NeurIPS 2026 Papers

Humans, animals, and modern machine learning models exhibit impressive abilities to learn complex behaviors and generalize these behaviors to unseen situations. This ability requires us to learn rules and regularities that allow for such generalizations. At the same time, in most complex environments, any rule will have its exceptions. How do learning systems balance between learning general regularities and memorizing exceptions? We argue that a lack of task paradigms has hindered the study of this essential ability. To address this gap, we introduce a novel task, transitive inference with exceptions, that tests for relational generalization and memorization of an exception to the relational rule. We then analytically characterize the behavior of a simple, theoretically tractable model of neural network learning (kernel ridge regression) across a broad family of representations and task parameters. We find that these models can balance between relational generalization and memorization, but unlike for transitive inference without an exception, successful generalization is sensitive to the specific representational geometry. We explain why this task is more challenging mechanistically by drawing on our analytical theory. Finally, we validate our theoretical insights in pretrained language models that are finetuned on ordered relations, finding that these models successfully generalize according to the transitive rule, but also make the kinds of systematic mistakes predicted by our theory. Overall, our theory shows how learning systems can balance between relational generalization and memorization, explains how this can go wrong, and emphasizes the need for new task paradigms designed to probe this ability.

Foundation-model-based predictors of perturbation response are evaluated primarily by aggregate accuracy, yet lack principled per-prediction reliability criteria. We audit the state-transition (ST) decoder~\citep{adduri2025predicting} shared by recent predictors across three encoders and four cell lines under CRISPRi perturbation, and identify a rank-$1$ attention bottleneck whose leading direction maps in gene space to the same cycling/p53 stress-response program in every cell line tested. The bottleneck implies a distance-defined reliability boundary: per-prediction quality degrades smoothly with the gene-space distance from a model's predicted perturbation response ($\Delta$, the predicted change relative to control) to its nearest training $\Delta$, and biological-family identity, not training-pool size, drives held-out quality. We propose \emph{predicted-NN-distance}, this same distance computed from model output alone, as a per-prediction trust signal that tracks per-perturbation quality at Spearman $|\rho| \approx 0.81$ (oracle $0.88$) and admits a single pooled threshold that transfers across cells and encoders under leave-one-out evaluation. The signal outperforms a simpler predicted-magnitude baseline in most cases. Per-prediction reliability is bounded by a low-rank decoder geometry and by gene-space coverage of training perturbations, not by aggregate benchmark accuracy.

The development of embodied models of animal behavior is a major goal of the neuro-AI community. Embodied models will enhance our ability to make direct comparisons between biological and artificial agents. To make such comparisons effective, though, we need embodied models that actually move like animals. Previous work has developed virtual animal bodies and techniques for training realistic motion through imitation. However, to-date, there is no system for embodied animal modeling that produces natural movements both during trained, goal-directed behavior, and during exploration driven by random generation. Here, we introduce Simulated Control via Augmented Motor Priors for Embodied Reinforcement learning (SCAMPER), a system for training an embodied virtual rat model, enabling natural movements during both goal-directed behavior and random exploration. SCAMPER uses a variational architecture with two distinct priors, a motion prior for control and a behavior prior for exploration. We show that combining both of these priors allows SCAMPER to generate realistic behavior during exploration and exploit the task structure effectively. As well, SCAMPER can learn from sparse rewards as a result of the diverse movements induced by the behavior prior, allowing the system to model realistic sparse reward tasks from experimental neuroscience. Altogether, SCAMPER provides the neuro-AI community with an effective new system for training embodied models of rodents on realistic tasks.

Kernel methods, and Gaussian Processes (GPs) in particular, require a conditionally negative-definite (CND) distance measure to guarantee positive semi-definiteness (PSD) of the kernel matrix — a condition that fails for many natural input spaces, including smooth manifolds and spaces of probability distributions. We propose the Sparse Landmark Embedding (SLE) kernel, which eliminates this requirement entirely. Each input is embedded into a sparse feature vector via compactly supported bump functions centered at all training points $|\mathcal{D}|$; applying any standard PSD kernel in this embedding space yields a kernel that is provably PSD for arbitrary distance measures. The compact support automatically controls embedding sparsity, keeping kernel matrices well-conditioned and computationally tractable despite the high ambient dimension. We provide theoretical guarantees on PSD, sparsity, stability, and universal approximation, and demonstrate, using geodesic and Wasserstein distances, that the SLE kernel matches or substantially exceeds domain-specific baselines in both predictive accuracy and uncertainty quantification.

