NeurIPS 2026 Papers

While the approximation properties of single-layer Transformer architectures have been studied in recent works, a rigorous theoretical understanding of the multi-layer setting remains limited. In this work, we establish that multi-layer Transformers possess fundamentally different approximation capabilities from single-layer ones: for certain retrieval tasks, any single-layer Transformer requires least $\Omega (\varepsilon^{-k})$ parameters to achieve precision $\varepsilon$, where $k$ grows linearly with sequence length $T$, whereas a two-layer Transformer with a single head per layer achieves the same approximation precision with at most $O (\varepsilon^{-1})$ parameters. To understand this separation, we identify two structural mechanisms underlying multi-layer approximation. Specifically, softmax attention can only efficiently retrieve the token attaining the maximum attention score, incurring exponential-in-length parameter cost for $k$-th largest retrieval with $k \geq 2$. Moreover, the parameter cost of decoding coupled information scales with the size of the retrieved token set. Motivated by these findings, we propose **InfoFlow**, a framework for multi-layer Transformers. The framework tracks an information set of accessible input positions at each token and layer, assigning an explicit approximation rate to each mode of information propagation. This abstraction recovers known approximation bounds, remains consistent with experimental observations on trained networks, and yields concrete predictions in settings where direct theoretical analysis is currently intractable. Our results provide a principled framework for reasoning about the approximation efficiency of multi-layer Transformers.

Processing ultra-long multimodal inputs efficiently remains a critical bottleneck for Vision-Language Models (VLMs). This systematic challenge is essentially three-fold: (1) \textbf{Efficient Architecture}: compressing redundant visual sequences without sacrificing fine-grained details; (2) \textbf{Knowledge Transfer}: seamlessly migrating the capabilities of strong pretrained VLMs into more efficient novel architectures; and (3) \textbf{Generalization}: maintaining robust perception and reasoning across diverse multimodal domains. To address this, we introduce \textbf{InfiniteVL}, a linear-sparse hybrid VLM framework designed for efficient long-context understanding. At its core, InfiniteVL pairs a linear architecture to compress long-range visual context with sparse attention to retrieve precise local details. To support this architecture in moderate academic resources, we developed a three-stage knowledge transfer pipeline backed by capability-oriented data construction instead of training from scratch. This ensures smooth architectural alignment, rapid capability recovery, and robust adaptation across diverse domains. Furthermore, we adapt this foundation to specific deployment scenarios, deriving Sparse InfiniteVL for long-video analysis and Streaming InfiniteVL for real-time scene perception. Extensive experiments demonstrate that InfiniteVL matches the performance of leading VLMs while achieving a 1.7$\times$ decoding speedup and a 2.7$\times$ reduction in memory. Notably, Sparse InfiniteVL accelerates prefilling by 5$\times$ at a 256K context length, while Streaming InfiniteVL delivers stable 25 FPS real-time processing with a constant memory footprint.

A major goal in computational neuroscience is to understand how animals learn to perform a new behavior from a sequence of actions and rewards. Recent work from Liebana et al. (2025) has argued that animal learning trajectories are inconsistent with learning in shallow (1-layer) networks and are better explained by gradient descent (GD) in a deep neural network (DNN). However, previous work on inferring animal learning rules from behavioral data has focused on either 1-layer networks or fits to group behavior, highlighting the need for methods to fit DNN learning rules to individual animal learning trajectories. To address this gap, we develop a method for inferring single-animal DNN-based learning rules, parametrized by a set of initial weights, a learning rate, and a softmax parameter governing stochasticity in choice behavior. We first prove that GD in a shallow network can be arbitrarily well approximated by GD in a deep network, establishing a theoretical limit on network identifiability. Using this result to refine our inference method, we analyze two behavioral datasets from mice learning a sensory decision-making task. Specifically, we compare three model architectures: 1-layer linear (1L) and 2-layer linear (2L) models considered in Liebana et al., as well as a 2-layer nonlinear network (2NL) with a sigmoidal nonlinearity after the first layer. The 2NL model achieved the best fit for 84 out of 88 mice in both datasets (by AIC). Moreover, simulated learning trajectories from the fitted 2NL model closely matched the timecourse of key behavioral metrics such as bias, stimulus sensitivity, and accuracy. These results show that both depth and nonlinearity are critical for capturing individual learning trajectories. Strikingly, we found that the inferred learning rate and initial layer-1 weights of the 2NL model systematically predicted individual differences in accuracy and task bias, linking network initialization and learning rate to individual differences in learning performance across mice.

