NeurIPS 2026 Papers

Simulating trajectories of multi-particle systems on complex energy landscapes is a central task in molecular dynamics (MD) and drug discovery, but remains challenging at scale due to computationally expensive and long simulations. Previous approaches leverage techniques such as flow or Schrödinger bridge matching to implicitly learn joint trajectories through data snapshots. However, many systems, including biomolecular systems and heterogeneous cell populations, undergo *dynamic* interactions that evolve over their trajectory and cannot be captured through static snapshots. To close this gap, we introduce **Entangled Schrödinger Bridge Matching (EntangledSBM)**, a framework that learns the first- and second-order stochastic dynamics of interacting, multi-particle systems where the direction and magnitude of each particle's path depend dynamically on the paths of the other particles. We define the Entangled Schrödinger Bridge (EntangledSB) problem as solving a coupled system of bias forces that *entangle* particle velocities. We show that our framework accurately simulates heterogeneous cell populations under perturbations and rare transitions in high-dimensional biomolecular systems. Anonymous code is provided at https://anonymous.4open.science/r/EntangledSBManon.

Structure-informed protein representation learning is essential for effective protein function annotation and $\textit{de novo}$ design. With the rapid progress of protein structure prediction and experimental structure determination, a central challenge in the field is shifting from merely obtaining structural models to reliably leveraging predicted or measured structures for downstream learning. However, both crystal and AlphaFold-like predicted structures can contain structural uncertainty, which can bias local neighborhood construction and make robust protein representation learning challenging. To address these issues, we propose a novel equivariant Transformer-State Space Model (SSM) hybrid framework, termed $E^3$former, designed for efficient and robust protein representation. Our approach uses energy function-based receptive fields to construct proximity graphs that adaptively stabilize neighborhood selection under structural deviations, and incorporates an equivariant high-tensor-elastic selective SSM within the transformer architecture. These components allow the model to adapt to complex geometric interactions and extract structural features with a higher signal-to-noise ratio. Empirical results demonstrate that our model outperforms existing methods in structure-intensive tasks, such as inverse folding and binding site prediction, particularly when using predicted structures, owing to its enhanced tolerance to data deviation and structural uncertainty. Our approach offers a novel perspective for conducting biological function research and drug discovery using imperfect but increasingly available protein structure data. Our code is available on \url{https://anonymous.4open.science/r/E3former-207E}.

Building state-of-the-art (SOTA) predictive models for drug discovery requires expensive search over tools, architectures, and training strategies. Current LLM-based agents can find SOTA solutions through extensive trial and error, but they do not retain the experience accumulated along the way and therefore pay the full search cost on every new task. We propose DrugSAGE (Self-evolving Agent Experience), a framework that accumulates and reuses experience across tasks to build SOTA drug discovery models efficiently. DrugSAGE maintains a cross-task memory of verified skills, statistical evidence about effective strategies, and a record of recurring errors and their fixes. In some cases, DrugSAGE transfers a working solution directly without test-time search. In 33 molecular property prediction tasks, DrugSAGE ranks first among nine SOTA agents in a single-task setting. With memory accumulated from 16 smaller tasks, DrugSAGE achieves a averaged normalized score of 0.935 on 17 held-out tasks in a cross-task evaluation setting and outperforms all baseline agents by 10-30\% in a zero-test-time search regime. In summary, our work shows the advantage of cross-task memory for efficient SOTA model development in drug discovery.

Dexterous object manipulation remains a fundamental challenge in robotics, typically requiring intensive supervision through explicit rewards, goals, or demonstrations. While unsupervised reinforcement learning (RL) holds the promise of discovering dexterous skills, state-of-the-art metric-aware methods have yet to be successfully applied to complex, high-dimensional manipulators like multi-fingered hands. We argue that this limitation stems from two key factors: existing methods lack the necessary inductive biases to prioritize object interaction over agent motion, and they fail to respect the non-Euclidean topology of object configuration space $\mathrm{SE}(3)$. To address these limitations, we propose a novel Wasserstein dependency measure between skills and object motions, formulated in the Lie algebra $\mathfrak{se}(3)$. Our approach, Topology-Aware SKill discovery (TASK), enables the discovery of fundamental manipulation skills—such as multi-axial object translation and rotation—without manual supervision. Across a range of embodiments, including non-prehensile and multi-fingered hands, our method learns dexterous behaviors where previous approaches fail, marking a significant step toward autonomous robotic dexterity.

