NeurIPS 2026 论文列表

Automated discovery of governing equations remains challenging when models rely only on numerical tokens and ignore the phase-space and trajectory evidence that is informative in low-dimensional dynamics. We propose Visual Induction for Physics-based Equation Reasoning (VIPER-R1), a multimodal framework for visual formula discovery from phase portraits, trajectory plots, and aligned measurements. VIPER-R1 uses a supervised Motion Structure Induction (MSI) curriculum for joint rationale-and-equation generation, and is then refined by \textbf{Reward-Guided Symbolic Calibration (RGSC)}, a GRPO-based stage optimized with a structure-aware reward that emphasizes topological correctness over coefficient matching. At inference time, we optionally apply Symbolic Residual Realignment (SR$^2$), an external symbolic regression module that models only the residual numerical mismatch of the base hypothesis. We release PhysSymbol, a 10{,}000-instance two-part multimodal corpus; the quantitative evaluation in this paper uses its Part 1 mechanics split, which provides paired visualizations, trajectory data, and expert C-CoT traces. On this benchmark, VIPER-R1-7B achieves the best structural score ($S_{\mathrm{struct}}=0.812$), is effectively tied with VIPER-R1-3B on exact-match accuracy ($S_{\mathrm{acc}}=0.487$ vs.\ $0.488$), and, after optional SR$^2$ refinement, reaches a Post-SR$^2$ MSE of $0.032$, nearly $3\times$ lower than the best VLM baseline. These results show that VIPER-R1 improves symbolic structure induction in focused low-dimensional dynamics by combining paired visual evidence with structure-aware calibration to produce stronger first-order hypotheses for downstream refinement.

Inspired by long-standing open problems in algebraic combinatorics, we show that modern machine learning can meaningfully contribute to verifiable mathematical discoveries. In particular, we focus on the construction of simple mathematical functions under exact distributional constraints, a setting we formalize as Simple Learning Under Rigid Proportions (SLURP). We tackle this problem by introducing two methods: MapSeek-Functional, which models the desired function alternating pseudo-labeling and supervised training steps; and MapSeek-Symbolic, designed to directly produce symbolic formulas. We successfully apply both methods to a research problem in algebraic combinatorics, discovering a new combinatorial interpretation of the $q,t$-Narayana polynomials arising from representation theory. To our knowledge, this is the first such interpretation based on noncrossing partitions. Using one discovered statistic, we find a combinatorial proof of the symmetry of these polynomials in a previously unsolved case. To streamline verification and reproducibility, we release all code, including a formalization of the mathematical discoveries of this paper in Lean 4.

Causal representation learning (CRL) seeks to recover latent variables with identifiability guarantees, typically up to permutation and component-wise reparameterization under appropriate assumptions. However, identifiability does not imply interpretability: latent semantics are typically assigned post hoc by alignment with known ground-truth factors. This limitation is particularly acute in scientific time series, where underlying mechanisms are unknown and discovering interpretable structure is a primary goal. In contrast, scientific observations (such as residue-pair distances, climate indices, or process sensors) are inherently semantic, as they correspond to named physical quantities. This raises a key question: can the interpretability of observations be transferred to the identifiable latent space? We propose MOSAIC (Module discovery via Sparse Additive Identifiable Causal learning), a sparse temporal VAE that integrates temporal CRL identifiability with support recovery over observed variables. MOSAIC identifies latent variables via regime-conditioned temporal variation, and recovers for each latent a sparse set of associated observations through an additive decoder, yielding module-level interpretability. We show that ANOVA main-effect supports are identifiable under general smooth mixing functions, and provide finite-sample recovery guarantees for a tractable sparse-additive variant. Empirically, MOSAIC recovers domain-consistent variable groups across RNA molecular dynamics, solar wind, ENSO climate, the Tennessee Eastman process, and a synthetic tokamak benchmark, enabling interpretable discovery of latent mechanisms in scientific time series.

