. Evaluating 17 mainstream LMMs, we find that models faithfully perceive video content yet systematically underexploit it during causal reasoning. We further observe that stronger post-training amplifies rather than mitigates textual prior reliance, and that higher baseline performance correlates with greater fragility under perturbation. To address these, we propose Anti-Distillation Policy Optimization (ADPO), a reinforcement learning framework built on negative teacher alignment, which augments GRPO by explicitly pushing the policy away from a prior-only counterfactual teacher induced by visual corruption. Specifically, ADPO maximizes the divergence between the policy distributions conditioned on the original and visually corrupted inputs, thereby forcing the model to ground its reasoning in visual evidence rather than textual shortcuts. Extensive experiments show that ADPO improves visual engagement without sacrificing fundamental comprehension, thus offering a preliminary step toward reliable causal discovery.

NeurIPS 2026

Perceive-then-Plan: Layout-as-Policy for Monocular 3D Scene Layout Estimation

Junwei Zhou, Yu-wing Tai

Building structured 3D scene layouts from a single image requires reconciling visual observations with physical and spatial constraints, a challenge that is difficult to address with direct prediction alone. In this work, we formulate monocular 3D layout estimation as a perceive-then-plan problem with vision-language models, where a Perceiver first grounds the 3D objects and then a Planner iteratively refines the scene hypothesis through actions that improve physical plausibility while preserving consistency with the input image. We propose Layout-as-Policy (LaP), which casts the planning stage as a policy learning problem: 3D layouts are represented as structured states, and refined via discrete actions such as translation, rotation, and rescaling. Starting from an observation-aligned initialization with the geometry-enhanced Perceiver, the LaP Planner is trained to produce action sequences that progressively resolve geometric inconsistencies and enforce realistic spatial relations. To enable effective learning, we combine supervised trajectory initialization with preference-based optimization, allowing the model to learn corrective behaviors without requiring explicit reward engineering. This formulation transforms layout estimation from a one-shot prediction task into an iterative refinement process, enabling better handling of global constraints and complex object interactions. Experiments demonstrate that our approach produces layouts that are more physically coherent and better aligned with visual observations, while naturally supporting downstream tasks such as scene editing and manipulation.

NeurIPS 2026

Perceive, Interact, Reason: Building Tool-Augmented Visual Agents for Spatial Reasoning

Changye Li, Meng Lu, Yi Wu, Ligeng Zhu

While recent vision-language models (VLMs) demonstrate strong multimodal understanding, they remain limited in spatial reasoning tasks that require active evidence acquisition and multi-step visual interaction. This limitation suggests that relying solely on implicit visual representations from vision encoders is insufficient for recovering fine-grained spatial evidence. We introduce *PERception-Interaction-reason Agent* (**PERIA**), a tool-augmented visual agent for spatial reasoning tasks across map reasoning, visual probing, and vision reconstruction. **PERIA** uses two lightweight tool families: *vision perception tools* for exposing textual, symbolic, and spatial evidence, and *vision interaction tools* for manipulating visual context, tracing paths, and verifying spatial relations. To train **PERIA**, we develop a unified recipe that combines supervised tool-use trajectory synthesis, composite rewards, and Observation-Relaxed Group-in-Group Policy Optimization (OR-GIGPO) for effective multi-tool behavior. Experiments on 13 benchmarks from 8 datasets show that **PERIA**-8B improves over the Qwen3-8B backbone by 10.0% on in-distribution benchmarks and 4.4% on out-of-distribution benchmarks, while outperforming previous state-of-the-art baselines of similar size by 7.0%–14.8%. It also achieves performance comparable to much larger models such as Qwen3-VL-235B-A22B-Thinking and GPT-5, demonstrating the effectiveness of **PERIA** in enhancing spatial reasoning capabilities.

NeurIPS 2026

Per-Starting-Point Plausibility and Diversity Bounds for Score-Based Diffusion Models

Minh Quang Nguyen, Hady Lauw

Score-based diffusion is well-studied at the mixture level—averaged over the prior—but many practical pipelines (posterior sampling, SDEdit, OOD detection) fix the starting point and care about the per-start output. To our knowledge, this per-starting-point regime has no prior non-asymptotic analysis. We give two coupled bounds: a *plausibility* upper bound on how close the per-start output is to the data distribution, and a matching *diversity* lower bound on how distinguishable outputs from two different starts remain. The same score-contraction rate governs both—where plausibility is tight, diversity is vacuous, and vice versa—predicting a sharp horizon beyond which starting-point identity is erased. We illustrate the phenomenon qualitatively on 2D toy datasets, MNIST, and CIFAR-10.

