NeurIPS 2026 Papers

We introduce **AutoSpec**, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization. Our self-supervised models adapt to input operators using coarse spectral information (e.g., eigenvalue estimates and residual norms), and predict recurrence coefficients for computing or applying a matrix polynomial tailored to a downstream task. The effectiveness of **AutoSpec** relies on three ingredients: an architecture whose inference pass implements short, executable numerical linear algebra recurrences; efficient training on small synthetic problems with transfer to large-scale real-world operators; and task-defined objectives that enforce the desired approximation or preconditioning behavior across the range of spectral profiles represented in the training set. We apply **AutoSpec** to discovering algorithms for representative tasks on spd matrices: accelerating matrix function approximation; accelerating sparse linear solvers; and spectral filtering/preconditioning for eigenvalue computations. On real-world matrices, the learned procedures deliver orders-of-magnitude improvements in accuracy and/or reductions in iteration count, relative to basic baselines. We find clear connections to classical theory: the induced polynomials may exhibit equioscillation behavior characteristic of Chebyshev polynomial approximation.

Large language model (LLM)-based coding agents achieve strong results on controlled benchmarks yet routinely produce pull requests that real maintainers reject. The cause is not functional incorrectness but a lack of organicity: generated code ignores project conventions, duplicates internal APIs, and violates implicit architectural constraints. The latest repository snapshot is insufficient-it reveals the final codebase state, not the change patterns that shaped it. We make three contributions. (1) Paradigm: we propose next-commit prediction as a paradigm for learning agentic coding skill from a repository's own history-each historical commit is a self-supervised target whose oracle diff supplies dense supervision. (2) Evaluation: we establish Organicity Evaluation as a measurable objective for coding agents and contribute the Learning to Commit benchmark-5 curated open-source GitHub repositories under strict per-repository temporal splits-scoring patches along file localisation, internal API reuse, patch bloat, and code-style consistency. (3) Method: we instantiate the paradigm with the Learning to Commit framework, in which the agent performs supervised contrastive reflection: it blindly attempts each historical commit, contrasts its prediction against the oracle, and incrementally distils a reusable skill document that conditions subsequent generations. On the Learning to Commit benchmark and on SWE-bench Pro reframed under our temporal-split protocol, our framework consistently improves organicity on held-out future tasks and further lifts test-pass rates on SWE-bench Pro, narrowing the gap between benchmark success and real-world mergeability.

Masked diffusion models (MDMs) have emerged as a promising alternative to autoregressive models, enabling parallel token generation while achieving competitive performance. Despite these advantages, MDMs face a fundamental limitation: once tokens are unmasked, they remain fixed, leading to error accumulation and ultimately degrading sample quality. We address this by proposing a framework that trains a model to perform both unmasking and correction. By reusing outputs from the MDM denoising network as inputs for corrector training, we train a model to recover from potential mistakes. During generation we apply additional corrective refinement steps between unmasking ones in order to change decoded tokens and improve outputs. We name our training and sampling method **Pro**gressive **Se**lf-**Co**rrection (**ProSeCo**) for its unique ability to iteratively refine an entire sequence, including already generated tokens. We conduct extensive experimental validation across multiple conditional and unconditional tasks, demonstrating that \method~yields better quality-efficiency trade-offs (up to ~4x faster sampling) and enables inference-time compute scaling to further increase sample quality beyond standard MDMs (up to ~1.2x improvement on benchmarks).

Transformers update token representations through multi-head attention and residual connections as $X \leftarrow X + \sum_{i} P^{(i)}XW_{V_i}W_{o_i}$, where $P^{(i)}$ is the softmax attention matrix in head $i$. We propose replacing a subset of $P^{(i)}$'s with the Laplacian $I - P^{(i)}$, giving $X \leftarrow X + \sum_{i \in \mathcal{A}} P^{(i)}XW_{V_i}W_{o_i} + \sum_{i \in \mathcal{L}} (I - P^{(i)})XW_{V_i}W_{o_i}$. Our proposal has two motivations. First, it allows attention heads to update the mean of token representations, while Laplacian heads can directly control within-sequence variance. Second, if tokens are viewed as nodes in a graph with edge weights \(P^{(i)}\), then \(I - P^{(i)}\) is the corresponding graph Laplacian, and the update can be interpreted as one step of heat diffusion on the graph. We show that this simple modification improves performance across supervised learning, language modeling, and self-supervised learning tasks. To investigate why, we examine the token representations learned with and without Laplacian heads. In supervised learning, Laplacian heads collapse token representations within the same sequence and align the sequence means with the geometry of Neural Collapse. In language modeling, they increase the separability of token representations that share the same next-token prediction. In self-supervised learning, they produce token representations whose principal components are better suited for segmentation. Across modalities, they also lead to faster-decaying spectra, indicating stronger token smoothing. Overall, our findings challenge the prevailing view that token oversmoothing is inherently harmful, showing instead that certain forms of smoothing can be beneficial.