Multi-omics drug-drug interaction (DDI) prediction forecasts DDI outcomes from heterogeneous multi-omics data and complex structured rules, where multi-omics interpretability of hierarchical biological factor interactions is extremely crucial, which remains unexplored in literature. In this paper, we are the first to study the problem of Multi-Omics Interpretable DDI Prediction, which is highly non-trivial with three challenges: i) how to identify interaction-relevant biological entities from large-scale knowledge sources, which lay the foundation for interpretability; ii) how to capture multi-omics cross-modal connections that elucidate underlying mechanisms under diverse interaction contexts; and iii) how to explicitly enable mechanism-aware reasoning over structured biological rules. To tackle the challenges, we propose a Multi-omics Interpretable prediction framework with joint optimization of graph structure, Neural architecture, and symbolic rules to hanDle DDI prediction (MIND-DDI), which follows a novel interpretable learning paradigm that tightly couples biomedical graph sampling, hierarchical neural representation learning, and symbolic rule modeling under a unified optimization scheme. Specifically, we propose a curriculum-guided biological subgraph sampler for progressively constructing informative subgraphs, then introduce a hierarchical multi-omics neural architecture search module to capture multi-omics alignment as well as cross-modal interactions, and finally present a mechanism-aware pathway-based symbolic reasoner for multi-hop reasoning over a unified neural-symbolic space. Extensive experiments show the superiority of MIND-DDI in both predictive accuracy and interpretability.

One strategy to scale up ML-driven science is to increase wet lab experiments' information density. We present a method based on a neural extension of compressed sensing to function space. We measure the activity of multiple different molecules simultaneously, rather than individually. Then, we deconvolute the molecule-activity map during model training. Co-design of wet lab experiments and learning algorithms provably leads to orders-of-magnitude gains in information density. We demonstrate on antibodies and cell therapies.

Diffusion models have recently emerged as a powerful paradigm for generating 3D molecules. Despite showing remarkable promise, they learn atomic distributions implicitly from data, without explicitly encoding physicochemical rules into their generative dynamics. Consequently, generated samples can be statistically plausible yet chemically invalid. To address this problem, we propose Sequential Neuro-Symbolic Constrained Diffusion (SensDiff), a framework that integrates symbolic rules into generative modeling, enabling the model to internalize scientific priors during training. Central to SensDiff is the observation that the diffusion trajectory of 3D molecule generation exhibits a coarse-to-fine evolution: valid molecules arise by first mitigating macroscopic geometric conflicts and then refining structures toward microscopic chemical consistency through iterative denoising. Accordingly, SensDiff mirrors this dynamic by sequentially enforcing constraints with adaptive weighting during training, progressively steering generation toward valid molecular geometries. Moreover, SensDiff translates domain knowledge into interpretable generative controls, grounding opaque neural denoising in scientific principles. Experiments on molecular benchmarks and real-world constrained generation tasks confirm that SensDiff consistently improves chemical validity while adhering to physicochemical rules and user-specified targets.

Test-time scaling (TTS) has become an effective approach for improving large language model performance by allocating additional computation during inference. However, existing TTS strategies are largely hand-crafted: researchers manually design reasoning patterns and tune heuristics by intuition, leaving much of the computation-allocation space unexplored. We propose an environment-driven framework, **AutoTTS**, that changes what researchers design: from individual TTS heuristics to environments where TTS strategies can be discovered automatically. The key to AutoTTS lies in environment construction: the discovery environment must make the control space tractable and provide cheap, frequent feedback for TTS search. As a concrete instantiation, we formulate width--depth TTS as controller synthesis over pre-collected reasoning trajectories and probe signals, where controllers decide when to branch, continue, probe, prune, or stop and can be evaluated cheaply without repeated LLM calls. We further introduce beta parameterization to reduce search-set overfitting and fine-grained execution trace feedback to improve discovery efficiency by helping the agent diagnose why a TTS program fails. Experiments on mathematical reasoning benchmarks show that the discovered strategies improve the overall accuracy--cost tradeoff over strong manually designed baselines. The discovered strategies generalize to held-out benchmarks and model scales, while the entire discovery costs only **$39.9** and **160 minutes**.

