NeurIPS 2026 Papers

Equilibrium Propagation (EP) is a training framework for energy-based models (EBMs) that has attracted interest in the context of neuromorphic computing platforms such as continuous Hopfield networks, nonlinear resistive networks and coupled phase oscillators. However, EP's practical applications have so far remained limited to relatively small-scale problems. Predictive coding networks (PCNs), another class of EBMs rooted in computational neuroscience, are typically trained with a specialized algorithm and have likewise not yet been demonstrated at large scale. In this work, we develop a more effective training method for PCNs which combines the centered variant of EP with a novel equilibration scheme for PCNs. Using this approach, we train a 10-layer convolutional PCN (VGG10) on full-size ImageNet, achieving 13.23% test error rate on the top-5 classification task, close to the 12.2% backpropagation baseline. To our knowledge, this is the first demonstration of both PCNs and EP-based training at ImageNet scale. These results significantly extend the scalability of both approaches and suggest that the primary challenges in scaling EP in other EBMs may not be attributed to inherent limitations of the EP framework.

Unsupervised learning in Vision Transformer models, such as DINO, enables robust visual perception without requiring labeled data by leveraging large-scale image datasets. However, these models lack a focusing mechanism during training, resulting in perceptual representations that are often ambiguous or overly similar. In this work, we introduce two visual focusing loss functions designed to establish correspondences between the model's attention and specific regions within images. Specifically, we leverage the multi-head attention mechanism within the model to selectively steer the model's focus, leading to the emergence of multiple, diverse, and focused perceptual capabilities without requiring supervision. Through both qualitative and quantitative evaluations, we demonstrate that our method substantially increases the spatial selectivity and diversity of attention heads, improving both explainability and fine-grained recognition performance.

Training quality is the primary determinant of reasoning efficiency in large language models, yielding greater returns than proportional increases in inference computation. Evaluating 44 language models (0.5B--685B parameters) across six reasoning benchmarks totalling over 67000 assessments, this study establishes when additional inference tokens are beneficial, redundant or actively harmful. Standard models exhibit near-universal accuracy convergence at approximately 1000 tokens regardless of architecture or parameter count. Causal intervention experiments demonstrate that constraining generation length improves reasoning accuracy by 15.4 percentage points, identifying over-generation rather than capacity exhaustion as the primary efficiency bottleneck. Among 13 reasoning-specialised models, training methodology yields 18.8-fold efficiency improvement at matched parameter scales, exceeding gains from ten-fold parameter increases. Graduate-level evaluation reveals that arithmetic benchmark performance does not predict reasoning capability on complex tasks ($r = -0.03$, $P = 0.91$), exposing fundamental limitations invisible to standard evaluation practice. Mechanistic profiling reveals two orthogonal dimensions of training quality---quality control and decomposition efficiency---that independently predict efficiency profiles, providing a measurable framework linking training decisions to inference-time behaviour.

We introduce Quokka, the first comprehensive scaling law for diffusion language models (DLMs), encompassing both compute- and data-constrained regimes alongside key modeling and optimization designs. Under compute constraints, we find that optimal parameter and dataset sizes scale equally with compute ($N_{\mathrm{opt}} \propto C^{0.5}$, $D_{\mathrm{opt}} \propto C^{0.5}$); however, DLMs are 2--5$\times$ more data-hungry than autoregressive (AR) models, requiring larger corpora and proportionally smaller models for a given FLOP budget. Under data constraints, validation loss follows a U-shaped curve across epochs, with the onset of overfitting scaling as $e_{\mathrm{opt}} \propto U_D^{0.39}/N^{0.55}$. This indicates that optimally leveraging a fixed unique data budget ($U_D$) requires allocating both modestly larger models and more training epochs. Beyond data and parameter allocation, we provide actionable guidance on DLM design choices: absorbing-mask transitions outperform uniform diffusion, linear noise schedules are the most stable and performant, and principled diffusion ELBO objectives ultimately surpass MaskGIT losses despite slower initial convergence. Furthermore, we demonstrate that easy-to-hard noise curricula accelerate early learning, established AR scaling laws for batch size and learning rate transfer seamlessly to DLMs, and weight decay, while unhelpful for single-epoch runs, is essential for multi-epoch regularization.