We derive closed-form ODEs for the learning dynamics of a linear recurrent policy network trained with REINFORCE on sparse-reward tasks in a high-dimensional teacher–student setting. Under alignment assumptions between student and teacher networks, the dynamics reduce to a finite system of coupled order-parameter ODEs whose reward terms are governed by trajectory-level orthant probabilities of a structured correlated Gaussian process. The theory predicts that recurrence can accelerate escape from sparse-reward plateaus by accumulating task-relevant memory, and that each episode length admits an optimal recurrent scale that minimizes learning time. Our results provide a quantitative theory of how recurrence, and sparse reward interact during learning.

Radiologist eye-tracking data provide a rich record of how experts search, compare, and accumulate evidence during image reading, yet existing methods exploit this signal only partially, either as a static spatial prior or as an auxiliary prediction target decoupled from diagnosis. We propose GazeWorld, a medical imaging world model that treats the image as the world and the radiologist's fixation sequence as a trajectory through it. GazeWorld autoregressively predicts the latent representation of the next fixated patch from all previously visited ones, while a spatial-completion branch covers unvisited regions. At inference, GazeWorld generates a sequence of patch representations from the image alone without requiring real gaze data. Frozen GazeWorld features achieve state-of-the-art diagnostic accuracy across all nine supervised settings on CheXpert, RSNA Pneumonia, and SIIM-ACR Pneumothorax, as well as the highest zero-shot accuracy on all three benchmarks. On the GazeSearch benchmark, a generic decoder trained on the same frozen features outperforms the purpose-built LogitGaze-Med by over 16\% in ScanMatch and 22\% in SED, despite not being explicitly trained to predict gaze. GazeWorld demonstrates that modeling how experts read, not just what they conclude, offers a promising pretraining paradigm for medical imaging AI.

Anchored fixed point and monotone equation methods, including Halpern iteration, extra anchored gradient, and their relatives, add a vanishing pull toward a reference point to obtain last-iterate guarantees. Existing anchored variants often achieve sharp last-iterate guarantees, but from the update-level perspective the placement of the anchor can be algorithm-specific and conceptually opaque. We show that anchoring admits a single operator-side construction: regularize the operator queried by the base method with a vanishing Tikhonov term, then run the unmodified base method. Applied to the Picard iteration, this recipe reproduces the Halpern iteration; applied to the forward step, extragradient, and Popov methods, it yields three variants whose anchor placements inherit the base method's query pattern. The four analyses share a residual recurrence, recovering the \(O(1/k)\) Halpern residual-norm convergence rate, giving \(O(1/\sqrt{k})\) for the regularized forward step, and giving \(O(1/k)\) for the regularized extragradient and Popov variants in the unconstrained monotone Lipschitz setting.

A wide range of methods have been proposed for interpreting language models, delivering important insights into their inner workings. However, different methods and their resulting insights stand in relative isolation: what could the underlying structure of language models be, such that they give rise to all our interpretations? In this work, we propose using Tensor Product Representations (TPRs; Smolensky 1990) as a unifying hypothesis. TPRs give a concrete proposal for how compositional structure can be represented in vector space. We show, both mathematically and empirically, that TPRs can unify several prior interpretability methods: additive analogies, linear probing, sparse autoencoders, and activation patching. Mathematically, we show that these methods can all be derived from TPRs. Empirically, we apply the derivations to a range of different models — from small toy models to LLMs — to construct instances of each of the above interpretability methods; these constructed variants perform comparably to their standard variants. We view this work as a step toward what interpretability will ideally provide: a unified account of the nature of neural networks, corroborated not just by individual observations but also by an explanation of the connections between them.

