NeurIPS 2026 Papers

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.

We present Leak-CURBER, the largest multimodal, leakage-controlled benchmark for evaluating machine learning and deep learning models for enzymatic reactions. Leak-CURBER standardizes data from 10 biochemical databases and curates datasets with multimodal inputs, metrics, and leakage-controlled splits for 4 tasks. The benchmark comprises 10 subtasks: prediction of reaction outcomes (2), enzyme function (2), kinetic parameters (3), and protein–ligand binding (3). Leak-CURBER establishes new evaluation protocols that control for train/validation/test overlap across protein sequence and structure, molecule string and structure, and reaction similarity, thereby exposing generalization failures of learning methods. Evaluating the state-of-the-art (SOTA) models on Leak-CURBER shows that their strong performance degrades sharply under these splits, often approaching random classification or retrieval performance, and near-zero regression performance. Leak-CURBER includes precomputed embeddings, continual benchmark releases, reproducible curation scripts, and a public leaderboard to support reliable comparison of enzymatic-reaction models.

Joint Embedding Predictive Architectures (JEPAs) offer a compelling framework for learning world models in compact latent spaces, yet existing methods remain fragile, relying on complex multi-term losses, exponential moving averages, pre-trained encoders, or auxiliary supervision to avoid representation collapse. In this work, we introduce LeWorldModel (LeWM), the first JEPA that trains stably end-to-end from raw pixels using only two loss terms: a next-embedding prediction loss and a regularizer enforcing Gaussian-distributed latent embeddings. This reduces tunable loss hyperparameters from six to one compared to the only existing end-to-end alternative. With ~15M parameters trainable on a single GPU in a few hours, LeWM plans up to 48x faster than foundation-model-based world models while remaining competitive across diverse 2D and 3D control tasks. Beyond control, we show that LeWM's latent space encodes meaningful physical structure through probing of physical quantities. Surprise evaluation confirms that the model reliably detects physically implausible events.

Representation learning for single-cell RNA-seq has been evaluated by the identities representations capture — cell types, lineages, perturbations — rather than how faithfully they model the distribution of cell states on the gene expression manifold. As a result, density estimation, rare-state detection, perturbation scoring, and gene-level attribution are bolted onto frozen embeddings as separate models, disconnected from the geometry of the data. We argue that the density model should be the primary object and that representation quality follows from it. Building on LeJEPA, whose SIGReg objective enforces a provably optimal isotropic Gaussian latent, we introduce LeCellModel, which exploits this Gaussian latent to recover data density on the gene expression manifold via the encoder's Jacobian log-volume (JEPA-SCORE). Across several datasets, LeCellModel outperforms established methods on scIB benchmark for representation quality. Furthermore, we show that LeCellModel enables estimation of rare expression states using JEPA-SCORE as a typicality measure – applying it to a controlled cytokine panel, where it identifies stimulated cells across minority fractions and tracks pathway-response magnitude. We introduce gene-level interpretability of density estimates — to our knowledge, the first method for analyzing JEPA-SCORE in feature space. Leveraging this framework, LeCellModel recapitulates the known association of a profibrotic macrophage program with idiopathic pulmonary fibrosis, and discovers a novel CD177$^{+}$ activated regulatory T cell subpopulation previously described only in tumor contexts. Both findings emerge directly from the geometry of the learned embedding, without relying on supervised annotations.

Modern reasoning models depend on reasoning data, today sourced from human annotations or distilled from stronger LLMs. However, a rich and largely untapped source of supervision lies in expert systems (e.g., game engines, classical planners, theorem provers), which routinely produce near-optimal actions across diverse domains. But these experts are silent: they commit to an action without writing down the chain of thought (CoT) behind it. Recovering that CoT as natural-language reasoning would distill expert knowledge into a student that generalizes beyond the demonstrated actions. We treat it as a latent variable and study how to recover it from the action alone. Our approach, LeAct (**Le**arning to reason from **Act**ions), optimizes this latent variable: the student samples candidate CoTs for each expert action, and we retain those that measurably improve its own probability of recovering the action. Across imperfect-information games at multiple scales and a simulated robotics benchmark, LeAct reaches the solver's numerical floor on small enumerable games. At larger scale, it is $5\times$ closer to the solver than the strongest expert-iteration baseline. At Flop Hold'em ($\sim 10^9$ infosets), LeAct wins head-to-head by $+60$ mbb/g, and on the robotics probe it is the only training recipe that improves on direct imitation. We present a principled framework and the result: expert systems become a categorically new source of reasoning teachers for foundation models.