Neural responses to the same stimulus can vary dramatically with fluctuations in the brain's internal state and the organism's behavioral state. Yet studying how brain state shapes neural responses is difficult: limited experimental recordings sparsely sample this joint space, leaving many biologically valid state-stimulus pairings unobserved. Existing methods either capture state-dependent modulation with restricted model assumptions or synthesize neural activity without explicitly controlling internal brain state. We introduce **BrainStateDiff**, a conditional diffusion framework that models the spatiotemporal distribution of future neural activity and behavior given external stimuli and recent brain states. Motivated by two gaps in finite recordings, missing state-stimulus combinations and limited repeats of observed conditions, BrainStateDiff introduces two state-aware sampling strategies: *cross-state sampling*, which recombines observed states and stimuli to synthesize plausible neural responses from unobserved pairings, and *matched-state sampling*, which resamples from observed pairings to capture local trial-to-trial variability. We evaluate BrainStateDiff on our newly collected wide-field calcium imaging data in mouse V1, electrophysiology data in monkey V4, and two-photon calcium imaging data in mouse striatum. Our results show that BrainStateDiff generates biologically meaningful samples that preserve the state-dependent structure of real recordings and expand neural response space coverage beyond the original recordings. BrainStateDiff establishes state-conditioned generative modeling as a practical framework for studying how internal brain state shapes neural responses beyond the state-stimulus combinations directly observed in the experiments.

The ventral visual stream is widely modeled as a serial feedforward hierarchy in which V1, V4, and IT population codes develop sequentially during object recognition. We ask whether a second, concurrent coding mode exists—one organized not by anatomical order but by joint population structure across areas. Using Partial Information Decomposition applied to simultaneous multielectrode spiking recordings across all three areas at millisecond resolution—the first simultaneous three-area spiking PID analysis of the primate ventral stream—in two macaque monkeys viewing 25,000+ natural images, we decompose population coding into serial (unique per area) and synergistic (joint across areas) components at 5 ms resolution across five CNN target representations spanning low-level spatial features to high-level object identity. Three findings replicate across both animals and all five representations. First, synergistic inter-area coupling emerges before IT carries any unique object-related information—a dissociation of 15–65 ms that replicates in direction without exception across both animals—such that the joint population integrates before the apex encodes; moreover, V1–IT synergy persists for over 120 ms after V1’s unique information reaches zero. Second, although V1↔IT and V1↔V4 coupling emerge simultaneously and rise in parallel, V1↔IT exhibits stronger peak synergy at mid-to-high-level targets in both animals, suggesting a dominant role for non-serial joint coding. Third, when V1 and V4 are treated as an integrated feedforward block, their synergistic coupling with IT emerges last across all tested conditions—the feedforward foundation is the final component to join the synergistic mode, not the first. Together, these results show that serial and synergistic population codes co-occur in the same recordings, overlap in time, but follow different organizational principles, Providing a new level of nuance in our understanding of the primate ventral stream and introducing concrete constraints for biologically grounded models of vision.