Dataset pruning reduces the storage and training costs of deep learning by selecting an informative subset from a large dataset. However, most existing pruning methods require fully labeled data, which limits their applicability in realistic settings where unlabeled data are abundant and annotation is costly. Recent label-free pruning methods address this issue, but they rely on features from pre-trained models to estimate example difficulty. This dependence can be unreliable when the target dataset differs substantially from the pre-training distribution. We propose a label-efficient dataset pruning framework that, given only a small labeled subset, uses semi-supervised learning to generate pseudo-labels for unlabeled data, allowing existing supervised pruning methods that require label information to be seamlessly applied to the resulting pseudo-labeled training pool. We then estimate example difficulty from pseudo-label-induced training dynamics and select a coreset. By learning directly from the target dataset, our method better captures the target distribution and provides more reliable signals for difficulty estimation and coreset selection. We validate our approach on domain-specific, image-corrupted, and long-tailed datasets, where it achieves state-of-the-art performance among label-free and label-efficient baselines, while also demonstrating competitive performance on standard benchmarks.

Contextual Integrity (CI) defines privacy not merely as keeping information hidden, but as governing information flows according to the norms of a given context. As large language models are increasingly deployed as personal agents handling sensitive workflows, adhering to CI becomes critical. However, even frontier models remain unreliable in making disclosure decisions, and existing mitigation strategies often degrade underlying task performance. To overcome this privacy-utility trade-off, we propose SelfCI, a complementary self-distillation framework that decouples information suppression from task resolution. SelfCI jointly optimizes two independent reverse KL divergences over distinct teacher distributions derived from feedback: one encourages preserving task-relevant information for utility, while the other enforces minimal and appropriate disclosure. This complementary formulation induces a Product-of-Experts (PoE) target, aligning the policy with the intersection of capability and privacy requirements. Without relying on costly external supervision, empirical evaluations demonstrate that SelfCI consistently outperforms competitive baselines such as online reinforcement learning algorithms (e.g., GRPO). These trends further extend to out-of-domain settings involving agentic workflows and accumulated private context, suggesting that SelfCI provides a practical path toward CI alignment.

Operator-valued concentration inequalities are foundational to the analysis of modern high-dimensional statistics and randomized algorithms. However, standard oracle bounds are frequently limited in practice: they require explicit a priori knowledge of the true variance, and often explicitly scale with the ambient dimension, rendering them vacuous for infinite-dimensional or heavily structured operators. Motivated by these challenges, we establish the first empirical Bennett and Bernstein inequalities for sums of independent, bounded, compact self-adjoint operators. Our fully data-driven bounds replace the unknown variance with an empirical estimate and rely strictly on the intrinsic dimension rather than the ambient dimension. This structural shift yields computable, dimension-free guarantees that are strictly sharper for non-isotropic random matrices and seamlessly extend to infinite-dimensional Hilbert spaces. We demonstrate that our empirical bounds achieve asymptotic sharpness with the best known oracle rates. Finally, as an independent byproduct, we derive novel empirical concentration guarantees for the intrinsic dimension itself.

Neural surrogate models for computational fluid dynamics (CFD) are typically trained as forward operators that map explicit problem specifications, such as geometry and boundary conditions, to solution fields. This ties the model to the conditioning variables seen during training and limits reuse under boundary-condition shifts or local geometry changes. We propose to reformulate steady CFD inference as an inpainting problem: instead of training on explicit boundary conditions, we learn a self-supervised prior over velocity fields and impose boundary constraints only during inference by fixing known regions such as inlet, outlet or unchanged regions from previous simulations. To scale this idea to large 3D meshes, we introduce a local neighbourhood tokeniser that represents high-resolution velocity fields as compact spatial latent tokens and train latent flow-matching and masked-autoencoder models on these tokens. On intracranial aneurysm hemodynamics, our method reconstructs full velocity fields from sparse boundary context, outperforms supervised neural surrogates under boundary-condition and dataset shift and enables local geometry editing by reusing unchanged simulation context. These results suggest that viewing CFD inference as context-conditioned inpainting can turn neural surrogates from task-specific predictors into reusable flow priors.

