NeurIPS 2026 Papers

Hypergraph Neural Networks (HNNs), designed to model higher-order relations beyond pairwise interactions, typically rely either on fixed structural weights or on normalized attention. Fixed weights can propagate misleading information in heterophilic settings, while normalization makes attention coefficients competitive, in the sense that, in a message-passing framework, increasing the weight of one sender must reduce the weight of others in the same aggregation set. Our main contribution is the introduction of PANDA (Prior-guided AttentioNal Dual-path Architecture), a plugin for two-stage message passing HNNs applicable to both undirected and directed settings. The *main path* interpolates between learned receiver-normalized attention and structural incidence priors, while a non-competitive (not normalized) *auxiliary path* lets each sender contribute its own transformed information. We also show that, with fixed structural coefficients, PANDA recovers a certain complex-valued, convolution operator adopted in previous works. Across four HNNs spanning spatial and spectral methods in both directed and undirected settings, plugging PANDA in yields an average improvement of $5.18$ percentage points across eight real-world benchmark datasets.

We introduce SODA, a generalization of Optimistic Dual Averaging, which provides a common perspective on state-of-the-art optimizers like Muon, Lion, AdEMAMix and NAdam, showing that they can all be viewed as optimistic instances of this framework. Based on this framing, we propose a practical SODA wrapper for any base optimizer that eliminates weight decay tuning through a theoretically-grounded $1/k$ decay schedule. Empirical results across various scales and training horizons show that SODA consistently improves performance without any additional hyperparameter tuning.

Identifying molecular structures from LC-MS/MS spectra is a central problem in computational metabolomics, often approached by predicting molecular fingerprints and retrieving candidates via similarity search. Despite widespread use, the relationship between training objectives for fingerprint prediction and downstream retrieval performance remains poorly understood. In this work, we show that these objectives are fundamentally misaligned. Adopting a decision-theoretic perspective, we derive novel regret bounds that characterize when Bayes-optimal predictors for fingerprint similarity diverge from those for molecular retrieval. Our analysis reveals that optimizing standard similarity-based losses can provably degrade retrieval performance, and that the extent of this mismatch depends on the similarity structure of candidate sets. Empirically, we validate our theory on the MassSpecGym benchmark, demonstrating a Pareto frontier between fingerprint accuracy and retrieval metrics across commonly used loss functions. These results expose an inherent trade-off in fingerprint-based molecular identification and provide principled guidance for the design of learning objectives in computational mass spectrometry.

We investigate the approximation capabilities of dense neural networks. While universal approximation theorems establish that sufficiently large architectures can approximate arbitrary continuous functions when there are no restrictions on the weights, we show that dense neural networks do not possess this universality. Our argument is based on a model compression approach, combining the weak regularity lemma with an interpretation of feedforward networks as message passing graph neural networks. We consider ReLU neural networks subject to natural constraints on weights and input and output dimensions, which model a notion of dense connectivity. Within this setting, we demonstrate the existence of Lipschitz continuous functions that cannot be approximated by such networks. This highlights intrinsic limitations of neural networks with dense layers and motivates the use of sparse connectivity as a necessary ingredient for achieving true universality.

Long-context dialogue systems must decide both when to access memory and which parts of the interaction history are relevant. Existing approaches typically rely on heuristic retrieval signals or always-on memory usage, failing to account for the changing and potentially inconsistent nature of user preferences. In this work, we propose a unified framework for memory access and selection based on changing preferences. We formulate personalized memory retrieval as identifying which historical turns provide evidence about a user’s latent preference state, rather than relying on surface-level semantic similarity. To this end, we quantify the utility of each memory turn using a Bayes factor, defined as the improvement in the model’s likelihood of the reference response when the turn is included in context. This provides a principled measure of evidence strength and a unified signal for both memory access and selection. By framing memory retrieval as utility estimation, the model learns to identify salient turns and regulate memory usage based on expected utility. Experiments on four heterogeneous memory benchmarks show that our approach outperforms existing embedding-based retrieval on long-context, preference-intensive tasks where modeling changing preferences is essential, while remaining competitive in low-density regimes where semantic similarity suffices.