Estimating how often an ML model will fail at deployment scale is central to pre-deployment safety assessment, but a feasible evaluation set is rarely large enough to observe the failures that matter. Jones et al. (2025) address this by extrapolating from the largest k failure scores in an evaluation set to predict deployment-scale failure rates. We give a finite-k decomposition of this estimator's forecast error and show that it has a built-in bias toward over-prediction in the typical case, which is the safety-favorable direction. This bias is offset when the evaluation set misses a rare high-failure mode that the deploy set contains, leaving the forecast to under-predict at deployment scale. We propose a fine-tuning objective, the forecastability loss, that addresses this failure mode. In two proof-of-concept experiments, a language-model password game and an RL gridworld, fine-tuning substantially reduces held-out forecast error while preserving primary-task capability and achieving safety similar to that of supervised baselines.

Long context is becoming a core capability of modern large vision-language models (LVLMs), enabling sustained context management across long-document understanding, video analysis, and multi-turn tool use in agentic workflows. However, practical training recipes remain under-documented, such as how to construct and mix long-context data. In this work, we present a systematic study of long-context continued pre-training for LVLMs, extending a 7B LVLM from 32K to 128K context with extensive ablations on long-document data. We find that: 1) synthesizing long-document VQA data provides effective and diverse long-context supervision, covering tasks from information extraction to numerical reasoning; 2) retrieving relevant evidence remains the primary long-context bottleneck, favoring retrieval-heavy mixtures with a small amount of reasoning data to preserve task diversity; 3) surprisingly, pure long-document VQA data largely preserves short-context capabilities, suggesting that instruction-formatted long data lessens the need for short-data mixing. Instantiating these findings, we obtain MMProLong by continuing training from Qwen2.5-VL-7B, improving long-document VQA performance by 7.11 points under only a 5B-token budget. More importantly, MMProLong generalizes beyond its 128K training window, maintaining strong performance at 256K and 512K without additional training. More broadly, it also transfers to webpage-based multimodal needle-in-a-haystack tasks, long-context vision-text compression, and long-video understanding without task-specific supervision. Overall, our study provides a practical LongPT recipe and an empirical foundation for advancing the next generation of LVLMs.

Can language models (LMs) learn to faithfully describe their internal computations? Are they better able to describe themselves than other models? We study the extent to which LMs' privileged access to their own internals can be leveraged to produce new techniques for explaining their behavior. Using existing interpretability techniques as a source of ground truth, we fine-tune LMs to generate natural language descriptions of (1) the information encoded by LM features, (2) the causal structure of LMs' internal activations, and (3) the influence of specific input tokens on LM outputs. When trained with only tens of thousands of example explanations, explainer models exhibit non-trivial generalization to new queries. This generalization appears partly attributable to explainer models' privileged access to their own internals: fine-tuning a model to explain its *own* computations generally works better than fine-tuning a different model (even if the explainer model is significantly more capable than the target). Our results suggest not only that LMs can learn to reliably explain their internal computations, but that such explanations offer a scalable complement to existing interpretability methods.

Inference-time scaling provides a promising path for improving agentic reasoning performance, and one widely adopted form is sample-then-select: first sample a pool of candidate reasoning trajectories, then select from the resulting candidates. While this keeps scaling lightweight without updating the policy, it exposes a training-deployment mismatch. Standard trajectory-wise Reinforcement Learning (RL) objectives optimize normalized signals for individual trajectories, whereas choosing from a large candidate pool with the policy's own selection signal is inherently set-conditional: it requires calibrated ranking and confidence aggregation across correlated trajectories. To address this challenge, we propose AutoPortfolio, a set-conditional policy alignment framework for efficient and effective sample-then-select scaling. AutoPortfolio builds a tractable environment-informed target on the sampled candidates, and uses its induced Plackett-Luce (PL) ranking to calibrate the policy which trajectories to prioritize within that set. It trains the policy with a balanced PL-motivated objective that reallocates probability mass among competing trajectories, preserving reward-aligned alternatives while sharpening away from low-quality distractors. Aligned with our policy training, our lightweight inference-time Mass Aggregation scaling adaptively perceives confidence from candidate trajectories and selects the most promising answer(s). Theoretically, we show that reducing our set-conditional loss narrows the discrepancy between policy-induced and environment-informed PL rankings on the sampled set. Empirically, across 12 challenging reasoning benchmarks, AutoPortfolio improves over strong agentic RL baselines, with the clearest gains in larger candidate pools where the set-level selection is crucial.