Self-supervised Vision Transformers learn strong image-level representations, but their patch-level representations can be unreliable for dense prediction. We study this mismatch and find that the class token concentrates global semantics on a small number of representative patches, while dense prediction errors often occur on low-attention regions. We provide a local gradient analysis showing that, along the [CLS] attention readout, image-level self-distillation gradients are weighted by [CLS]-to-patch attention mass. To provide masked patches with global semantics without changing the architecture, we propose Cross Distillation (CODI), which mixes a small amount of the teacher class-token distribution into each teacher patch-token target. CODI gives every masked patch an attention-independent semantic correction while preserving the standard self-distillation architecture. Experiments on dense and image-level benchmarks show that CODI improves both dense and image-level performance under aligned pretraining settings.

Confronted by the existing prototype-based methods that often fail to capture complex intra-class variations and inter-class semantic relationships, weakly supervised semantic segmentation (WSSS) faces persistent challenges due to the inherent incompleteness and boundary inaccuracies of Class Activation Maps (CAMs). To tackle these critical limitations, we propose a relationally optimized prototype Memory bank (RO-PMB) framework in this paper, where the integration of Graph Neural Networks (GNNs) with a dynamically optimized global prototype memory bank is pioneered to explicitly model and learn the intricate semantic relationships among all prototypes. Specifically, our Prototype Relationship Diagram Construction (PRDC) module leverages GNNs for contextual message passing over a learned prototype graph, enriching global prototypes with crucial associative knowledge. As a result, a subsequent context-aware refinement process is sustained to inject structured semantic information into local image-specific prototypes, thereby generating CAMs with unparalleled completeness and boundary precisions. Extensive experiments validate that, compared with the existing representative state of the arts in multi-stage WSSS baselines, our proposed RO-PMB achieves competitive and superior performances on a range of challenging benchmarks, such as PASCAL VOC and MS COCO etc. Code will be released.

Self-play fine-tuning enables large language models to improve beyond supervised fine-tuning without additional human annotations by contrasting annotated responses with self-generated ones. Many existing methods rely on a fixed divergence regime. SPIN is closely related to a KL-based regime, SPACE to a Jensen-Shannon-style objective via noise contrastive estimation, and SPIF to $\chi^2$-regularized self-play. Since these divergences exhibit different strengths depending on the distributional gap between model and target, no single choice appears to provide favorable learning dynamics across training stages. We propose IRIS (Interpolative R\'enyi Iterative Self-play), a R\'enyi-based self-play fine-tuning framework with a continuously adjustable objective. IRIS decomposes into two independent tilted risk terms over annotated and synthetic data, with exponential importance weights controlled by the order parameter $\alpha$. We show that several self-play objectives can be interpreted as limiting or representative regimes at particular values of $\alpha$, providing a unified theoretical perspective on these methods. An adaptive order schedule further adjusts $\alpha$ to the distributional gap, shifting from sharper importance weighting early in training to smoother refinement near convergence. Theoretically, we establish the fixed-point property of IRIS and analyze how $\alpha$ controls gradient concentration. Experiments on Zephyr-7B and Qwen2.5-3B across ten benchmarks show that IRIS improves upon baselines, reaching 44.57\% average score with gains across iterations. In our setting, IRIS with only 26$k$ annotated samples surpasses standard supervised fine-tuning trained on the full 200$k$ dataset.

Federated self-supervised learning (FSSL) enables collaborative training of self-supervised representation models without sharing raw unlabeled data. While it serves as a crucial paradigm for privacy-preserving learning, its security remains vulnerable to backdoor attacks, where malicious clients manipulate local training to inject targeted backdoors. Existing FSSL attack methods, however, often suffer from low utilization of poisoned samples, limited transferability, and weak persistence. To address these limitations, we propose a new backdoor attack method for FSSL, namely Hallucinated Positive Entanglement (HPE). HPE first employs hallucination-based augmentation using synthetic positive samples to enhance the encoder’s embedding of backdoor features. It then introduces feature entanglement to enforce tight binding between triggers and backdoor samples in the representation space. Finally, selective parameter poisoning and proximity-aware updates constrain the poisoned model within the vicinity of the global model, enhancing its stability and persistence. Experimental results on several FSSL scenarios and datasets show that HPE significantly outperforms existing backdoor attack methods in performance and exhibits strong robustness under various defense mechanisms.