Multilingual Information Retrieval reflects real-world search settings where users issue queries over mixed-language corpora. Existing evaluations mainly reward language-agnostic semantic relevance, treating relevant passages equally regardless of language. Yet retrieval utility also depends on the language of the retrieved passages: users expect results they can read and verify in the query language, and query--passage language mismatch can complicate downstream grounding in Retrieval-Augmented Generation systems. To evaluate this aspect, we introduce **MLAIRE**, a **M**ultilingual **L**anguage-**A**ware **I**nformation **R**etrieval **E**valuation protocol that disentangles cross-lingual semantic retrieval from query-language preference. MLAIRE constructs controlled pools with parallel passages across languages, enabling measurement of whether retrievers find relevant passages and whether they prioritize query-language passages when equivalent translations are available. We further propose language-aware metrics, including Language Preference Rate (LPR) and Lang-nDCG, together with a 4-way decomposition separating semantic and language-preference failures. Evaluating 31 dense, sparse, and late-interaction retrievers, we show that standard metrics obscure distinct behaviors: semantically strong retrievers may return correct content in a non-query language, while language-preserving retrievers may retrieve less relevant passages.

In long-context use, large language models frequently synthesize answers from the meaning of a relevant context span rather than literally copy-pasting them. Identifying which attention heads perform this synthesis matters for interpreting long-context model behavior. Yet existing detectors miss these heads by construction: they reward heads whose attended token matches the generated token, a literal-copy criterion that captures where a head reads but not what it writes through its output-value (OV) circuit, the very mechanism that carries non-literal retrieval. We introduce Logit-Contribution Scoring (LOCOS), a write-aware detector that scores each head by the projection of its OV-circuit output onto the answer-token unembedding direction, contrasting needle and off-needle source positions in a single forward pass. Across three model families (Qwen3, Gemma-3, OLMo-3.1), mean-ablating the top LOCOS heads on the NoLiMa non-literal retrieval benchmark collapses ROUGE-L at lower head counts than every attention-based baseline; on Qwen3-8B, ablating 50 heads drives ROUGE-L from 0.401 to 0.000 while the strongest baseline still retains 0.292. The selected heads are retrieval-specific: parametric recall and arithmetic reasoning stay at baseline under the same ablation.

Neural models such as YOLO and HuBERT detect local properties such as objects ("car") and emotions ("angry") in video frames and audio clips, with scores in [0, 1]. Lifting these scores to temporal properties over sequences enables applications such as query matching (e.g., "does the speaker eventually sound happy in this audio clip?") and ranked retrieval (e.g., "retrieve top 5 videos with a 10 second scene where a car is detected until a pedestrian is detected"). We formalize this problem of assigning Scores for TempOral Properties (STOPs) over sequences, given noisy score predictors for local properties. We propose LogSTOP, a scoring function that efficiently computes scores for temporal properties represented in Linear Temporal Logic. Empirically, LogSTOP with YOLO and HuBERT outperforms Large Vision / Audio Language Models by at least 16\% on query matching with temporal properties over objects-in-videos and emotions-in-speech, while matching or improving over temporal-logic baselines. On ranked retrieval with temporal properties over objects and actions in videos, LogSTOP with OWLv2 and SlowR50 improves mean average precision over zero-shot text-to-video retrieval baselines by 28\% and 18\% respectively.

Open-vocabulary dense perception requires grounding language-specified concepts in local regions for recognition, localization, and segmentation beyond closed category sets. CLIP learns image-level vision-language alignment, whereas dense prediction requires spatially precise and semantically reliable local features. Although recent dense CLIP adaptation methods reduce this gap through region-level semantic transfer and spatial correlation guidance, maintaining stable local semantics under contextual variation remains challenging. Specifically, the global contextual modeling in CLIP may introduce undesirable dependencies into local features. Changes in background, scale, viewpoint, or scene layout may cause identical object regions to yield inconsistent dense representations, leading to unstable correspondences and semantic drift. Moreover, spatial correlation guidance from visual foundation models captures visual relatedness between patches, but not whether coherent regions correspond to the queried textual concept, leaving concept-level dense alignment under-constrained. To address these issues, we introduce Semantic Spatial Consistency Learning $\textbf{(SSCL)}$, an adaptation method with two complementary objectives: 1) Context-Invariant Spatiotemporal Consistency (CISC) enforces semantic consistency for the same anchor region under varying contexts to mitigate context-induced feature drift; 2) Structure-Guided Semantic Refinement (SGSR) leverages spatial affinities from a frozen visual foundation model to refine CLIP text-patch responses, producing text-conditioned dense supervision with improved spatial coherence and concept-level alignment. Experiments on video instance segmentation, region classification, semantic segmentation, and object detection show consistent gains over the baseline methods, demonstrating the effectiveness and generalization capability of the proposed SSCL. Our code and models will be made publicly available.