Many training-free sparse attention methods are effective for accelerating diffusion models. Recently, several works suggest that making sparse attention trainable can further increase sparsity while preserving generation quality. We study three key questions: (1) when do the two common masking rules, i.e., Top-k and Top-p, fail, and how can we avoid these failures? (2) why can trainable sparse attention reach higher sparsity than training-free methods? (3) what are the limitations of fine-tuning sparse attention using the diffusion loss, and how can we address them? Based on this analysis, we propose SpargeAttention2, a trainable sparse attention method that achieves high sparsity without degrading generation quality. SpargeAttention2 includes (i) a hybrid masking rule that combines Top-k and Top-p for more robust masking at high sparsity, (ii) an efficient trainable sparse attention implementation, and (iii) a distillation-inspired fine-tuning objective to better preserve generation quality during fine-tuning using sparse attention. Experiments on video diffusion models show that SpargeAttention2 reaches 95% attention sparsity and a $16.2\times$ attention speedup while maintaining generation quality, consistently outperforming prior sparse attention methods.

Retrieval-augmented diffusion models (RAG-DMs) have significantly advanced image synthesis by incorporating external knowledge bases. However, their security vulnerabilities against malicious external data remain largely underexplored. Existing data poisoning attacks against diffusion models primarily corrupt internal parameters. They fail against RAG-DMs because clean retrieved images easily override these compromised parameters. Furthermore, recent attack tailored for RAG-DMs requires training the retriever, resulting in high computational costs and overfitting to specific retrievers. To bridge this gap, we propose PoisonedRDM, a novel and train-free data poisoning attack tailored to execute concept hijacking against RAG-DMs. Specifically, PoisonedRDM poisons the knowledge base with a minimal number of optimized images and optimizes adversarial perturbations through a joint optimization strategy, steering unknown retrievers toward the poisoned images via surrogate ensemble alignment and aligning the generated outputs with a malicious target concept, while adhering to a strict perturbation budget to maintain high visual stealthiness. Experiments show that PoisonedRDM effectively attacks RAG-DMs, achieving high success rates and outperforming state-of-the-art baselines.

Recent progress in computer vision has produced a wide range of powerful specialized models for detection, segmentation, counting, and other visual tasks. However, these models are usually optimized for isolated task formulations, making it difficult to directly support general-purpose visual intelligence, especially when a task requires complex language understanding and dense small-object perception. In this paper, we propose VisHarness, a trainable visual agent that decouples high-level perception, reasoning, and decision-making from low-level task execution. Instead of training a model to solve a specific visual task, VisHarness learns to harness a set of carefully designed heterogeneous visual experts. This paradigm preserves the general intelligence of the agent while fully leveraging the precision advantages of specialized visual models in concrete visual tasks. With only lightweight training, VisHarness learns a generalizable visual expert-harnessing policy and can solve common fundamental vision tasks under various complex conditions through multi-turn interactions with visual expert models. To enable efficient on-policy reinforcement learning training in a live environment, we introduce dynamic visual memory archiving, which mitigates the rapidly accumulating visual-token overhead caused by multi-turn interactions with visual expert models. Experiments on four representative benchmarks covering reasoning segmentation, generalized referring segmentation, dense small-object detection, and referring counting demonstrate that VisHarness substantially outperforms existing general-purpose models and achieves competitive or superior performance compared with task-specific models.

The analysis of electrostatic induction effects on transmission lines in real-world power distribution systems requires inferring induced surface charge density $\sigma$ on overhead-line corridors at deployment scale, where dense $\mathcal{O}(N^3)$ boundary-element solvers for the underlying Poisson boundary integral equation (BIE) are infeasible. We present a recipe for training cheap PDE surrogates from canonical-case closed forms (flat ground, grounded sphere) plus sparse dense-solver fine-tuning where the canonical case breaks like in our case study. The recipe also avoids a structural degeneracy between training operator $A_\theta$ and solution $\sigma$ in self-supervised operator learning that tends to lead to internally consistent but non-physical solutions. The recipe combines a closed-form local-tangent-plane baseline plus a small neural correction; a frozen analytic kernel; an $SE(3)$- and scale-invariant dimensionless feature stack derived from a $2$-term identity $\sigma = -(\nabla\phi\cdot\hat{n})/(2\pi) + H\phi/(4\pi)$, exact on flat ground and the grounded sphere and supervised training against this identity. An $8$-parameter linear head recovers the analytic curvature coefficient $+1/(4\pi)$ from data to within $2\%$; holds to $1\%$ relative RMS in $\sigma$ across $12$ orders of magnitude in source-charge scale, where DeepONet, Set Transformer, and FNO baselines miss the analytic answer by orders of magnitude out-of-distribution; and matches direct-collocation boundary-element ground truth on a synthetic curved patch to $3.8\%$ relative RMS. A regime-of-validity result delineates when the canonical $2$-term identity applies; outside it (terrain curvature radius $\kappa^{-1}$ much greater than source clearance height $|h|$, the corridor regime), we extend the recipe with sparse dense-BEM-target supervision. On several industrial transmission-line corridors with native triangulated meshes, the extended recipe attains $9.2\%$ median relative RMS to dense BEM on held-out corridors, $20\times$ tighter than the analytic 2-term plug-in. Deployment: a $1.7$kB MLP, seconds per corridor on a single CPU core.