Compared with residential layouts, public indoor floorplans present more substantial challenges with open corridors, complex room relations, and non-Manhattan geometries, which do not conform to conventional residential-layout assumptions. Consequently, existing methods are prone to boundary discontinuities, leading to fragmented corridors and irregular wall structures. To address the above issues, we propose \textit{LayoutBridge}, a structure-conditioned generative framework for floorplan production. By moving beyond the Manhattan-geometry assumptions commonly adopted in residential scenarios, LayoutBridge reformulates the task as a latent-space Brownian-bridge diffusion process from structural constraints to target layouts. We have constructed our PISF dataset with 3,517 representative floorplans in public indoor spaces, and LayoutBridge reduces FID by 132.35 and improves BIoU by 15.52\% over the latest image-to-image baselines. Regarding the residential benchmarks MSD and RPLAN, it also reduces FID by at least 2.53 compared with state-of-the-art. These results demonstrate its potential for scalable automated architectural design. Code implementing the proposed method is publicly available at \href{http://github.com/lalalalaxxx/LayoutBridge}{http://github.com/lalalalaxxx/LayoutBridge}.

Transcriptome-conditioned whole-slide image (WSI) synthesis aims to decode the complex mapping from molecular states to histologic phenotypes. Existing generative paradigms predominantly rely on a direct black-box transcriptome-to-image mapping, tasking a single generator with the simultaneous interpretation of transcriptome signals, inference of multicellular spatial organization, and rendering of fine-grained textures. This formulation, however, is structurally under-constrained; the underlying tissue architecture, the critical substrate linking gene expression to morphology, remains latent and only weakly supervised by pixel-level objectives. We present \textsc{TopoScape}, a topology-anchored framework for transcriptome-to-histology generation under a \emph{Layout-Before-Pixels} principle. Instead of synthesizing pixels directly from transcriptomic embeddings, \textsc{TopoScape} first resolves molecular states into explicit, multi-class cellular topologies via an RNA-guided Topological Prior Generator, reinforced by persistence-based topological regularization. These resolved topologies are further reparameterized into a suite of topology-derived controls, including structure-aware initialization, continuous density fields, and distance representations, which guide a hierarchical, frequency-decoupled flow-matching trajectory. By introducing multicellular organization as an explicit structural mediator, \textsc{TopoScape} allows molecular states to deterministically shape both the macroscopic tissue architecture and the microscopic generative process. Across five TCGA benchmarks, \textsc{TopoScape} consistently outperforms state-of-the-art methods in generative fidelity, biological realism, and downstream predictive utility. Code and pretrained models will be released.

Training binary neural networks (BNNs) from scratch is dominated by the straight-through estimator (STE), whose forward/backward mismatch produces severe accuracy degradation as networks deepen. We study an orthogonal axis: when and where binarization is enforced during training. We introduce StoMPP (Stochastic Masked Partial Progressive Binarization), which gradually replaces clipped weights and activations with their hard binary counterparts layer by layer from input to output, using stochastic partial masks with soft refresh. StoMPP delivers two complementary benefits. As a standalone training rule, it provides a fully STE-free procedure that improves over vanilla STE with gains that grow with depth (ResNet-50 BNN: +18.0/+13.5/+3.8 on CIFAR-10/100/ImageNet), and the pattern holds across ResNet-18/34/50, MobileNetV2, and BERT fine-tuning. Composed with surrogate gradients by applying STE only to frozen entries, it reaches +27.1/+19.8/+17.7 over vanilla STE on the same setting. Underlying both regimes is a single mechanistic finding: progression order is decisive. Forward layerwise progression prevents depth collapse, reverse progression collapses to near-chance, and binary-weight networks (without binary activations) are insensitive to order. We trace this asymmetry to activation-induced gradient blockades: a committed binary activation severs gradient flow upstream, and ordering controls when these blockades form. To isolate the progression's contribution from any benefit conferred by STE, we conduct all ablations in the STE-free regime; the resulting characterization (schedule, refresh, ordering, dynamics) thus reflects the progression itself rather than its interaction with surrogate gradients.