Proving theorems in Lean 4 often requires identifying a scattered set of library lemmas whose joint use enables a concise proof---a task we call *global premise retrieval*. Existing tools address adjacent problems: semantic search engines find individual declarations matching a query, while premise-selection systems predict useful lemmas one tactic step at a time. Neither recovers the full premise set an entire theorem requires. We present LeanSearch v2, a two-mode retrieval system for this task. Its standard mode applies a hierarchy-informalized Mathlib corpus with an embedding--reranker pipeline, achieving state-of-the-art single-query retrieval without domain-specific fine-tuning (nDCG@10 of 0.62 vs. 0.53 for the next-best system). Its reasoning mode builds on standard mode as its retrieval substrate, targeting global premise retrieval through iterative sketch-retrieve-reflect cycles. On a 69-query benchmark of research-level Mathlib theorems, reasoning mode recovers 46.1% of ground-truth premise groups within 10 retrieved candidates, outperforming strong reasoning retrieval systems (38.0%) and premise-selection baselines (9.3%) on the same benchmark. In a controlled downstream evaluation with a fixed prover loop, replacing alternative retrievers with LeanSearch v2 yields the highest proof success (20% vs. 16% for the next-best system and 4% without retrieval), confirming that retrieval quality propagates to proof generation. All code, data, and benchmarks will be open-sourced.

Retrieval-Augmented Generation (RAG) has become a standard approach for enhancing large language models (LLMs) with external knowledge, mitigating hallucinations, and improving factuality. However, existing systems rely on generating natural language queries at each hop and maintaining a strict architectural separation between retriever and generator, preventing them from leveraging the full representational capacity of the LLM. We propose LAnR (Latent Abstraction for RAG), a unified framework in which a single LLM jointly performs encoding, retrieval, and generation entirely within its own latent space. Rather than generating textual queries, LAnR produces dense retrieval vectors from the hidden states of a designated [PRED] token and uses them to match against encoded document representations from the same model. Furthermore, LAnR adaptively decides when sufficient evidence has been retrieved using a lightweight MLP control head over those same hidden states, eliminating explicit token-level stopping reasoning. Extensive experiments on five QA benchmarks spanning single-hop and multi-hop settings demonstrate that LAnR outperforms existing RAG methods, while achieving improved inference efficiency through reduced number of retrieval calls and tighter model integration.

Why does the low dimensionality of representations, typically $d\approx 1000$, not prevent modern embedding-based retrieval models from scaling to billions, or even trillions, of data points? To answer this question, we study maximal-margin embeddings in the following retrieval model, classically studied in communication complexity [PS86] and more recently in embedding-based retrieval [WBNL25]. Let $A$ be a binary $N\times n$ matrix indicating whether each of $N$ queries is relevant to each of $n$ documents. We are interested in the largest margin $m>0,$ denoted by $\mathsf{m}^{\mathsf{rd}}(d, A),$ for which there exist unit norm embeddings of the queries and documents $U_1, U_2, \ldots, U_N, V_1, V_2, \ldots, V_n$ with the following property. $\langle U_j, V_i\rangle \ge m$ whenever $A_{ji} = 1$ and $\langle U_j, V_i\rangle \le -m$ when $A_{ji} = 0.$ A large margin is a key proxy for representation quality: it controls both robustness to perturbations and compositional generalization across queries. Our main theorem establishes that the best possible margin without a restriction on the dimension, $\mathsf{m}^{\mathsf{rd}}(+\infty, A),$ can be nearly achieved in dimension $d = O(\mathsf{m}^{\mathsf{rd}}(+\infty, A)^{-2}\log n)$ which improves a theorem of [BDES02]. Together with a matching lower bound in Theorem 1.5, we conclude that when $A$ is the $\binom{n}{k}\times n$ matrix containing all possible $k$-sparse rows once, dimension $d = O(k\log (n/k))$ is necessary and sufficient for the maximal possible margin $\mathsf{m}^{\mathsf{rd}}(+\infty, A) = \Theta(k^{-1/2})$ in this setting. This fully resolves the setup of [WBNL25]. We also give several constructions for large margins when $d = o(k\log (n/k)).$ Our proofs are based on connections between this problem and the literature on compressed sensing and the restricted isometry property. Finally, we empirically test the InfoNCE and sigmoid losses for producing large margin embeddings and demonstrate a clear advantage of the sigmoid loss.