Symbolic library --- or Koopman dictionary --- selection is a fundamental challenge in data-driven dynamical systems. Extended Dynamic Mode Decomposition (EDMD), Sparse Identification of Nonlinear Dynamics (SINDy), and Kolmogorov--Arnold Networks for Dynamics (KANDy) all require the practitioner to commit to a function library at training time; Deep-Koopman Operators avoid this commitment but produce uninterpretable latent observables. We propose Deep-Koopman-KANDy, a structured approach to post-hoc symbolic dictionary readout that combines Deep-Koopman modeling with Kolmogorov-Arnold Networks for Dynamics (KANDy). The encoder and decoder of a Deep-Koopman Operator are replaced with two-layer Kolmogorov--Arnold Networks (KANs), and a level-set construction together with a chain-rule gradient identity exposes the compositional structure of the learned observables in a basis chosen \emph{after} training. We evaluate the method on the Lorenz system, the Chirikov standard map, the Ikeda map, and the Arnold cat map. On Lorenz it recovers the target dictionary $\{x,y,z,xy,xz\}$ with perfect recall and Jaccard score $0.79\pm0.06$; on the standard map it recovers a low-order Fourier basis matching the analytical structure; on Ikeda---which has no sparse polynomial representation---a misspecified polynomial readout still recovers the correct foliation coordinate $g\approx x^2+y^2$ together with a nontrivial outer function; and on the Arnold cat map --- used as a negative control because finite-dimensional Koopman closure is provably impossible --- the method fails to find a sparse closure, as expected.

Recent advances in reinforcement learning have made verifiable rewards a central post-training paradigm for improving multimodal reasoning. However, methods such as GRPO remain data- and compute-inefficient, often spending rollout and annotation budget on prompts that provide little learning signal. We propose DISCOVER, an online data-discovery framework for budgeted multimodal GRPO that enables vision-language models to dynamically identify prompts that are most useful for the current policy. DISCOVER first organizes the multimodal sample pool into semantic clusters and queries a small set of density-diverse representative samples to obtain initial reward observations. During training, it estimates the utility of unannotated samples by transferring sparse reward feedback from queried samples. Since sample utility changes as the policy evolves, DISCOVER dynamically updates these estimates with recency-weighted rollout observations. It then selects only high-utility prompts for annotation using a policy-conditioned score that accounts for reward variance and difficulty, and continues utility-based replay once the discovery budget is exhausted. Experiments on ViRL39K and VLAA-Thinking with Qwen3-VL-2B show that DISCOVER substantially improves multimodal mathematical reasoning under a strict 10\% unique-sample budget, outperforming budget-matched random selection, hard-example sampling, full-pool GRPO under the same training-step budget, and online selection baselines. Ablations further validate the importance of semantic coverage, online reward transfer, and stable discovery cadence, establishing DISCOVER as a practical framework for data-efficient multimodal RL post-training.

Scientific measurements inherently contain variance. Standard regression, however, treats noisy data as absolute ground truth, leading models to memorize noise rather than physical laws. This overfitting hampers generalization, particularly when transferring from abundant theoretical proxies to scarce experiments. We introduce DETS, a framework replacing rigid point estimation with Physical Tolerance Modeling. Our Interval-Censored Evidential Engine (ICEE) maximizes probability mass within acceptable error margins, explicitly decoupling aleatoric noise from epistemic uncertainty. Using this filtered uncertainty signal, a Thermodynamic Sampling strategy dynamically selects theoretical data to align source and target domains. Experiments across thermodynamics, drug affinity, and bandgap prediction show DETS outperforms state-of-the-art methods. Crucially, it exhibits superior robustness in high-noise, data-scarce settings.

Benchmarks for large language models typically evaluate the accuracy of answers against fixed reference labels. But a central step in many complex real-world tasks is identifying which questions are worth asking in the first place: decomposing a difficult problem into subquestions whose answers provide key steps on the path toward solving the larger problem. To evaluate this capability of information discovery, we introduce CruxBench, a benchmark that grades LLM-generated questions by their Value of Information (VOI): how much a model-proposed subquestion updates beliefs about a target outcome. To automate this measurement at scale, we target as outcomes the prices in continuously updating forward-looking prediction markets. Our benchmark has three rare properties: it is contamination-resistant by construction, since ground truth is generated by future world events; it is open-ended, admitting unbounded and complex text-based submissions rather than one correct numeric answer; and it is grounded, with informativeness measured against quantified changes in real-world beliefs (prices). We evaluate eight frontier and open-weight models on 336 target outcomes and find that VOI correlates highly with independent measures of model quality ($r=0.87$) and predicts downstream usefulness when the generated questions are passed to a separate forecasting agent.