Scientific discovery is a closed-loop process in which hypotheses guide data acquisition, and observations refine the hypothesis space. Yet most approaches reduce discovery to supervised learning over fixed datasets, where limited observations can support multiple plausible mechanisms that fit locally but fail to generalize. Thus, the key challenge is selecting informative observations to resolve uncertainty, shifting the focus from static inference to adaptive data acquisition. To address this, we propose LLM-AutoSciLab, a closed-loop framework that couples hypothesis generation with hypothesis-conditioned experiment selection and mechanism refinement. Rather than fitting models to passively collected data, LLM-AutoSciLab iteratively proposes plausible hypotheses, selects informative experiments to distinguish among them or refine them, and updates its state based on the resulting evidence. To evaluate dynamic, closed-loop scientific discovery with active data acquisition, we introduce ActiveSciBench-Chem (57 enzyme-kinetics domains) and ActiveSciBench-GRN (45 gene-regulatory-network tasks), benchmarks that model discovery as a budget-constrained process requiring adaptive experiment design, variable selection, and recovery of true mechanisms. Across NewtonBench, ActiveSciBench-Chem, and ActiveSciBench-GRN, LLM-AutoSciLab outperforms prior methods, achieving 67.6% and 35.1% symbolic accuracy and 31.1% exact graph recovery, respectively. Moreover, hypothesis-guided experimentation is 2x--5x more sample-efficient than the strongest competing baselines.

Protein language models (pLMs) encode information about protein sequences which enable downstream tasks such as structure prediction, but their internal representations are not well understood. Sparse autoencoders (SAEs) provide a promising tool to disentangle latent pLM representations into interpretable features, but existing annotation pipelines largely rely on protein-level annotations derived from database labels and LLM annotations of top activating sequences. Such annotations can overlook the localized residue-level and geometric patterns encoded by sparse features. We introduce an automated and scalable method for interpreting SAE features in ESM-2 by using geometrically inspired features of the protein $\text{C}_{\alpha}$ backbone. Across ESM-2 8M layers, geometric annotations explain a large fraction of SAE features, expanding coverage beyond database and sequence-based methods. In particular, geometry can distinguish SAE features sharing the same database annotation, revealing substructure within known biological labels. A significant portion of SAE features activate on unannotated metagenomic protein sequences enabling us to use our SAE annotations to better understand these sequences. In addition, ablation experiments at the level of contact predictions hint toward SAE features controlling protein geometry. This provides a robust method of annotating proteins activated within SAE neurons at a residue level, providing a bridge between mechanistic interpretability and structural biology.

Expert background knowledge is often available in practical applications of causal discovery. Such constraints on the true causal graph can help causal discovery in terms of identifiability of causal effects and accuracy of the learned structure, but also in reducing the space of candidate causal graphs. As causal discovery can become computationally expensive for large number of variables, it is crucial to utilize background knowledge effectively \emph{during} the causal discovery process. However, most current methods only use background knowledge in a postprocessing step after causal discovery to refine the learned graph. In this work, we develop a framework for utilizing background knowledge during the causal discovery process, focusing especially on scalable causal discovery methods that recover only a subset of the whole graph. We implement our framework for multiple algorithms and empirically show that utilizing background knowledge can both reduce computational requirements and increase the quality of the learned structures.

Constraint-based causal discovery recovers causal DAG structure from conditional independence (CI) relations. Classical methods such as PC orient v-structures first, then propagate edge directions from these seeds, relying on accurate CI tests and rich separating-set searches. In practice, these conditions often fail, causing cascading orientation errors. Recent work uses large language models (LLMs) as experts to augment edge orientation when standard assumptions fail, but often treats LLM outputs as reliable or assumes stable error behavior, despite hallucinations and instability. We propose MosaCD, a constraint-based framework that robustly combines CI tests with LLM inference to obtain high-confidence orientation seeds, then propagates them with Seeded Propagation Rules (SPR), which mitigate the fragility of collider-first orientation. We prove oracle-level soundness for SPR under explicit assumptions on the skeleton, separating-set record, and seed orientations, and give a stylized finite-sample analysis showing why prioritizing non-collider evidence can reduce orientation errors. Across 13 real-world benchmarks, MosaCD and SPR achieve substantially higher accuracy than existing methods through more reliable seeds and more robust propagation.