Dense Associative Memory (DenseAM) is a promising family of AI architectures that is represented by a neural network performing temporal dynamics on an energy landscape. While hyperparameter transfer methods are well-studied for feed-forward networks, these methods have not been developed for settings in which weights are shared across layers and within the layer, which is common in DenseAMs. Additionally, DenseAMs utilize rapidly peaking activation functions that are rarely used in feed-forward architectures. The confluence of these aspects makes DenseAM a challenging framework for using existing methods for hyperparameter transfer. Our work initiates the development of hyperparameter transfer methods for this class of models. We derive explicit prescriptions for how the hyperparameters tuned on small models can be transferred to models trained at scale. We demonstrate excellent agreement between these theoretical findings and empirical results.

Retrieval-augmented in-context learning faces a budget problem under distribution shift: increasing top-$k$ can improve evidence coverage, but it can also add off-direction, conflicting, or overly long context that a finite reader cannot use. We introduce a theory-guided diagnostic framework based on \emph{effective evidence coverage}: retrieval is useful only while aligned evidence grows faster than reader-facing ambiguity. In a local linear-ICL model, coupled covariate and task-prior shifts create a mixed risk term that aligned retrieval can reduce up to a residual ambiguity term; a conditional transfer result extends the same budget boundary to frozen readers satisfying a prompt-level stability condition. This yields a falsifiable prediction: recall can keep rising after answer accuracy has saturated or declined. Across QA, verification, and NLI tasks, dense top-$k$ sweeps together with oracle and shuffled-context controls expose this recall--accuracy decoupling. The resulting framework separates coverage- and saturation-limited QA from interference-limited verification/NLI, while calibrated selected-context controllers are reported only as operational probes of the diagnosis.

When a text description is extended with an additional detail, image-text similarity should drop if that detail is wrong. We show that CLIP-style dual encoders often violate this intuition: appending a plausible but incorrect object or relation to an otherwise correct description can increase the similarity score. We call such cases \emph{half-truths}. On the verified COCO evaluation set, CLIP prefers the correct shorter description only 41.0\% of the time, and performance drops to 28.2\% when the added detail is a relation. We trace this vulnerability to weak supervision on caption parts: contrastive training aligns full sentences but does not explicitly enforce that individual entities and relations are grounded. We propose CS-CLIP (Component-Supervised CLIP), which decomposes captions into entity and relation units, constructs a minimally edited foil for each unit, and fine-tunes the model to score the correct unit above its foil while preserving standard dual-encoder inference. CS-CLIP raises half-truth accuracy to 78.2\% and improves average performance on established compositional benchmarks by 5.7 points, suggesting that reducing half-truth errors aligns with broader gains in compositional understanding.