Autoencoders (AEs) are widely used in unsupervised anomaly detection (AD) due to their ability to model complex data distributions. However, their strong reconstruction capacity, while effective for capturing normal patterns, often enables them to also reconstruct anomalous objects, including both individual and collective anomalies, which reduces detection performance. This limitation is particularly severe for collective anomalies, which are frequently misinterpreted as normal clusters. To address this issue, we propose Layer Precision Reduction (LPR), a novel technique that systematically constrains the numerical precision of weights and biases in neural network layers to strategically reduce the learning capacity of neural networks, such as the reconstruction capacity of AEs. LPR encourages the network to prioritize dominant manifold structures while suppressing the reconstruction of rare or anomalous patterns. While LPR was primarily developed for AE-based detectors (the focus of this paper), it is applicable to any neural network. Simulations are conducted with 24 AD models across 30 real-world public datasets. LPR is applied to 10 deep AD models, including 5 unsupervised AE-based methods, 2 unsupervised non-AE-based methods, 1 semi-supervised method, 1 weakly supervised method, and 1 fully supervised method. LPR consistently improves all 10 models, most notably enhancing the best-performing unsupervised AE-based detector from an average AUROC of 72.12\% to 83.06\%, surpassing the strongest unsupervised non-AE-based competitor, which achieves an average AUROC of 77.36\%, across the remaining 14 detectors. These results reveal a previously unexplored link between layer-level numerical precision and manifold pattern prioritization, demonstrating that LPR serves as a simple yet powerful mechanism for enhancing AD performance while offering broad applicability to diverse neural architectures and potential extensions to tasks beyond AD.

Forward-Forward (FF) training allows each layer to learn from a local goodness criterion. In cumulative-goodness variants, however, later layers can inherit a task that earlier layers have already partially separated. We formalize this phenomenon as layer free-riding: under the softplus FF criterion, the class-discrimination gradient reaching block $d$ decays exponentially with the positive margin accumulated by preceding blocks. We then study three local remedies---per-block, hardness-gated, and depth-scaled---that recover current-layer separation measures without relying on backpropagated gradients. On CIFAR-10 and CIFAR-100, these remedies dramatically improve layer-separation statistics, with $4\times$--$45\times$ gains in deeper layers, while changing accuracy by less than one percentage point for non-degenerate training procedures. Tiny ImageNet provides a tougher cross-dataset check for our selected block-wise configuration and reveals the same qualitative gap between layer-health diagnostics and final accuracy. Calibration experiments further show that architecture and augmentation choices have a larger effect on final accuracy than the training-rule modifications studied here. Cumulative free-riding is therefore a real and repairable optimization pathology. Nonetheless, for the FF training rules, architectures, and datasets we study, it is not the dominant factor limiting achievable accuracy.

We introduce the Lattice Deduction Transformer (LDT), a recurrent transformer that approximates logically sound deduction by projecting its latent state through a lattice between forward passes. We train on-policy in a process that mirrors deduction in a search-based constraint solver and supervise training via a domain-agnostic, abstract-interpretation-based approximation of the set of solution candidates. An $800$K-parameter LDT achieves $100\%$ accuracy on Sudoku-Extreme and Snowflake Sudoku, at a fraction of the training cost of prior small recurrent reasoners, while remaining empirically sound: the model returns a correct answer or abstains. A $1.8$M-parameter variant reaches $99.9\%$ accuracy on Maze-Hard. Frontier LLMs score $0\%$ on all three benchmarks.

Multimodal large language models (MLLMs) have heterogeneous strengths across OCR, chart understanding, spatial reasoning, visual question answering, cost, and latency. As a result, effective MLLM routing requires more than estimating query difficulty: a router must match the multimodal requirements of the current image-question input with the capabilities of each candidate model. We propose \textsc{LatentRouter}, a router that formulates MLLM routing as counterfactual multimodal utility prediction. Given an image-question query, \textsc{LatentRouter} extracts learned multimodal routing capsules, represents each candidate MLLM with a model capability token, and performs latent communication between these states to estimate how each model would perform if selected. A distributional outcome head predicts model-specific counterfactual quality, and a bounded capsule correction refines close decisions while limiting the influence of noisy routing signals. The resulting utility-based policy supports both performance-oriented and performance-cost routing, and can handle changing candidate pools through shared per-model scoring with availability masking. Experiments on MMR-Bench and VL-RouterBench show that \textsc{LatentRouter} outperforms strong fixed-model, feature-level, and learned-router baselines. Additional analyses show that the gains are strongest on multimodal task groups where model choice depends on visual, layout-sensitive, or reasoning-oriented requirements, and that latent communication is the main contributor to the improvement. The code is available at: https://anonymous.4open.science/r/LatentRouter-8718.