Real-world image datasets are deeply hierarchical, yet unsupervised hierarchical representation learning remains underdeveloped. Hyperbolic space is geometrically ideal for embedding trees with low distortion due to its exponential volume growth, but existing unsupervised hyperbolic methods either fail to scale beyond a few thousand points or depend heavily on class supervision. We bridge this gap with HyperTree, a fully unsupervised, scalable, and capacity-efficient framework for hierarchical representation learning in hyperbolic space, built on three contributions: (i) a geometrically consistent, closed-form definition of the hyperbolic Lowest Common Ancestor, valid across hyperbolic manifolds of arbitrary curvatures; (ii) a differentiable hierarchical objective based on Dasgupta's cost that is bounded and invariant to dataset scale; and (iii) a sample-complexity guarantee that enables scaling to datasets such as ImageNet-1k and iNaturalist-2018. Across four benchmarks, HyperTree outperforms Euclidean baselines by wide margins on hierarchical dendrogram purity, matches supervised hyperbolic baselines on CIFAR-100, and surpasses them on TinyImageNet at 16 dimensions — a highly capacity-efficient regime where competing methods collapse.

Prior Laplacian-based option-discovery methods build options from 0-form Laplacians defined on nodes, where the resulting eigenvectors induce routes toward isolated boundaries or extrema, thereby skewing visitation toward specific states. In contrast, kernel eigenvectors of the 1-form Hodge Laplacian represent interpretable, topology-aware edge flows and naturally capture cyclic behaviour known as harmonic flows. These kernel eigenvectors are particularly attractive because they define zero-divergence edge flows, offering a natural solution for non-isolated visitation to sources and sinks in regions in which they are active. Despite this appeal, harmonic flows have not previously been explored as a basis for option discovery in reinforcement learning. This is what we do here. We first introduce harmonic-flow skills and show that, on state graphs with tree-like “dead-end” appendages, purely harmonic flows can become nearly inactive in those regions, which can limit coverage. To address this limitation, we propose quasi-harmonic flow options: skill-inducing edge flows that preserve harmonic cycles where harmonic activity is strong, while injecting drift into appendages using the lowest-magnitude non-harmonic eigenvector of the Hodge Laplacian, a low divergence solution, where harmonic activity is weak. Our approach is eigenvector-only, relying solely on spectral components of the Hodge Laplacian. We compare quasi-harmonic flow options against a harmonic-flow options baseline and state-of-the-art skill-discovery methods from the literature, demonstrating empirical gains and analytical improvements on hitting-time-based metrics.

Finding frequently occurring subgraph patterns or network motifs in neural architectures is crucial for optimizing efficiency, accelerating design, and uncovering structural insights. However, as the subgraph size increases, enumeration-based methods are perfectly accurate but computationally prohibitive, while sampling-based methods are computationally tractable but suffer from a severe decline in discovery capability. To address these challenges, this paper proposes GraDE, a diffusion-guided search framework that ensures both computational feasibility and discovery capability. The key innovation is the $\underline{\textnormal{Gra}}\textnormal{ph}$ $\underline{\textnormal{D}}\textnormal{iffusion}$ $\underline{\textnormal{E}}\textnormal{stimator}$ (GraDE), which is the first to introduce graph diffusion models to identify frequent subgraphs by scoring their typicality within the learned distribution. Comprehensive experiments demonstrate that the estimator achieves superior ranking accuracy, with up to 114\% improvement compared to sampling-based baselines. Benefiting from this, the proposed framework successfully discovers large-scale frequent patterns, achieving up to 30$\times$ higher median frequency than sampling-based methods.

Molecules in equilibrium follow a Boltzmann distribution, making the underlying energy landscape a physically grounded modeling objective. However, such landscapes are difficult to learn from data and, once learned, hard to sample from. Diffusion and flow-matching models sidestep these difficulties by learning a time-conditional score or transport field between noise and data, losing the energy inductive bias in exchange for a more tractable training objective. We introduce EBMol, an energy-based model (EBM) that restores this inductive bias by learning an atom-additive scalar potential without explicit simulation during training. Our method employs a flow-inspired Restoring Field Matching objective to approximate the energy landscape. We adopt the Mirror-Langevin algorithm for sampling, enabling unified updates of atomic positions and types, and incorporate parallel tempering for inference-time compute scaling. EBMol is the first EBM for 3D molecular generation to achieve state-of-the-art performance on QM9 and GEOM-Drugs. Moreover, we show that the learned energy landscape serves as a principled quality metric for ranking and filtering configurations, and demonstrate controllable generation without retraining through shape-steered sampling via potential composition and zero-shot linker design.