Foundation models are billion-parameter neural networks that are trained under statistical learning principles to reason inductively regarding multifarious tasks at inference. However, foundation models are increasingly deployed in settings where the statistical principles that they were trained on may not hold. During deployment, users intervene in these systems' functionality through prompts, instructions, demonstrations, analogies, retrieval, tool calls, memory, verification, search, and multi-step reasoning. These operations change the effective knowledge state available at inference time, all of which are not well described by induction alone. This paper argues that Michalski’s Inferential Theory of Learning (ITL) provides a useful conceptual basis for describing deployed foundation models as multistrategy, goal-directed inference systems. In ITL, learning is modeled as the transformation of knowledge through transmutations such as generalization, specialization, abstraction, concretion, association, discrimination, explanation, derivation, reformulation, insertion, deletion, replication, and sorting. We reinterpret these classical transmutations in the context of modern test-time computation techniques, showing that the functionality of reasoning models, intelligent prompting, retrieval-augmented generation, tool use, memory, and agentic search can be understood as transmutation programs over knowledge states. We then identify limitations of classical ITL for contemporary machine learning and propose a probabilistic extension in which transmutations are stochastic operators selected under uncertainty and cost. Finally, we connect this view to a system-level information bottleneck principle, quantifying the new knowledge that is acquired during the inference process. The resulting framework positions ITL as a bridge between statistical learning, symbolic reasoning, abductive explanations, prompting, and agentic foundation models.

Token-level steering has emerged as a pivotal approach for inference-time alignment, enabling fine-grained control over large language models (LLMs) by modulating their output distributions without parameter updates. While effective, existing methods rely on dense intervention at every decoding step. This persistent manipulation not only incurs substantial computational overhead but also risks compromising generation quality by excessively drifting from the model’s intrinsic distribution. In this work, we show that dense intervention is unnecessary and propose Sparse Inference-time Alignment (SIA), which performs sparse junction steering, intervening only at critical decision points along the generation trajectory. Our key insight is that high-entropy junctions are empirically consistent with pivotal decision points in the generation trajectory and are particularly susceptible to misalignment, suggesting that these points benefit from alignment-related reward signal. Extensive experiments across different model families and alignment objectives show that steering only 20%–80% of tokens achieves the superior alignment–efficiency trade-offs. For strong base models such as Qwen3, intervening on as few as 20% of tokens matches or even surpasses heavily post-trained instruct models. This sparsity enables stronger guidance while better preserving the model's native distribution, integrates seamlessly with search-based methods (e.g., Best-of-N), and improves efficiency by reducing the required sampling budget while yielding practical wall-clock speedups under matched-quality comparisons.

Safety-aligned Large Language Models (LLMs) remain vulnerable to interventions during inference that redirect generation toward harmful outputs. Recent work attributes this to shallow safety, where alignment concentrates in the first few output tokens. We show that shallow safety is a special case of a broader inference-time vulnerability, in which short token injections at any generation step can substantially alter subsequent safety behavior. We also find that a model's alignment with refusal directions in its hidden states does not predict its robustness to such injection, revealing that internal state alone does not determine generation behavior under perturbation. To address this, we align models directly on generation trajectories constructed by simulating mid-sequence perturbation, and show that this improves robustness to mid-sequence injection and generalizes to attacks that exploit early-token generation. Our work argues that robust safety alignment requires training on the generation process itself, not only its outputs.

Flow Matching (FM) provides an efficient formulation for continuous-time generative modeling via straight optimal transport (OT) trajectories. However, during accelerated sampling, these models face a fundamental variance-fidelity dilemma. Under few-step deterministic Ordinary Differential Equation (ODE) integration, the rigid OT trajectories suffer from mean concentration, leading to severe variance collapse and the loss of high-frequency details. Conversely, traditional Stochastic Differential Equations (SDEs) inject blind, exogenous Brownian noise to recover variance, but this isotropic exploration incurs inherent numerical attrition over long integration paths, bottlenecking peak fidelity. To resolve this, we introduce Self-Aligned Drifting (SADrift) to mitigate these challenges without external priors. SADrift is an inference-time framework that augments flow matching inference with self-interacting dynamics, without additional training. By maintaining a momentum history of the sampling trajectory, SADrift extracts the \emph{kinematic residual} to generate a deterministic extrapolative field. This mechanism forces the trajectory to efficiently explore the local tangent space, effectively decoupling exploratory variance into targeted deterministic dispersion and a minimal stochastic buffer. To safely anchor these dispersed trajectories and prevent out-of-distribution divergence, the residual drift is analytically integrated into a micro-time Ornstein-Uhlenbeck (OU) process, providing a mathematically sound, mean-reverting geometric safeguard. Requiring exactly zero additional Neural Function Evaluations (NFE), SADrift empowers a frozen base model to achieve a highly competitive FID of 2.00 at just 20 NFE on ImageNet-256. By successfully bypassing the numerical attrition of the 250-step SDE baseline (FID 2.06), SADrift establishes a new Pareto frontier for variance injection. Beyond image synthesis, we further validate SADrift on fast video generation paradigms (e.g., TurboDiffusion with Wan2.1-1.3B), demonstrating its universal capability to unlock latent generative quality across different modalities and acceleration regimes.