Reliable deployment of graph neural networks requires calibration, out-of-distribution (OOD) detection, and robustness to distribution shift, yet existing methods typically address these requirements with separate models and objectives. A key obstacle is the lack of a single learned representation whose structure can serve all three tasks through different readouts. Inspired by spectral approaches in graph signal processing and polynomial chaos theory, we model uncertainty-bearing node embeddings as random graph signals: graph Fourier filters capture structural variation, while a scalar orthogonal-polynomial chaos coordinate captures latent stochastic variation. This yields a \emph{doubly-spectral stochastic} (DSS) expansion in which the mean coefficient carries evidence for classification and energy-based OOD scoring, higher-order coefficients encode structured logit variation, and quadrature averaging turns that variation into a calibration-sensitive predictive distribution. Calibration thus uses the quadrature-averaged predictive distribution, OOD detection uses the mean-logit energy score, and distribution-shift robustness uses the corresponding DSS branch as a regularized spectral residual when paired with a deterministic encoder. Under mild conditions this representation universally approximates Gaussian-latent random graph signals with exponentially decaying truncation error. The resulting model, \emph{DSS-GNN} (Doubly-Spectral Stochastic GNN), can be used standalone or as a residual branch alongside a deterministic encoder (\emph{DSS-Hybrid}). In standalone form, DSS-GNN achieves the lowest Brier score among the compared uncertainty-aware baselines on all 14 node classification benchmarks without post-hoc correction; in hybrid form, DSS-Hybrid achieves the best AUROC on most node-OOD settings, competitive cross-graph OOD performance, and the strongest shifted accuracy among compared baselines on all 7 GOOD concept-shift benchmarks under standard ERM training.

Modern vision--language models are trained with very different objectives: CLIP-style contrastive alignment, SigLIP-style match/no-match prediction, caption-style token generation (Flamingo, LLaVA), and latent-space prediction (VL-JEPA). Each has been claimed as best-in-class for its target task. Yet practitioners lack clear guidelines for choosing between them, and existing identifiability theory analyzes only the contrastive case. In this work, we unveil the core statistical mechanisms that distinguish each objective family using a unified spectral analysis. By leveraging closed-form solutions for the linearized losses under a latent structure in which modality-specific nuisances may spuriously carry shared semantic content, we characterize what each objective recovers from the data. We demonstrate that contrastive alignment, match/no-match prediction, and latent-space prediction collapse to the same cross-modal solution, while directed token-space generation recovers a different one. Our findings indicate that in scenarios where one modality is heavily contaminated by spurious nuisance, token-space generation is preferable because it imposes a strictly weaker, one-sided alignment condition. In scenarios where two modalities are both clean, retrieval is maximized by the latent-prediction objective whose target matches the query modality. These results clarify the trade-offs between the four objective families. We validate our theoretical predictions on numerical, controlled synthetic, and real (Flickr30k, COCO, CC3M) data.

We introduce COMONet (Convex-Concave and Monotonicity-Constrained Neural Networks), a unified architecture for enforcing variable-wise shape constraints in neural networks. COMONet addresses the limitations of prior methods that either support only a restricted subset of monotonicity and curvature constraints or enforce them through penalties without strict architectural guarantees. Our framework assigns each input variable to one of eight shape regimes, covering monotonicity, convexity, concavity, and their combinations. This is achieved through a partially connected architecture that routes each variable to specialized units equipped with sign-constrained weights and constraint-preserving activation functions. We also provide theoretical guarantees showing that COMONet satisfies the prescribed variable-wise shape constraints by construction. Experiments on synthetic and real-world datasets demonstrate that COMONet achieves competitive performance and remains robust to noise while preserving its architectural guarantees. COMONet thus offers a practical and principled framework for incorporating domain knowledge as shape constraints into neural network training.

Learning-rate selection is one of the most consequential and repeatedly tuned decisions in modern deep learning, and the ability to transfer it quickly across widths, depths, and architectures can substantially reduce the cost of scaling new models. Existing transfer laws explain width through maximal-update parameterization and depth through depth-based scaling laws, but many modern architectures are better described as neural computation graphs with heterogeneous merge rules rather than by depth alone. We develop a unified merge calculus for learning-rate scaling on such graphs. Its central object is a graph-aware complexity coefficient that combines local merge semantics with global path structure and induces a $-1/2$ power law for the target learning-rate scale. We further show that depth alone is generally insufficient once merge semantics vary across architecture families. We validate the framework on controlled graph families and lightweight representative architectures covering uniform sum, residual-aware sum, concat, weighted fusion, and hybrid designs. Across these settings, the resulting graph coefficients organize optimal learning rates more effectively than depth alone and support practical learning-rate transfer.