Supervised post-training, including supervised fine-tuning (SFT) and knowledge distillation (KD), is essential for adapting large language models (LLMs) to specialized domains. However, traditional supervised post-training methods often suffer from catastrophic forgetting, training instability, and prohibitive computational costs. While layer-wise strategies have emerged as efficient alternatives, they introduce a representation bottleneck, where constrained updates in early stages limit feature diversity and impair final generalization. To resolve these issues, we develop HALO (Homotopy-Augmented Layer Optimization), a homotopy-driven layer-wise strategy for LLM post-training. By introducing a continuous homotopy parameter and a sequence of monotonically increasing auxiliary functions, we formulate the post-training process as a continuous deformation of the optimization problem that progressively incorporates layers into the trainable set. Specifically, HALO unfreezes the model from the output back to the input in a structured sequence. We theoretically prove that this approach establishes a differentiable solution path, ensuring a stable transition from a restricted optimization state to a fully converged LLM. Extensive experiments across diverse model families and sizes demonstrate that HALO consistently enhances performance and generalization. Notably, HALO exhibits strong robustness in challenging scenarios, especially in low-resource settings, while significantly reducing convergence time and iteration counts. Our results position HALO as an effective and accessible framework for high-performing LLM specialization.

Parametric human models capture global pose but overlook fine-grained surface dynamics. Generic scene flow estimates dense motion but struggles with articulated humans and lacks 4D ground truth. To bridge this gap, we introduce H-Flow, a dense 4D motion representation that captures non-rigid deformations beyond skeletal kinematics. We estimate H-Flow from monocular video via a unified multi-head architecture that jointly perceives pose, depth, and flow. To overcome the scarcity of dense motion annotations, we propose a self-supervised learning paradigm that embeds geometric, structural, and biomechanical priors into optimization. These cross-modal constraints tightly couple pose, depth, and flow, so that improving any one modality simultaneously drives the others toward consistency. For evaluation, we present DynAct-4D, a high-fidelity synthetic benchmark providing dense 4D ground truth for complex human movements. Extensive experiments show that our method outperforms state-of-the-art scene flow baselines. Furthermore, H-Flow serves as an effective motion primitive, bringing substantial improvements to downstream tasks including action recognition and video generation. Models, code, and resources will be released upon publication.

Precise localization of recording electrodes is fundamental to systems neuroscience; yet, current methods depend on labor-intensive post-hoc histology, which is incompatible with real-time feedback or chronic implants. We test the hypothesis that the electrical signals being recorded themselves carry sufficient anatomical information to localize their recording site in 3D atlas coordinates, without the need for histology. To probe this, we introduce a self-supervised framework that learns geometry-aware representations of single-channel local field potentials (LFP), leveraging probe channel geometry as a self-supervisory signal. We compare speech-based SSL objectives (e.g., masked prediction) against geometry-aware objectives that constrain the embedding space to mirror physical channel layout along the probe. These representations outperform masked-prediction baselines, and the gains compound at larger data scales. We test downstream analysis with 3D coordinate regression and brain region classification, benchmarking three SSL backbones (Wav2Vec 2.0, Whisper, and Data2Vec) against supervised baselines (AnyNet, ViT, and classical spectral classifiers) across datasets, laboratories, species, and probe technologies. Our method achieves state-of-the-art results in brain region classification and 3D coordinate regression from raw single-channel LFP, outperforming all baselines, affirming our hypothesis.