Dictionary learning methods - such as Sparse Autoencoders (SAEs) and crosscoders - decompose model activations into human-interpretable building blocks. We introduce _temporal crosscoders_, a simple and flexible framework for feature discovery in Large Language Models (LLMs). To properly evaluate temporal crosscoders we develop TempBench: a panel of synthetic and real-world tasks for evaluating temporal structures. Temporal crosscoders outperform both conventional and temporal architectures in both of our synthetic settings and on two out of four of the real world settings - more than any other current architecture. Most strikingly, they can detect backtracking - a key reasoning behavior - at a 40\% higher rate than conventional SAEs, and are 15\% more effective in inducing it. Our results establish temporal crosscoders as a simple and flexible framework for feature discovery, both local and temporal. We provide full code at the following anonymous repository: \url{https://anonymous.4open.science/r/temp-bench-anon/}.

Consider two large vision models. They process the same image and both correctly predict the class ``rabbit.'' How much of the circuit computation along the way was shared? Model diffing offers a natural lens on this question. So far, however, it has largely operated on a single layer and at the level of representations rather than circuits. In this work, we introduce Universal Circuits (UCs), enabling model diffing at the circuit level. Specifically, we extend CLTs across both layers and models, with losses that encourage sparsity for interpretability and output fidelity for faithfulness. We train UCs between pairs of standard large vision models. We find that a compact cross-model intersection of pruned class circuits, typically a few hundred universal (shared) features per pair, produces $89$-$98\%$ of full-circuit classification accuracy in both models, while a complementary set of universal features (hundreds per pair) is kept by only one model's circuit, reflecting how each model weights shared concepts differently in its own representations. To demonstrate a downstream use of UC, we perform model \textit{surgery}: a class is successfully transferred from one model to another with no gradient steps taken in the new model. More broadly, our work demonstrates that large vision models leverage shared multi-layer algorithms for downstream performance, and that these algorithms can be discovered, compared, and reused across models.

LLM agents are increasingly used for open-ended, data-driven scientific discovery, yet most systems remain pointwise: they evaluate one candidate hypothesis at a time for surprise, novelty, or evidential support. This is information-inefficient: rejecting a hypothesis reveals that one explanation is unlikely, but not which alternatives are better supported. We argue that the proper epistemic unit of discovery is not a single hypothesis but a scientific question together with the mutually exclusive and collectively exhaustive (MECE) explanations that could answer it. We introduce Contrastive discovery, which scores candidate discoveries by how evidence redistributes belief across competing explanations. This allows a single experiment to both rule out hypotheses and identify the most plausible alternative. Across six scientific domains, Contrastive discovery yields substantially more resolved scientific questions than pointwise baselines under the same evaluation budget. High-surprisal pointwise candidates are overwhelmingly rejection-heavy, yet many become resolved alternatives when evaluated contrastively, showing that an explicit representation of alternatives can turn negative evidence into resolved discoveries.

Structure-based drug design with diffusion models seeks to generate 3D molecules that bind tightly to target protein pockets, but full-step sampling is too slow for high-throughput use. Extending the recent development of training-free fast sampling methods for diffusion models (e.g., DDIM and DNDM) to high-quality 3D molecule generation is non-trivial, given that both discrete variables (atom types) and continuous variables (atom coordinates) are involved. In this paper, we propose a unified fast sampling framework that allows a shared time schedule across discrete and continuous variables for strategically accelerating the 3D ligand generation. Guided by an error-equalization principle, we combine the continuous and discrete error rates of hybrid sampling into a single step-importance density and derive a training-free coupling-aware schedule. We further propose a confidence-guided sampling strategy that integrates constraints of model prediction confidence, motion stability, and steric clash to control the acceleration based on geometric readiness. Extensive experiments demonstrate that our method achieves $18$-$20\times$ speedup compared to full-step diffusion models while preserving state-of-the-art generation quality across chemical properties, binding affinity, and chemical validity.