Reinforcement learning (RL) has become essential for post-training large language models (LLMs) in reasoning tasks. While scaling rollouts can stabilize training and enhance performance, it introduces substantial computational overhead. In algorithms like GRPO, multiple rollouts per prompt incur prohibitive costs, as a large portion of prompts provide negligible gradients and are thus of low utility. This raises a key question: \textit{how to identify high-utility prompts before an expensive rollout?} Our experimental analysis reveals that sample utility is non-uniform and dynamic: the strongest learning signals concentrate at the ``learning edge'', the intersection of intermediate difficulty and high response entropy, which shifts throughout training. Motivated by this observation, we propose HIVE, a history-informed and online-verified prompt selection framework for data-efficient RL training. HIVE first uses historical reward statistics and response entropy as a cheap prior to filter candidate prompts, and then employs prompt entropy as a real-time proxy to prune instances with stale utility. Across multiple reasoning benchmarks and base models, HIVE maintains reasoning accuracy with substantial rollout cost reduction, achieving up to 2.3× total training speedup.

Dense 3D tracking from monocular video is fundamental to dynamic scene understanding. While recent 3D foundation models provide reliable per-frame geometry, recovering object motion in this geometry remains challenging and benefits from strong motion priors learned from real-world videos. Existing 3D trackers either follow iterative paradigms trained from scratch on synthetic data or fine-tune 3D reconstruction models learned from static multi-view images, both lacking real-world motion priors. Pre-trained video diffusion transformers (video DiTs) offer rich spatio-temporal priors from internet-scale videos, making them a promising foundation for 3D tracking. However, their frame-anchored formulation, which generates each frame's content, is fundamentally mismatched with reference-anchored dense 3D tracking, which must follow the same physical points from a reference frame across time. We present TrackCraft3R, the first method to repurpose a video DiT as a feed-forward dense 3D tracker. Given a monocular video and its frame-anchored reconstruction pointmap, TrackCraft3R predicts a reference-anchored tracking pointmap that follows every pixel of the first frame across time in a single forward pass, along with its visibility. We achieve this through two designs: (i) a dual-latent representation that uses per-frame geometry latents and reference-anchored track latents as dense queries, and (ii) temporal RoPE alignment, which specifies the target timestamp of each track latent. Together, these designs convert the per-frame generative paradigm of video DiTs into a reference-anchored tracking formulation with LoRA fine-tuning. TrackCraft3R achieves state-of-the-art performance on standard sparse and dense 3D tracking benchmarks, while running 1.3x faster and using 4.6x less peak memory than the strongest prior method. We further demonstrate robustness to large motions and long videos. Our code and weights will be publicly released.

We introduce Track4D, a method that formulates dense 3D tracking as conditional video generation. Repurposing large-scale pretrained video generators for 3D tracking is non-trivial: 3D point tracking in world space produces signals far from natural video, making it difficult for the video diffusion model (VDM) to learn. We systematically study two representations for encoding 3D tracking in the VDM latent space: a Residual 3D Tracking Video (RTV) that directly encodes metric 3D offsets, and a Normalized Coordinate Map Video (NCMV) that implicitly encodes the underlying geometric correspondences as canonical 2D coordinate maps. We further condition the VDM on point maps from an off-the-shelf 3D reconstructor to provide an explicit geometric scaffold for tracking. Trained exclusively on limited synthetic data with LoRA adaptation, Track4D achieves competitive zero-shot tracking performance across five benchmarks, demonstrating the potential of leveraging video generation priors for dense 3D tracking.