Multimodal large language models (MLLMs) have rapidly advanced machine intelligence by integrating visual perception with powerful linguistic reasoning. However existing visual backbones predominantly encode videos in a rigid per-frame manner and delegate temporal modeling entirely to the language model. This paradigm fundamentally constrains long-range temporal understanding and imposes severe computational inefficiencies. To resolve these bottlenecks we propose FuxViT, a unified Vision Transformer natively supporting a 64K-token context window to seamlessly process diverse inputs ranging from static images to hour-scale videos. By employing a joint spatiotemporal pretraining paradigm, FuxViT generates highly coherent and information-rich visual representations. This strategic early fusion frees the downstream language model from reconstructing low-level temporal structures to focus entirely on high-level reasoning. Furthermore we introduce Frame Selective Attention (FSA) as a native sparse routing mechanism. FSA dynamically attends to the most relevant historical frames to achieve exceptional computational efficiency without sacrificing fine-grained spatial or temporal details. Extensive experiments across 16 image and video benchmarks demonstrate that FuxViT consistently outperforms existing baselines and establishes itself as a vastly superior alternative to standard static ViTs for multimodal understanding. We will fully open-source all model checkpoints.

Leveraging Graph Neural Networks (GNNs) as graph encoders and aligning the resulting representations with Large Language Models (LLMs) through alignment instruction tuning has become a mainstream paradigm for constructing Graph Language Models (GLMs), combining the generalization ability of LLMs with the structural modeling capacity of GNNs. However, existing GLMs that adopt GNNs as graph encoders largely overlook the problem of aligning GNN-encoded representations across domains and tasks with the LLM token space to obtain unified graph tokens, thereby limiting their ability to generalize across diverse graph data. To bridge this gap, we aim to incorporate a multi-domain, multi-task GNN encoder into GLMs and align its representations with LLMs to enable multi-domain, multi-task graph alignment instruction tuning. This alignment problem remains underexplored and poses two key challenges: 1) learning GNN-encoded representations that are simultaneously generalizable across domains and tasks and well aligned with textual semantics is difficult, due to substantial variations in graph structures, feature distributions, and supervision signals, together with the lack of textual-semantic alignment guidance in task-specific GNN training; 2) diverse graph data and task-specific instructions can exhibit different degrees of compatibility with the LLM token space during instruction tuning, leading to varying alignment difficulty and rendering a fixed alignment strategy suboptimal. To tackle these challenges, we propose UniGraphLM, a Unified Graph Language Model that incorporates a multi-domain, multi-task GNN encoder to learn generalizable graph representations aligned with textual semantics, and then adaptively aligns these representations with the LLM. Specifically, we first develop a graph-text pair pretraining strategy with a tailored GNN encoder, trained on large-scale graph-text data spanning multiple domains and tasks to obtain generalizable representations naturally aligned with textual semantics. We further design a curriculum alignment tuning strategy that adaptively adjusts the alignment process by accounting for varying alignment difficulty across diverse graph data. Extensive experiments demonstrate that UniGraphLM consistently outperforms state-of-the-art baselines across graph datasets from different domains and tasks.

Mechanisms for allocating a divisible resource among strategic agents have been widely studied. The prominent paradigm is the proportional (Kelly) mechanism, which elicits a scalar bid per agent, allocates the resource proportionally, and charges payments equal to the bids. Follow-up mechanisms improve social welfare, but sacrifice simplicity by introducing complex allocation rules or unintuitive payments. We introduce a unified framework for designing simple resource allocation mechanisms with proportional-style allocations and uniform pricing. Our framework yields a family of mechanisms that interpolate between the Kelly mechanism and the first-price auction. These mechanisms strictly improve upon Kelly’s efficiency guarantees, even achieving full efficiency in equilibrium, while also providing revenue guarantees relative to the VCG mechanism. In settings with budget-constrained agents, our mechanisms achieve nearly optimal price of anarchy with respect to the liquid welfare. When budgets are public, our framework further enables the design of mechanisms that ensure budget feasibility, even when agents do not explicitly account for their constraints in their strategies.