Dynamic mechanism design provides a principled framework for coordinating self-interested agents whose private information evolves over time, but history dependence and dynamic incentive constraints make general analytical solutions difficult. Using a dynamic revelation principle, we formulate optimal dynamic mechanism design as a bilevel optimization problem over parameterized direct mechanisms: the principal optimizes the mechanism, while agent-side unilateral deviation problems verify incentive compatibility. We model each agent’s problem as a parameterized POMDP, and use stochastic natural policy gradient to solve these POMDPs with finite-sample error bounds. These policies serve as oracle outputs for the principal’s problem, yielding first-order optimization procedures with convergence guarantees that approximate stationary solutions under bounded oracle error. This formulation separates two representation choices: principal-side history compression and agent-side sufficient statistics. Experiments in dynamic bandit and budget-constrained auctions show that the framework can recover known benchmarks and learn approximately incentive-compatible mechanisms beyond analytical settings. Furthermore, they reveal how representations affect optimization.

SO(3) equivariant graph neural networks have become the dominant paradigm for atomistic foundation models, achieving high accuracy and data efficiency by building rotational symmetry directly into the architecture. Yet the computational cost of their higher-order tensor operations creates a tough trade-off between model accuracy and inference efficiency. In this paper, we propose a structural pruning method for SO(3) equivariant atomistic foundation models to bridge this accuracy-efficiency gap. The pruning is applied along the channel and order dimensions, with each irreducible representation kept or removed as a complete block, thereby retaining SO(3) equivariance. Starting from a large checkpoint, the pruned model substantially reduces the inference cost while retaining higher accuracy than an independently trained small model. The pruned MACE-MP model outperforms the official from-scratch trained small model on 7 of 9 metrics on the Matbench Discovery leaderboard. In terms of efficiency, compressed MACE-MP and MACE-OFF models contain 1.5$\times$ to 4$\times$ fewer parameters and require 2.5$\times$ to 4$\times$ less pre-training compute than training a small model from scratch. For downstream applications, fine-tuning the pruned model reduces energy and force errors by 70.1\% and 34.4\% compared to training task-specific models from scratch across eight representative downstream datasets. We demonstrate that the method generalizes to other SO(3) equivariant architectures (SevenNet, eSCN) and can be combined with quantization and knowledge distillation for further gains.

Cold-start drug-drug interaction (DDI) prediction tests whether models can identify clinically significant interactions for drugs without training-time interaction history. Existing benchmarks mostly report aggregate edge-prediction scores, leaving a key evaluation question unanswered: when models receive molecular, textual, or knowledge-graph (KG) evidence, do they actually use the evidence that pharmacologically supports the interaction? We introduce ColdDDI, a reconstructible evaluation benchmark built from the latest DrugBank 5.1.13, with 1,900 approved small-molecule drugs and 565,731 positive DDI pairs. ColdDDI evaluates three levels of drug novelty, namely test pairs whose two drugs were both seen during training, pairs with one unseen drug, and pairs with two unseen drugs. It also annotates each interaction by whether it changes drug exposure or drug effect, and by whether the biomedical knowledge graph contains shared enzymes, transporters, or targets that can plausibly mediate the interaction. These annotations allow ColdDDI to separate two factors that aggregate metrics conflate, namely whether mechanistic evidence is available, and whether a model prediction depends on that evidence. We evaluate eight conventional DDI methods and 13 LLMs; for open-weight LLMs, we test five prompt patterns and use masking, drug replacement, and channel-sensitivity metrics to probe knowledge utilization. ColdDDI exposes that, in the hardest split where both drugs are unseen, the main performance divide is mediator availability. A fine-tuned 1B LLM recovers 89-93% of interactions with a shared enzyme, transporter, or target, but only 40-62% without such a mediator. More importantly, KG-provided evidence is not always used; several KG-augmented baselines change little when the shared mediator is masked or disrupted, whereas fine-tuned LLMs respond strongly to this intervention. Thus, ColdDDI evaluates knowledge utilization rather than knowledge access alone, showing where cold-start DDI models rely on mechanistic evidence and where they fail despite receiving it. We release derivative annotations, splits, prompts, diagnostics, evaluation code, and a DrugBank reconstruction pipeline.