Skill-augmented agents increasingly rely on large reusable skill libraries, but retrieving relevant skills is not the same as presenting usable context. Existing methods typically return atomic skills or dependency-aware bundles whose internal roles remain implicit, leaving the agent to infer the execution entry point, support skills, visible requirements, and failure-avoidance guidance. We introduce **G**roup **o**f **Skills** (**GoSkills**), an inference-time group-structured retrieval method that changes the agent-facing retrieval object from a flat skill list to a compact, role-labeled execution context. **GoSkills** builds anchor-centered skill groups from a typed skill graph, expands support groups through a group graph, bottlenecks the selected group plan into a bounded set of atomic skill payloads, and renders a fixed execution contract with **START**, **SUPPORT**, **CHECK**, and **AVOID** fields, without changing the downstream agent, skill payloads, or execution environment. Experiments on SkillsBench and ALFWorld show that \goskills preserves visible-requirement coverage under a small skill budget, improves over flat skill-access baselines, and often improves reward and agent-only runtime relative to structural retrieval references. Code is available at https://anonymous.4open.science/r/Group-of-Skills-E861.

3D geometric understanding is undergoing a major transition where rigid, deterministic, optimization-based pipelines are being replaced by large-scale, deep learning models. While recent methods achieve impressive performance on tasks such as multi-view 3D reconstruction and camera pose estimation, they suffer from two critical limitations: $\textbf{(i):}$ current state-of-the-art (SOTA) models require industry-level compute and training corpora, severely limiting accessibility, and $\textbf{(ii):}$ recent approaches remain constrained to modifying existing pretrained transformer models, since substantially changing their architecture would require retraining from scratch. We instead study a complementary direction: training an attention-free state space model for dense 3D understanding. We introduce $\textbf{FlashSSM-3D}$, the first 3D reconstruction state space model capable of performing accurate geometric reasoning over hundreds of images with linear computational complexity. However, training such a model from scratch with competitive performance is impractical under typical academic compute constraints. To address this, we train FlashSSM-3D by distilling knowledge from VGGT, avoiding the need to learn 3D geometric priors entirely from scratch. However, standard distillation losses are poorly suited for dense 3D reconstruction, where preserving real-world spatial structure is essential. We therefore propose a $\textbf{geometry-aware knowledge distillation}$ method specifically tailored for large-scale 3D reconstruction models. Our method introduces two novel losses: a Procrustes-based alignment loss that enforces global structural consistency between student and teacher 3D point predictions, and a camera reprojection loss that directly supervises view-consistent camera geometry between teacher and student. Extensive experiments across multi-view 3D reconstruction and camera pose estimation benchmarks demonstrate that FlashSSM-3D achieves competitive performance while requiring only $\sim25\\%$ of the training data and less than $10\\%$ of the training compute used by VGGT. At inference time, FlashSSM-3D benefits from the practical efficiency of state space models, reconstructing scenes from 500+ views in under 10 seconds while maintaining competitive accuracy.

Diffusion models achieve state-of-the-art generative performance but suffer from high computational costs during inference due to the repeated evaluation of a heavy neural network. In this work, we propose Dual-Rate Diffusion, a method to accelerate sampling by interleaving the execution of a heavy high-capacity context encoder and a light efficient denoising model. The context encoder is evaluated sparsely to extract high-dimensional features, which are effectively reused by the light denoising model at every step to refine the sample efficiently. This approach significantly accelerates inference without compromising sample quality. On ImageNet benchmarks, Dual-Rate Diffusion matches the performance of standard baselines while reducing computational cost by a factor of $2$--$4$. Furthermore, we demonstrate that our method is compatible with distillation techniques, such as Moment Matching Distillation, enabling further efficiency gains in few-step generation.

Cross-tokenizer knowledge distillation lacks a shared coordinatesystem between teacher and student vocabularies, and existingmethods each drop one of the two ingredients comparison needs:shape-based objectives preserve density but discard token identity,lexical alignment restores identity but uses surface form as a proxyfor meaning, and text-space matching compresses the teacher signalinto chunk-level events. We introduce SOLA (Semantic Optimal LocalAlignment), which reconstructs the missing coordinate systemexplicitly: it partitions inputs into decoded-text blocks viaMinimal Complete Correspondence, estimates a cross-vocabularycorrespondence cost from calibration text, and runs entropicoptimal transport on a bidirectional local support retrieved aroundeach teacher prediction. Under matched training and decodingprotocols, SOLA outperforms direct cross-tokenizer baselines onDolly instruction following, an UltraChat general-instructionbenchmark, and code and math domain transfer; a coverage--scorecorrelation and component ablations attribute the gain to theconstructed support.