Large language model (LLM) agents are increasingly deployed in scientific research, where reliability is critical, and the underlying knowledge is densely interconnected. In such settings, hallucinations are particularly damaging: a single erroneous claim on a foundational concept can propagate through multi-step reasoning and corrupt entire trajectories. Existing hallucination benchmarks largely operate at the surface level, treating facts in isolation and relying on uniform accuracy metrics that ignore this topological structure. We address this gap with \textsc{Schema}, the first evidence-grounded, topology-aware evaluation framework for scientific agents. Built on an automated concept-graph construction pipeline, \textsc{Schema} provides two complementary diagnostic instruments. A trajectory hallucination pipeline audits intermediate reasoning at scale via a topology-weighted severity score ($\mathrm{HS}^w$), while a multi-agent counterfactual attribution module pinpoints the causal mechanism behind selected failures. The framework supports diverse task formats spanning multi-hop reasoning, claim verification, and programmatic experimental execution. Across two biomedical subdomains and eleven contemporary LLM agents, \textsc{Schema} reveals that hallucinations concentrate at a small set of highly connected knowledge hubs, and that final-answer accuracy decouples from trajectory honesty—models often reach correct conclusions through structurally flawed reasoning. These results indicate that for high-stakes scientific applications, terminal accuracy alone is an insufficient signal of agent reliability, motivating mechanism-level evaluation grounded in knowledge topology\footnote{Code is available at \url{https://anonymous.4open.science/r/SCHEMA_NIPS2026}}.

Do large language models represent psychological constructs internally, or do they only generate outputs that resemble psychometric structure? We address this question using a cross-persona paradigm across 14 models (Llama3 and Qwen2.5, 0.5B--14B, base and instruct). Given responses on one psychological scale from real individuals ($N = 272$), models predict responses on six other scales. At the behavioral level, LLMs reproduce human cross-scale correlation structure and systematically amplify it, with model-generated correlations exceeding human estimates even after correcting for measurement attenuation. We then examine whether this structure is reflected internally. Contrastive direction analysis reveals an organized geometry in activation space aligned with psychometric relationships. This structure emerges in large instruct models but is not observed in base models. Across models, geometry strength predicts behavioral amplification ($r = 0.68$, $p = 0.008$; partial $r = 0.69$ controlling for log size), independent of model size. To relate internal structure to output behavior, a matched activation-probing paradigm shows that representational amplification is less variable than behavioral amplification ($1.38$--$1.77$ vs $0.53$--$1.53$). A synthetic control with known ground-truth structure shows that this range survives subtraction of a ridge-probe baseline ($\approx 1.3$), with adjusted slopes still predicting behavior at $r = 0.88$. We term the systematic representation-to-behavior gap \emph{readout attenuation}. Together, these findings suggest that LLMs encode structured representations aligned with psychological constructs, while differences in output primarily reflect how these representations are read out.

Halpernian actual causation, the formal study of which events in a specific situation caused a specific outcome in acyclic structural causal models, underpins legal responsibility, moral blame, and the assessment of causal harm. Despite the rich logical framework, no prior sound and complete enumeration procedure is known for finding *all* actual causes in a given setting, blocking downstream tasks such as responsibility attribution, blame assessment, and causal-harm grading that aggregate over the full cause set. We close this gap by introducing *witness targets*: sets of joint configurations containing every counterfactual witness. In combination with an *ancestor intervention grammar* we derive a finite directed acyclic *witness map*. We prove that for every actual cause there exists a contingency set such that the joint intervention set appears as a node of this map, and present an algorithm for *Tracing Actual Causes (TrAC)* that is sound and complete for enumerating all actual causes of any target event. We compare TrAC empirically with existing single-cause baselines on random Boolean structural causal models, demonstrating practical feasibility for graphs of up to 15 nodes.

While LLMs excel at isolated coding tasks, their ability to perform autonomous, long-horizon machine learning (ML) development remains bottlenecked by poor strategic planning. Because current benchmarks rely on outcome-based metrics, they obscure process-level failures, making it impossible to diagnose where agent strategies diverge from human expertise. To solve this, we introduce TraceML, the first large-scale dataset of paired human and agent trajectories for long-horizon ML tasks. TraceML contains 4{,}672 Kaggle trajectories across 134 MLE-bench competitions, with 430 expert humans paired head-to-head with 207 LLM-agent runs on 7 of those competitions. Using a unified extraction schema to analyze step-by-step behavior, we reveal systematic gaps: agents execute local edits well but exhibit unstructured exploration, poor experiment prioritization, and weak long-term memory attribution compared to experts. Translating these diagnostic insights into action, we design a novel, planning-oriented agent harness based on human priors that significantly improves both process efficiency and final competitive performance.