While joint audio-visual understanding is fundamental to advancing machine cognition, current multimodal large language models (MLLMs) still struggle with complex cross-modal reasoning. Existing text-based chain-of-thought (CoT) compresses rich multi-modal features into discrete text, incurring information loss and inducing a language-bound phenomenon that diminishes attention to audio-visual signals. In contrast, a continuous latent space inherently preserves dense representations, serving as an ideal carrier for audio-visual information. Motivated by this, we propose $\textbf{LatentOmni}$, a novel cross-modal reasoning framework. By introducing a feature-level supervision mechanism to directly reconstruct raw sensory inputs within the latent space, LatentOmni leverages native latent features to bridge audio-visual modalities and text, ensuring sustained attention on original audio-visual inputs throughout reasoning. Furthermore, to maintain temporal consistency across modalities in latent space, we design Omni-Sync Position Embedding (OSPE), which generalizes multimodal rotary position encodings to drive audio-visual synchrony. To supervise this reasoning process, we construct LatentOmni-Instruct-35K, a dataset interleaving text with audio-visual segments that serve as dense evidence for latent reconstruction. Comprehensive evaluation across multiple audio-visual reasoning benchmarks demonstrates that LatentOmni substantially outperforms strong explicit-CoT baselines, validating latent space joint reasoning as a promising path toward genuine omnimodal understanding.

Safety-aligned language models are trained to refuse harmful requests, yet refusal behavior can be suppressed by steering their internal representations. Existing methods do so by ablating a refusal direction from model activations, aiming to remove refusal from the model’s residual stream. Despite their empirical success, these methods lack a principled account of the latent-space transformation they induce and why it suppresses refusal. In this work, we recast refusal suppression as a latent-space evasion attack against linear probes trained to separate refused from answered prompts. Under this view, prior work’s difference-in-means direction naturally defines such a probe, and its ablation is exactly a projection onto its decision boundary, i.e., a minimum-confidence evasion attack. This perspective not only explains the empirical success of prior work but also admits a key limitation: evasion stops at the decision boundary, motivating the need to push representations further into the compliant region, i.e., where the model answers. We leverage this by proposing a Controlled Latent-space Evasion attack that projects representations past the boundary with an optimized confidence. We achieve state-of-the-art attack success rate across 15 instruction-tuned, multimodal, and reasoning models, outperforming existing refusal-ablation baselines and specialized jailbreak attacks.

Bridging independent vision-language models (VLMs) and small language models (SLMs) in a modular multi-agent system typically forces them to exchange information as discrete text, which creates a lossy bottleneck for spatial and fine-grained details. This constraint is especially acute for SLMs, whose limited capacity makes them more reliant on the quality of the input signal. While recent works on latent multi-agent communication have explored latent-space exchange between identical or homogeneous LLMs, propagating rich visual information across model boundaries without text generation has not been studied yet. We propose Latent-Lens, a lightweight codec that bridges the representation gap between a frozen VLM and a frozen SLM directly in latent space, enabling them to communicate purely through hidden states. The codec consists of a domain encoder that projects hidden states from the VLM into the SLM's embedding space, and an attention decoder formalised as a LoRA that teaches the SLM to attend to these visual prefixes, while training only 1.6M parameters (0.2\% of the combined model size). On free-form visual question answering (CLEVR, GQA), Latent-Lens achieves +10.2-28.3pp over a text-communication baseline given the same LoRA budget (+36.4-78.4pp when both agents are frozen); on image captioning (Flickr8k) it improves over the same baseline by +18.5 (+18.9 frozen). Replacing the SLM (TinyLlama-1.1B) or the VLM (InternVL2-1B) with alternative models of different architectures, vocabularies, and hidden dimensions yields consistent gains, confirming generality across heterogeneous model families.