Diffusion-based generators set the current state of the art for synthetic tabular data, deployed downstream wherever direct access to real records is restricted. These methods approach but rarely exceed real-data utility on downstream tasks, and closing this synthetic--real performance gap has so far been pursued exclusively at training time, via architectural advances, scaling, and retraining of monolithic generators. The inference-time alternative, i.e., refining the outputs of a pre-trained backbone with parameters left untouched, has remained largely unexplored for tabular synthesis. We introduce $\textbf{TARDIS}$ (Tabular generation through Refinement, Distillation, and Inference-time Sampling), an inference-time refinement framework that operates on a frozen pre-trained backbone, configured per dataset by a Tree-structured Parzen Estimator search over score-level guidance during reverse diffusion, with each trial's objective set by an inner grid search over post-hoc sample selectors and an optional soft-label distillation step. The search space encodes a single mathematical pattern we name $\textit{Bidirectional Chamfer Refinement}$ (BCR): the symmetric Chamfer functional between synthetic and real samples is minimized both continuously, via a score-level gradient during reverse diffusion, and discretely, via batch-ranking post-generation. On the majority of datasets the search selects BCR-aligned configurations over alternatives encoded in the search space, evidence both for BCR as the dominant refinement pattern and for TARDIS's per-dataset search as a procedure that recovers this pattern. Across 15 binary, multiclass, and regression benchmarks TARDIS achieves a median $+8.6\%$ downstream-task improvement over models trained on real data (95\% CI $[+3.3, +16.4]$, Wilcoxon $p=0.016$, 11/15 strict wins) and improves over the underlying TabDiff backbone on all 15 datasets (mean $+12.9\%$, $p<10^{-4}$), matching the backbone on manifold fidelity, diversity, and sample-level privacy. The synthetic--real gap is therefore not primarily a training-time problem: on the studied corpus, inference-time refinement of a pre-trained tabular diffusion backbone reaches and exceeds real-data utility in 1 to 80 minutes on a single consumer-grade GPU.

Scientists often need to analyze the samples in a study that responded to treatment in order to refine their hypotheses and find potential causal drivers of response. Natural variation in outcomes makes teasing apart responders from non-responders a statistical inference problem. We introduce the causal two-groups (C2G) model, a causal extension of the classical two-groups model for inferring treatment effects. The classical two-groups model posits that treated samples may or may not experience an effect, according to some prior probability. The C2G model extends this to consider the case where treatment, latent effect status, and effect size are all confounded. We propose two empirical Bayes procedures for the causal two-groups model, one under semi-parametric conditions and another under fully nonparametric conditions. The semi-parametric model assumes additive treatment effects and is identifiable from observed data. The nonparametric model is unidentifiable, but we show it can still be used to test for response in each treated sample. We show empirically and theoretically that both methods for selecting responders control the false discovery rate at the target level with near-optimal power. We also propose two novel estimands of interest and provide a strategy for deriving estimand intervals in the unidentifiable nonparametric model. We apply the C2G model to a cancer immunotherapy dataset, where the nonparametric model recovers clinically-validated predictive biomarkers of both positive and negative outcomes.