Causal discovery aims to recover directed causal relations from observational and interventional data, providing a basis for mechanistic understanding and reliable decision-making. Causal discovery foundation models (CDFMs) seek to amortize this problem by mapping a dataset directly to a causal graph in a single forward pass, avoiding per-dataset testing, search, or optimization. However, existing CDFMs remain limited, often failing to consistently match strong classical methods, and we find that a key bottleneck lies not only in model architecture but also in how causal pretraining tasks are constructed. Based on this observation, we propose CausalTab, a data-driven CDFM trained with broad causal pretraining over diverse graph priors, structural mechanisms, noise models, dimensions, sample sizes, and intervention regimes. A dynamic task construction strategy composes these causal environments into varied discovery tasks, enabling more transferable structural learning from observational and mixed-interventional data. On large-scale synthetic benchmarks, CausalTab achieves stronger and more robust performance than diverse causal discovery baselines. To further bridge abstract synthetic generators and realistic causal reasoning scenarios, we introduce an expert-knowledge-guided and LLM-audited semantic causal environment benchmark, where domain-grounded SCMs generate interpretable observational and interventional datasets for out-of-distribution analysis. Across both synthetic and semantic environments,CausalTab demonstrates robust structure recovery, especially under interventional evidence, highlighting broad causal pretraining as a key ingredient for transferable amortized causal discovery.

Protein-molecule virtual screening is increasingly cast as a problem of representation learning in a shared embedding space. Existing methods rely on dense holistic alignment, entangling invariant binding determinants with nuisance correlations and limiting transfer to new targets. It has been noted that binding in protein–molecule systems involves sparse cross-modality interactions: binding is governed by a small contact interface and a few decisive local interactions (e.g., hydrogen bonds, hydrophobic contacts, and salt bridges) rather than the global structures of the protein and molecule. We hypothesize that uncovering and leveraging sparse interaction patterns is critical for generalization beyond the training data, as these patterns are reusable and expected to improve performance across different scenarios. In this paper, we aim to identify and leverage sparse interaction patterns, and verify our hypothesis. Since the training data contain only observed binding pairs, we formalize this prior via a V-structure causal model under Heckman-style selection, and establish three theoretical results: (i) the latent concepts of interacting proteins and molecules are not identifiable without appropriate sparsity constraints;(ii) these concepts and their sparse interactions are component-wise identifiable under structural sparsity conditions; and (iii) a low-rank relaxation of these conditions yields subspace identifiability of the concepts and interactions. Inspired by these principles, we propose CausalBind with three implementation variants. Extensive experiments on DUD-E and LIT-PCBA benchmarks show that all variants consistently outperform strong baselines across all metrics, respectively.

There are many causal discovery algorithms, but few guiding principles for choosing between them. Methods are usually compared through three lenses: identifiability, consistency, and benchmarks. Each introduces assumptions about the data-generating process that are often untestable. We argue that there are no shared standards for comparing, prioritizing, or even discussing those assumptions. We support this claim by showing that (i) identifiability assumptions are often preferred by convention rather than by principle, (ii) uniform consistency requires further untestable assumptions, while also the weaker pointwise consistency has arguably narrowed algorithm design, and (iii) benchmarks are not neutral tests but carry an epistemic role of their own: they quietly fix which regimes matter, which guarantees come into play, and what counts as success. In doing so, they shape what algorithm comparisons are taken to show and thus perform some of the same epistemic work as theory, but less transparently. In this position paper we argue for a more transparent, integrated practice: Make the epistemic standards for discussing identifiability and consistency assumptions explicit, especially their failure modes and scope conditions; design benchmarks to operationalize those standards, by stress-testing and ablating both. Then, theoretical and empirical results jointly clarify when, why, and how algorithms may work rather than accumulate as disconnected advances.

Causal discovery methods produce data-driven hypotheses about causal relationships, which may become new scientific findings or inform decisions about downstream interventions. In such settings, false positive causal claims can be more consequential than false negatives. Yet few methods target false positive error control in causal discovery, and existing error guarantees are often asymptotic and require strong versions of the faithfulness assumption. We introduce the $m$-conservative PC algorithm and prove that it controls false discovery rate in the linear Gaussian setting under an extremely weak version of the faithfulness assumption. In our framework, false positive error for causal graphs is defined based on the conditional-independence information they entail, yielding a metric that penalizes both false adjacencies and incorrect edge orientations. The parameter $m$ quantifies a trade-off between algorithmic complexity and the strength of the required faithfulness assumption. The $m$-conservative PC algorithm combines undirected graph learning, a Benjamini-Yekutieli-style procedure for conditional independence testing, and a conservative orientation step that marks unresolved or contradictory edge directions as ambiguous. Our algorithm produces valid outputs and retains error guarantees even in the finite-sample setting, despite possible random errors in the conditional independence tests.