NeurIPS 2026

Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks

Bum Jun Kim, Gnankan Landry Regis N&#x27, guessan

Physics-informed neural networks (PINNs) train a single neural approximation by minimizing multiple physics- and data-derived losses, but the gradients of these losses often interfere and can stall optimization. Existing remedies typically treat this pathology either through scalar loss balancing or full-parameter-space gradient surgery, leaving it unclear which intervention is most appropriate. We show that PINN gradient conflict is not a uniform failure mode with one universal remedy. Instead, we identify distinct PINN gradient-conflict regimes, each associated with a different intervention class. Persistent directional conflict may require separate loss-indexed parameter subspaces, magnitude imbalance often favors scalar reweighting, and low or transient conflict may require no extra mitigation. To select between scalar reweighting and a lightweight architectural intervention, we propose a diagnostic-first framework. It profiles a 1000-step unmodified PINN run and, when intervention is warranted, uses one low-rank adapter per loss to create explicit loss-indexed parameter subspaces attached to a shared PINN trunk, providing each loss with a direct gradient pathway. Across more than 60 PDE configurations, including forward, inverse, multi-physics, parameter-varying, and high-dimensional problems up to 50D, persistent directional conflict dominates standard forward $K=3$ benchmarks and a natural $K=4$ thermoelastic system, where adapters combined with reweighting yield significant improvements. In contrast, $K=3$ inverse problems and natural $K=5$ and $K=6$ multi-physics systems are largely magnitude-dominated and often favor reweighting alone, while full-parameter-space gradient surgery can fail on heterogeneous parameter spaces. A regime-transition theorem and a blockwise neural tangent kernel analysis explain why gains from these separate adapter parameter subspaces arise selectively in persistent-conflict regimes.

NeurIPS 2026

PepSpecBench: A Unified Evaluation Benchmark for Peptide Tandem Mass Spectrometry Prediction

Zhiwen Yang, Pan Liu, Yifan Li, Yunhua Zhong, Jun Xia

Tandem mass spectrometry provides a high-throughput framework for identifying and quantifying proteins in complex biological samples. In computational proteomics, predicting peptide MS/MS spectra is a critical task, enabling downstream applications such as large-scale peptide identification and quantification. While deep learning architectures have substantially improved prediction accuracy, three evaluation challenges obscure the true progress of the field. First, inconsistent data preprocessing and incompatible model output spaces hinder fair model comparison. Second, flawed data splitting strategies can permit hidden sequence leakage and inflate reported performance. Third, existing evaluations typically lack comprehensive cross-species benchmarking and systematic assessment of model robustness to influential experimental conditions. To address these challenges, we propose PepSpecBench, a unified benchmark for peptide MS/MS spectrum prediction. PepSpecBench standardizes data preprocessing across complementary public datasets, enforces a strict backbone-disjoint splitting strategy to eliminate sequence leakage, and evaluates diverse architectures within a shared fragment-ion representation space. It further introduces a comprehensive multi-species evaluation suite and physically grounded metadata perturbation probes to assess model robustness and instrument awareness. We uncover previously unrecognized performance discrepancies and robustness limitations across six representative models, providing actionable insights for future model design, evaluation and practical deployment. Code and data are available at https://anonymous.4open.science/r/PepSpecBench-NeurIPS2026/.

NeurIPS 2026

PepDDG: Peptide–Protein Binding ΔΔ𝐺 Prediction via Information Channel Decomposition

Ruochi Zhang, Yusi Fan, Qiong Zhou, Li Jiao, Tian Wang, Qian Yang, Silong Zhai, Lan Wang, Fengfeng Zhou, Yajuan Huang, Liming Guo, Chang Liu, Xin Gao

Predicting mutation-induced changes in peptide--protein binding affinity ($\Delta\Delta G$) is central to therapeutic peptide optimization, but peptide-specific predictors remain limited by scarce labels, target overlap in supervised benchmarks, and costly molecular simulations. We introduce PepDDG, a zero-shot, training-free predictor that ranks peptide mutations by decomposing binding perturbations into three complementary information channels: energetic perturbation, geometric environment, and evolutionary compatibility. Each channel is computed from a wild-type complex structure, transformed into rank space, and combined by non-parametric Borda aggregation, without fitting fusion weights or fine-tuning neural predictors. PepDDG is motivated by rank-covariance analysis showing cross-channel fusion can improve rank correlation when channels retain complementary signal, whereas increasingly expensive refinement of a single energetic channel has diminishing returns. Empirically, the channels are individually moderate but capture distinct mutation regimes, and rank fusion consistently outperforms single-channel variants and training-free baselines. On our curated benchmark of 332 peptide-chain mutations across 33 targets, PepDDG reaches Spearman $\rho = 0.619$; the calibrated PepDDG-Cal variant reaches $\rho = 0.691$. Performance remains strong on short and cyclic peptide subsets, with $\rho = 0.813$ and $0.872$, respectively. These results support complementary evidence fusion on PDB-derived complex structures as a practical alternative to costly same-channel physical refinement for peptide $\Delta\Delta G$ ranking; a separate diagnostic shows that predicted structures can be used when no crystal structure is provided at inference time.