We address two open questions in streaming PCA via Oja's algorithm: sharp operator-norm convergence for general rank under sub-Gaussian data, and distributional inference for the resulting subspace estimator. Existing convergence analyses, even in the rank-one case, leave non-vanishing remainder terms that prevent adaptation to a vanishing tail spectrum, while existing distributional results are confined to the rank-one case. Our convergence theory removes these remainder terms and yields a sharp rate. In the dense-tail spiked covariance regime, this rate matches the minimax rate up to logarithmic factors. More generally, we prove a matching lower bound, up to logarithmic factors, across both dense-tail and sparse-tail regimes under a mild nondegeneracy condition. The analysis yields a linearization of Oja's iterates, which in turn enables a high-dimensional Gaussian approximation for the general-rank subspace estimation error with an explicit limiting covariance. We also establish a row-wise Berry--Esseen theorem for the aligned difference, recovering prior rank-one results as special cases. For practical inference, we develop an online multiplier bootstrap algorithm and prove its consistency. Beyond streaming PCA, our techniques contribute to Gaussian approximation and bootstrap inference for nonconvex stochastic approximation.

Preference-based fine-tuning methods such as RLHF and DPO require substantial compute and large preference datasets. They also need direct access to the model parameters which are not provided by many state-of-the art models. Inference-time alignment offers a cost-effective alternative without updating model parameters. However, existing inference-time methods rely on a scalar reward model derived under a Bradley-Terry assumption, which cannot represent general preferences. Following recent work on fine-tuning with generalized preferences, in this work, we initiate the study of inference-time alignment under general preferences. We formulate the problem as obtaining a Nash equilibrium of a two-player zero-sum game between policies. We propose two algorithms: \emph{Best-of-Nash} (BoN) and \emph{Nash Mirror Descent} (NMD). We prove that both algorithms achieve a duality gap that matches the problem lower bound. Empirically, we implement the two methods on three datasets, which shows that our methods substantially outperform the base policy, converging to the performance of the fine-tuned models. Moreover, our results show that NMD remains robust across the regularization parameter.

Wearable motion sensing provides a continuous and scalable window into human behavior and health, making it a natural fit for foundation models, yet its pretraining and scaling principles remain poorly understood. Prior work studies isolated design choices, such as sensor placement or sampling frequency, often under fixed settings and narrow downstream tasks that fail to capture real-world sensing diversity. We introduce Inertia-1, a fully open exploration of wearable motion foundation models. Using massive corpora of accelerometer data from global sources spanning more than 18.2M hours, we build a controlled framework for studying the full lifecycle of wearable motion foundation models, covering data choices such as sensor modality, device placement, sampling rate, window length; model choices such as architectures and model size; and training choices such as pretraining objective and data scale. Extensive evaluations across 15 datasets spanning human activity recognition, freezing-of-gait detection, and disease prediction reveal intriguing findings for building motion foundation models that generalize across tasks and sensing conditions. Collectively, Inertia-1 not only presents state-of-the-art recipes for diverse downstream tasks, but also serves as a comprehensive, practical, and open cookbook for wearable motion representation learning.

Code generation and comprehension by Large Language Models (LLMs) have emerged as core drivers of industrial intelligence and decision optimization, finding widespread application in fields such as finance, automation, and aerospace. Although recent advancements have demonstrated the remarkable potential of LLMs in general code generation, existing benchmarks are mainly confined to single domains and languages. Consequently, they fail to effectively evaluate the generalization capabilities required for real-world industrial applications or to reflect the coding proficiency demanded by complex industrial scenarios. To bridge this gap, we introduce IndustryCode, the first comprehensive benchmark designed to span multiple industrial domains and programming languages. IndustryCode comprises 579 sub-problems derived from 125 primary industrial challenges, accompanied by rigorous problem descriptions and test cases. It covers a wide range of NAICS sectors, including Aerospace Product Mfg, Chemical Mfg, and Information, and incorporates diverse programming languages such as MATLAB, Python, C++, and Stata. In our evaluation, the top-performing model, Claude 4.7 Opus, achieved an overall accuracy of 71.9\% on sub-problems and 48.9\% on main problems. The benchmark dataset and automated evaluation code are now publicly available.