Self-supervised video models are increasingly framed as world models, yet their evaluation remains largely confined to a single top-1 accuracy score on clean benchmarks. This leaves a major gap in comprehending their potential as world models. We present the first systematic study addressing this gap, analyzing four matched-capacity frontier video foundation models, V-JEPA 2.1, V-JEPA 2, VideoPrism, and VideoMAEv2, across five robustness axes relevant to their deployment as video world models: feature discriminability, corruption robustness, fine-grained discrimination, occlusion robustness, and sensitivity to temporal direction. Our evaluations establish that across all five axes, latent-prediction models form a distinct and consistent profile. They degrade more gracefully under pixel corruption, preserve usable class structure rather than mere geometric stability under occlusion, capture fine-grained physical contact cues without reconstructing pixels, and uniquely encode the arrow of time. These advantages can even survive task adaptation: a frozen V-JEPA 2 backbone with a lightweight attentive probe outperforms a fully fine-tuned VideoMAE and a supervised TimeSformer on corruption and occlusion robustness. Our extensive results offer concrete new evidence in favor of latent prediction for robust world modeling.

Humans effortlessly infer 3D structure, such as depth, occlusion, and spatial arrangement, from 2D images and reason about it fluidly. Multimodal large language models still struggle with such spatial reasoning. Current approaches attempt to bridge this gap by injecting explicit 3D priors at inference time or aligning features with 3D-aware teachers during training. While these strategies improve geometric perception, they typically treat 3D knowledge as static representations, rather than enabling the model to reason with 3D cues during inference. We argue that closing this gap requires internalizing 3D knowledge in a form that can participate in the model's reasoning dynamics. To this end, we introduce \textbf{Latent Spatial Reasoning (LSR)}, a framework that distills geometric knowledge into \emph{latent spatial tokens}: geometry‑aware representations that the model actively queries and conditions on to guide its spatial reasoning process. Through hierarchical distillation, LSR transfers 3D knowledge from foundation models, aligns it with the vision-language space, and trains the model to interleave spatial and linguistic reasoning, all without external 3D modules at inference time. Experiments on diverse spatial reasoning benchmarks demonstrate state-of-the-art performance.

Geometric foundation models, such as the Visual Geometry Grounded Transformer (VGGT), provide strong 3D priors from unposed images. However, such models operate purely in a feed-forward, deterministic regime, \ie~they cannot generate plausible geometry beyond what the input views directly support. Generative models for 3D scenes, on the other hand, must rely on strong geometric priors to produce coherent outputs from sparse inputs. We bridge these two paradigms by performing flow matching directly in VGGT's latent space, leveraging its learned 3D priors without committing to any explicit downstream representation such as Gaussians, meshes, or video-VAE latents. This requires respecting the latent geometry: VGGT tokens occupy a product of high-dimensional hyperspheres on which standard Euclidean flow matching fails. We address this with a Riemannian Flow Matching framework defined on a product manifold of four hyperspheres, aligned with VGGT's multi-scale encoder, which keeps generated tokens on the valid data manifold required by the frozen decoding heads. On RealEstate10K and ScanNet++, our method achieves strong performance against recent scene generation baselines in both per-view 3D geometry and appearance, establishing latent-space flow matching on geometric foundation models as a viable paradigm for 3D generation.

Autoregressive (AR) models remain the dominant paradigm for natural language generation, but their strictly sequential decoding process leads to high inference latency. Recent diffusion-inspired language models, such as LLaDA and Dream, alleviate this issue through parallel generation, yet they still face two key limitations: information loss, since predictive distributions over non-finalised tokens are discarded at each step, and unstable commitment dynamics, where local token decisions are not sufficiently coordinated at the global level. We propose Latent Refinement Decoding (LRD), a two-stage decoding framework consisting of Latent Refinement and a Predictive Feedback Loop. In the first stage, LRD keeps masked positions as distributional mixtures of predicted tokens and the mask embedding, enabling the model to form more globally consistent beliefs before committing tokens. In the second stage, LRD progressively finalises confident tokens while preserving uncertain ones for further iterative refinement, with KL-divergence dynamics serving as a stable criterion for convergence and early stopping. Experiments show that LRD improves performance on both coding tasks, including HumanEval by 6.3 and MBPP by 2.6, and reasoning tasks, including GSM8K by 2.9 and MATH500 by 3.8, while achieving up to 10.6× overall speedup. Moreover, LRD is compatible with single-token decoding, multi-token threshold commitment, and system-level accelerators; when combined with Fast-dLLM, it reaches up to 18.4× speedup over vanilla decoding while further improving accuracy.