NeurIPS 2026

Pause and Reflect: Conformal Aggregation for Chain-of-Thought Reasoning

Yu Gu, Zijun Yu, Vahid Partovi Nia, Masoud Asgharian

Chain-of-thought (CoT) reasoning with self-consistency improves performance by aggregating multiple sampled reasoning paths. In this setting, correctness is no longer tied to a single reasoning trace but to the aggregation rule over a pool of candidate paths, making aggregation uncertainty the central challenge. This issue is critical where confidently incorrect answers are far more costly than abstentions. We introduce a conformal procedure for CoT reasoning that directly addresses aggregation uncertainty. Our approach replaces majority voting with weighted score aggregation over reasoning paths and calibrates an abstention rule using conformal risk control. This approach leads to finite-sample guarantees on the confident-error rate--the probability that the system answers and is wrong. We further identify score separability as the key condition under which abstention provably improves selective accuracy, and derive closed-form expressions that predict accuracy gains from calibration data alone. The method is fully inference-time, and requires no retraining. Across four benchmarks, four open-source models, and three score classes, realized confident-error rates are consistent with the prescribed targets up to calibration-split and test-set variability. Our method achieves $90.1\\%$ selective accuracy on GSM8K by abstaining on less than $5\\%$ of problems, compared with $82\\%$ accuracy under majority-voting baseline.

NeurIPS 2026

PatternBloom: Empowering Agentic RAG with Externalized RL-Distilled Graph Patterns

Yi Ge, Heng Huang

Reinforcement-learning-trained agents for retrieval-augmented generation retrieve content (passages, knowledge-graph fragments, or hyperedges) and supervise training with outcome rewards on the final answer. Across these paradigms the reasoning route through retrieved content never leaves the language model's hidden state, conflating declarative knowledge with the procedural knowledge that recurs across queries of the same logical type; content-only methods consequently plateau as reasoning depth grows. We then introduce PatternBloom, an agentic RAG framework that shifts the unit of retrieval from content (what to read) to logic (how to reason). A first RL stage scores the agent's constructed evidence graph by a frozen oracle's information gain through the Information-Density Reward (IDR), a size-normalized mutual-information surrogate. High-reward trajectories are distilled into a Graph Pattern Memory (GPM) of type-abstracted reasoning skeletons, and a second RL stage uses the Pattern-Augmented Reward (PAR) to couple policy to memory, turning procedural reasoning into a learnable, externalized structural prior. A 7B PatternBloom outperforms 27 baselines by +15.0 Avg-OOD EM, with the gain compounding with reasoning depth precisely because procedural knowledge, once distilled, is reused rather than re-derived at every query.

NeurIPS 2026

Pattern-Based Matrix Analysis Under Permutations

Andrei Ermakov

Low-rank approximation captures one important notion of matrix simplicity: a matrix is simple if it is well described by a low-dimensional linear model. This paper studies a complementary notion. We consider matrices that become structurally simple only after permuting rows and columns, so that their mass concentrates in a prescribed geometric pattern such as a band, block-diagonal, arrowhead, or related form. We introduce a pattern distance that measures how close a matrix is to a given structural mask after optimal reordering, giving a common framework for latent ordering, community detection, and bandwidth minimization. The problem is NP-hard in general; we derive an alternating algorithm based on Linear Assignment subproblems, and establish identifiability of the target structure up to pattern automorphisms. We further introduce a pattern-plus-low-rank decomposition that combines permutation-structured fitting with a low-rank residual; it dominates pure low-rank approximation by feasibility and admits a strict rank separation on planted block-diagonal targets, with broad empirical gains across pattern families. We evaluate the framework on synthetic recovery tasks, real correlation and graph adjacency matrices, and transformer attention heads (GPT-2, Qwen2.5-0.5B and Qwen2.5-7B), showing that a single universal algorithm recovers qualitatively different forms of matrix structure.

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