AI agents increasingly excel at generating, testing, and refining code. However, they fall short on tasks requiring formal guarantees of full coverage that testing alone cannot provide. Distributed systems are a prime example: properties such as consistency between reads and writes must hold under every possible interleaving of events. Mechanized formal verification can guarantee such correctness, but typically demands months to years of expert effort. As evidence, even SOTA coding agents (Claude Code with Opus 4.6, Codex with GPT-5.4) succeed on only 2/7 distributed key-value-store specifications. In this paper, we present the first effective approach to addressing this gap, Inductive Deductive Synthesis (IDS), which jointly and incrementally synthesizes implementation and proof, and learns from failed attempts to systematically try promising strategies. Built as an agentic LLM system, IDS achieves 7/7 in about 6.8 hours and $106 per spec on average, roughly 200× faster than expert effort and 17% cheaper than SOTA agents. IDS further incorporates performance feedback into the same loop, yielding implementations up to 3× faster than published verified systems.

Multimodal large language models must adapt to evolving tasks and domains, yet continual improvement under bounded deployment footprint remains difficult because repeated parameter updates or growing replay stores can accumulate adaptation state over time. We study fixed-footprint continual adaptation: the deployed adaptation state is kept under a fixed memory budget, while the backbone model is left unchanged and task-specific updates are externalized. We propose **InduceKV**, a retrieval-based method that stores each selected training prefix as an attention-ready memory entry, consisting of a frozen retrieval key and compact layerwise key--value (KV) payloads that can be appended to the model's self-attention cache. Under a strict memory budget, **InduceKV** constructs a compact inducing set through bilevel selection: a lightweight calibration is fit for retrieval, while the selected memory balances current-task likelihood, anchor-based retention, and coverage in the frozen retrieval space. Across task-incremental instruction tuning, continual VQA, domain-incremental adaptation, and lifelong multimodal instruction tuning, **InduceKV** consistently improves over PEFT, MoE, replay, and prompt-retrieval baselines under matched memory budgets. We further report backbone-matched, stage-1 CoIN, compute-matched, and scalability diagnostics, showing that the gains are not due to a stronger backbone, replay alone, or an unbounded candidate pool.

Although existing deep multi-view clustering methods often achieve high performance, they predominantly focus on improving the fused representation while overlooking the enhancement of individual views, often resulting in stagnant or inconsistently improved view-specific representations that limit the final fusion quality. To address this, we propose Explicit single-View Enhancement (EVE), a novel deep multi-view clustering framework designed to explicitly optimize the clustering capability of each individual view. Specifically, EVE employs an attention-based module to generate a global consensus as a reliable anchor, which subsequently guides the refinement of individual views through two key components: feature-level selective alignment and structural-level neighborhood propagation. Crucially, the enhanced single views will further boost the fused representation, and finally leading to a mutually reinforcing closed-loop feedback process. Our method is also naturally applicable to incomplete deep multi-view clustering scenarios. Extensive experiments on multiple benchmark datasets demonstrate that EVE consistently outperforms state-of-the-art competitors, achieving substantial average improvements of **5.9%** in ARI across all datasets.**The code is available in the Supplementary Material**.

Rapid advancements in large language models (LLMs) have sparked the question whether these models possess some form of consciousness. To tackle this challenge, Butlin et al. introduced a list of indicators for consciousness in artificial systems based on neuroscientific theories. In this work, we evaluate a key indicator from this list, called HOT-3, which tests for agency guided by a general belief-formation and action selection system that updates beliefs based on meta-cognitive monitoring. We view beliefs as representations in the model's latent space that emerge in response to a given input, and introduce a metric to quantify their dominance during generation. Analyzing the dynamics between competing beliefs across models and tasks reveals three key findings: (1) external inputs systematically modulate internal belief formation, (2) belief formation causally drives the model's action selection, and (3) models can monitor and report their own belief states and adjust behavior in response to internal conflict. Together, these results provide empirical support for the existence of belief-guided agency and meta-cognitive monitoring in LLMs. More broadly, our work lays methodological groundwork for investigating the emergence of agency, beliefs, and meta-cognition in LLMs.