We present GenZ, a hybrid model that turns a foundational model (FM) into a {\bf knowledge-discovery engine} explaining variation in real-valued multidimensional targets. The FM is treated as a noisy oracle that can answer yes/no questions about a semantic item $s$ (text, image, or both) and GenZ learns {\bf which questions to ask} so that the answers $\bz$ explain the statistical link to a possibly high-dimensional target $\by$. Discovery is driven by {\bf group reasoning}: at each step, the model partitions items by the posterior of the current latent features, and asks the FM to articulate the semantic commonality that explains the divide. The resulting feature descriptors $\theta_f$ are the primary product---human-readable hypotheses about why $s$ predicts $\by$---while predictive accuracy is a secondary, but consistently strong, by-product (e.g.~beating both the 0-shot FM baseline and TabPFN on LLM embeddings of the same items in hedonic price regression). Across four domains---hedonic house pricing, Netflix cold-start recommendations, Arizona species ecology, and human visual-cortex fMRI---GenZ recovers dataset-specific structure that the FM does not surface from priors alone. Holding the items $s$ fixed and varying only the target $\by$ (Arizona species under spatial/taxonomic/functional targets; the same natural images under FFA/EBA/PPA brain responses) yields {\bf qualitatively different} discovered feature sets, demonstrating that GenZ characterizes the $s\!\to\!\by$ link rather than the marginal distribution of $s$.

The automatic synthesis of a program from any form of specification is regarded as a holy grail of computer science. Fueled by LLMs, NL2Code has achieved tremendous success, yet the fundamentally more challenging task of synthesizing programs from input-output behavior, which we refer to as IO2Code, remains largely unsolved. Whereas NL2Code can exploit the semantic alignment between natural language and code acquired during pretraining, IO2Code requires recovering underlying principles from concrete computational behavior, navigating a vast and underspecified hypothesis space. To address this, we propose DIO-Agent, a discovery agent for IO2Code. Our method frames IO2Code as an evolutionary search over discrete program space, in which an LLM serves as the mutation operator and concrete error signals from execution guide each mutation. To prevent the search from wandering into structurally complex yet incorrect dead ends, we introduce the Transformation Priority Premise as a mutation prior that biases the LLM toward the simplest hypothesis consistent with current evidence, progressively escalating from constants to conditionals to iteration only when simpler constructs are insufficient. To facilitate systematic study, we further construct an IO2Code benchmark spanning multiple difficulty levels. Extensive experiments show that DIO-Agent consistently outperforms both traditional program-by-example methods and evolutionary search baselines across all difficulty levels and various LLMs, while substantially surpassing test-time scaling strategies with equivalent sampling budgets. Our code and dataset are available at \url{https://anonymous.4open.science/r/IO2Code}.

Designing functional biological sequences requires navigating vast discrete spaces under strict evolutionary and biophysical constraints. Discrete Flow Matching (DFM) offers a generative framework over such spaces, but existing approaches rely on biologically uninformative couplings and offer limited flexibility for variable-length sequence generation and fine-grained control. We propose a structured coupling that encodes domain-specific preferences among sequence elements, biasing the source distribution toward plausible regions without modifying the flow objective or training procedure. Building on this, we introduce a latent edit-based rate parameterization that models variable-length generation via edit operations conditioned on a shared global latent, akin to a latent variable model, while remaining tractable. We further introduce a latent classifier-free guidance mechanism that steers generation coherently in continuous latent space, along with Dirichlet-prior temperature scaling for test-time control over edit operations. Our method achieves state-of-the-art performance across diverse biological sequence tasks, including density estimation, unconditional and conditional DNA sequence generation, and peptide sequence generation.

Scientific discovery relies on large-scale hypothesis testing. However, the capacity to identify true discoveries while controlling false discovery faces major challenges: obtaining relevant reference data (the null distribution) is resource-intensive, leaving finite-data uncertainty, and the procedure should account for the inherent structure in the hypothesis space, when such structure exists. Here, we present a framework for controlling the false discovery rate for hypotheses with uncertain p-values from finite reference samples within arbitrarily structured hypothesis spaces, requiring only that the structure be represented through a suitable reproducing kernel. We present two decision rules, both proven to control the FDR under any misspecification of the structural information, and show that one strictly dominates the other under correct specification. Furthermore, we suggest a policy for efficient allocation of samples from the hypotheses' null distributions.