Differential Privacy (DP) bounds the privacy leakage of a mechanism against worst-case membership inference, but the precise tradeoff between complex adversarial models and DP protections remains poorly understood. In this paper, we present a unified framework that generalizes the patchwork of existing bounds across membership inference, attribute inference, and data reconstruction attacks. Crucially, our framework is the first to evaluate attacks that target multiple individuals simultaneously and measure success beyond exact matches under a single cohesive bound. Our bounds capture this broad family of previously unexplored attack settings by relying solely on the privacy parameters and the adversary's baseline success rate (i.e. its prior without access to the mechanism's output). To illustrate this, we compare our high-probability guarantees to empirical attacks in two novel settings: extracting multiple non-uniform secrets (passwords and PII) from DP-finetuned language models, and reconstructing tabular data from noisy marginals. Ultimately, this framework provides a rigorous theoretical foundation to investigate the risk landscape of DP algorithms in new adversarial settings.

We present UniALM, a unified audio foundation model built on FactorCodec, a purely discrete tokenizer that factorizes audio into two role-separated representations. Analysis tokens are optimized to retain language-aligned, text-expressible information that can be decoded by a text LLM head into grounded natural-language analyses, while reconstruction tokens preserve the information required for waveform synthesis and are used exclusively for audio decoding. This factorization yields understanding performance competitive with continuous Whisper features on audio understanding tasks, while reducing the perplexity of reconstruction-token modeling for generation. UniALM further adopts functional layer specialization, partitioning the backbone into audio-understanding, cross-modal, and audio-generation experts. We train the model with a four-stage recipe on 100B text tokens and 60B audio tokens, together with a composed audio sequence construction strategy for unified multi-task pre-training. At 3B parameters, UniALM is competitive with strong 7B unified baselines on in-domain tasks and exhibits non-trivial \emph{compositional generalization} to unseen tasks under few-shot and zero-shot evaluation. Unlike prior unified systems that rely on hybrid continuous-discrete inputs or do not support generation beyond speech, UniALM provides a purely discrete interface for both understanding and generation across speech, sound, and music.

Video Moment Retrieval (VMR) aims to localize a temporal segment in a video based on a natural language query. While Multi-modal Large Language Models (MLLMs) are increasingly adopted for VMR due to their strong video understanding capability, they still face several limitations: (1) imprecise perception of event boundaries, (2) rigid dependency on precise object identification, and (3) inability to handle temporarily interrupted events. To address these, we propose three visual prompts: Event Segmentation (ES) prompt, Object Detection (OD) prompt, and Keyframe Marking (KM) prompt. Each prompt improves performance when applied individually, yet direct fusion degrades results because mixing prompts overcomplicates video content and inaccurate labels introduce noise. Although certain visual prompts may mislead the model, at least one of the three is likely to yield a positive effect. Even in the worst case where all three perform poorly, the prediction can fall back to the baseline. Motivated by this, we introduce a selection mechanism based on Yes/No Probability-Difference score to choose the most reliable prediction among the results produced by the three visual prompts and the baseline. We evaluate our method in a training-free setting across three datasets and four models, and obtain state-of-the-art performance.

Most temporal graph learning methods reduce future prediction to discriminative inference over past interactions, focusing on edges or node labels for a largely persistent set of nodes. This view breaks down when new nodes and edges appear, since the future graph becomes a new object with changing size, composition, and structure. We address this gap by framing temporal graph prediction as an inverse topology problem. Instead of predicting edges directly, we first predict a multiscale topological descriptor of the future graph and then reconstruct a plausible future snapshot that realizes this descriptor under inductive constraints. This approach makes global structure and node churn explicit prediction targets and produces forecasted graphs on which downstream tasks can be evaluated without retraining. Across 14 temporal graph datasets, we evaluate TopoGED on node, link and graph property prediction and compare it against state-of-the-art temporal graph models. TopoGED achieves a significant improvement in node-level forecasting accuracy over the strongest baseline, with a macro average of 0.49 versus 0.05. It also outperforms baselines in 60% of graph-structure metric evaluations and yields a substantial increase in macro-average edge prediction metrics, from near-zero to 0.12. Our results show that topology-guided graph forecasting can predict inductive future snapshots whose structure supports multiple downstream evaluations.