Self-supervised gait representation learning aims to learn transferable representations that generalize to unseen scenarios. However, existing methods rely solely on visual self-supervision, making it difficult to assess the semantic value of individual unlabeled sequences and limiting their ability to exploit latent semantic cues. To address this limitation, we introduce language priors into self-supervised gait pretraining. We construct GaitLP-1M, a million-scale silhouette-based gait pretraining dataset without identity labels. A two-stage caption generation pipeline further produces gait descriptions from the corresponding RGB sequences. To the best of our knowledge, GaitLP-1M is the first million-scale silhouette gait dataset paired with gait-centric captions. Building on this foundation, we propose GaitLingo, a language-guided self-supervised framework for gait representation learning. Specifically, we design a Caption-Guided Sample Weighting (CSW) mechanism to prioritize informative samples based on sequence-level semantic richness and attribute rarity. We then introduce a lightweight Temporal Adapter (TA) to better capture motion semantics and improve cross-domain robustness. Finally, we propose Soft Relation Distillation (SRD) to transfer caption-derived relational structures into the visual embedding space. Extensive experiments demonstrate that GaitLingo consistently outperforms prior self-supervised gait pretraining methods in the zero-shot setting across six benchmarks. Compared with GaitSSB, it achieves Rank-1 gains of +12.1% on Gait3D and +7.9% on GREW, as well as an average improvement of +9.1% across four CCPG settings.

Reinforcement learning (RL) can be used to improve the policy (denoiser) of diffusion large language models (dLLMs), while being hindered by the intractability of the policy likelihood. A dominant and efficient family of methods replaces the likelihood in standard RL with its evidence lower bound (ELBO), estimated from randomly masked sequences. Despite being well-aligned with pre-training, these approaches introduce bias from training-inference mismatch by applying the likelihood surrogate ELBO, which can potentially cause training collapse. In this work, we propose **Guided Denoiser Self-Distillation (GDSD)** to directly distill the denoiser of dLLMs from an advantage-guided self-teacher, derived from the closed-form optimum of reverse-KL regularized RL. GDSD matches the dLLM's denoiser logits to the teacher's via a normalization-free objective, which reduces RL to likelihood-free self-distillation and thus bypasses the TIM biases. Recent ELBO-based methods emerge as instances of applying different distillation divergences, but with diagnosable pathologies that GDSD avoids. On planning, math, and coding benchmarks with LLaDA-8B and Dream-7B, GDSD consistently outperforms prior state-of-the-art ELBO-based methods with a more stable training reward dynamics, achieving test-accuracy improvements of up to $+19.6\\%$. These results suggest that direct denoiser self-distillation, without relying on ELBO likelihood surrogate, can provide a more stable and effective RL procedure for dLLMs.

Large language models are increasingly used to estimate uncertain quantities from context, raising the question of whether their probabilistic outputs are internally consistent. A basic test of self-consistency is whether these estimates adhere to the law of total probability. We investigate this requirement through the lens of binary conditioning trees, which recursively partition a population into increasingly fine-grained subsets and expose multiple ways of estimating the same aggregate quantity. This construction yields a basic self-consistency check: marginal estimates must agree with prior-weighted aggregations of conditional estimates over any partition of the population. We find that current models systematically violate this requirement. In a case study on persona prompting, prior-weighted aggregates are consistently better aligned with human population statistics than direct estimates. Notably, this benefit of specificity persists even when the prior weights are themselves estimated by the LLM. Turning this discrepancy into a general evaluation criterion, we propose a family of self-consistency checks for LLMs grounded in the law of total probability. By evaluating these checks across frontier models, we show that failures of statistical consistency are widespread and not confined to persona prompting. Together with a benchmark dataset, our work provides a testbed for understanding when in-context learning can be treated as conditional inference.

LLM-based evolution has emerged as a promising way to improve agents by refining non-parametric artifacts, but its wall-clock cost remains a major bottleneck. We identify that this cost comes from synchronized stage execution and imbalance inside each LLM-heavy stage. We present FlashEvolve, an efficient framework that replaces synchronized execution with asynchronous workers and queues, allowing different stages and steps to overlap. To handle data staleness introduced by asynchrony, FlashEvolve tracks artifact versions and applies different policies to update, discard, or patch stale artifacts. Unlike weight-space staleness in asynchronous RL, language-space staleness is inspectable and repairable: a stale artifact is not just delayed work, but readable evidence that the LLM can reflect on, revise, and turn into useful evolution signal. FlashEvolve further improves throughput and token efficiency with speculative stage completion and adaptive workflow control. On GEPA workloads, FlashEvolve improves proposal throughput by 3.5x on local vLLM and 4.9x on API serving over synchronous GEPA. The same design also applies to ACE and Meta-Harness. Our code repository is available at https://anonymous.4open.science/r/FlashEvolve-FEC7/.