ICML 2026 论文列表

We study the problem of recovering the parameters of a multivariate Ornstein–Uhlenbeck (OU) process from steady-state observational and interventional data. In many applications, such as large-scale gene perturbation experiments, only stationary “snapshot” measurements are available, making standard stochastic differential equation estimation methods that rely on time-series trajectories inapplicable. We first establish an identifiability result: one intervention per strongly connected component (SCC) of the drift graph suffices to recover all OU process parameters generically up to a global scaling factor. This holds provided that the SCC condensation graph is connected with a single root and certain spectral nondegeneracy assumptions hold. We propose a recursive learning algorithm that orders SCCs topologically and, for each component, isolates its marginal dynamics and solves a linear system derived from the steady-state moment equations, leveraging parameters recovered for upstream components. Building on this theoretical foundation, we propose a regularized least-squares estimator that jointly minimizes residuals of the steady-state mean and covariance equations across observational and interventional data. Experiments on synthetic and real datasets demonstrate the effectiveness of our method in recovering parameters and predicting unseen interventions.

Despite strong average-case performance, deep learning models often exhibit systematic errors on specific population groups, known as *error slices*. Identifying these groups and the root causes of their failures is critical for model debugging and bias mitigation. However, existing error Slice Discovery Methods (SDMs) typically generate explanations disconnected from the model's inference process, thus only approximating the underlying error source and may be inaccurate. We address this limitation by leveraging Concept Bottleneck Models (CBMs), whose predictions are directly dependent on human-understandable semantic concepts. Since downstream task failures in CBMs commonly arise from concept mispredictions, concept representations provide a strong candidate for error slice identification, offering fine-grained explanations directly linked to the error source. Building on this insight, we introduce *CB-SLICE*, a concept-based SDM that groups samples with shared concept prediction failures and identifies the keyword-concepts most responsible for each slice’s failure-mode. Across multiple benchmarks, we show that CB-SLICE outperforms state-of-the-art methods in uncovering well-known biases while providing richer and more faithful explanations of model errors.

Generalized Category Discovery (GCD) aims to recognize known classes while autonomously discovering novel ones in open-world settings. However, current approaches primarily focus on designing clustering objectives, often overlooking a critical bottleneck: standard vision backbones yield high-rank, entangled token representations that are ill-suited for unsupervised discovery of latent concepts and structures. In this paper, we propose Compositional Primitive Fields (CPF-GCD), a novel representation learning framework that reshapes the feature space to make such latent structure identifiable by enforcing a low-rank compositional organization. Our core hypothesis is that all categories, whether known or novel, can be expressed as compositions and spatial arrangements of a finite set of learnable visual primitives that capture reusable concepts. CPF instantiates this geometric constraint via a spatial field mechanism. Inserted between the backbone and the head, it rewrites noisy patch tokens through low-rank primitive mixtures, effectively decomposing images into reusable atomic parts and their spatial layouts. By explicitly modeling the spatial distribution of primitives, CPF enables novel categories to emerge naturally as new activation patterns over a shared vocabulary. This shifts the focus of representation from merely partitioning global embeddings to constructing a structured and separable primitive field. Extensive experiments demonstrate that CPF serves as a generic, plug-and-play module that consistently boosts performance across diverse GCD baselines, validating that identifying and leveraging low-rank compositional structure is a crucial inductive bias for open-world recognition.

We study causal discovery from soft interventions in the presence of latent confounding. Beyond within-environment conditional independences, soft interventions induce cross-environment invariances that can be encoded using an augmented graph with intervention indicator nodes ($\mathcal{I}$-AUG). Taking its maximal ancestral graph (MAG) yields the $\mathcal{I}$-MAG, which characterizes the interventional Markov equivalence class. Building on this framework, we show that the FCI-inspired learner ($\mathcal{I}$-FCI) by Kocaoglu et al. (2019) is sound but not complete: it may output circle endpoints that are nevertheless compelled by the interventional equivalence class. To exploit intervention-node semantics, we propose two complementary methods. First, we introduce an enumeration-based completion procedure that is sound and theoretically complete, but whose worst-case cost depends on the number of MAGs compatible with the partial graph learned by $\mathcal{I}$-FCI. Second, we derive a set of additional local orientation rules that provably tighten $\mathcal{I}$-FCI without increasing asymptotic complexity. Both methods refine prior outputs in the controlled soft-intervention setting with latent variables.

Deep learning in de novo protein design has achieved atomic-level fidelity. However, existing models remain largely non-deliberative: they directly synthesize molecular geometries without explicitly reasoning about which residues or interactions are functionally essential. As a result, design decisions are entangled with continuous sampling dynamics, limiting interpretability, controllability, and systematic reuse of biochemical knowledge. We introduce Proteo-R1, a reasoning-guided protein design framework that explicitly decouples molecular understanding from geometric generation. Proteo-R1 adopts a dual-expert architecture, where a multimodal large language model (LLM) serves as an understanding expert, analyzes protein sequences, structures, and textual context to identify key functional residues that govern binding and specificity. These residue-level decisions are then passed to a separate diffusion-based generation expert, which performs conditional co-design while respecting the fixed interaction anchors. This factorization mirrors how human experts approach molecular engineering: first, reasoning about critical interactions, then optimizing geometry subject to those constraints. By operationalizing reasoning as explicit residue-level commitments rather than latent textual guidance, Proteo-R1 achieves stable, interpretable, and modular integration of LLM reasoning with advanced geometric generative models. Code and demos are at https://proteor1.github.io.

Dynamical systems model trajectory data generated by an underlying fixed dynamics, with applications ranging from biological systems to flows in physics. The identification problem concerns recovering the parameters of a system from observed trajectories. In many scientific settings, however, dynamical systems are not generic and instead exhibit symmetries imposed by physical laws, formalized as equivariance with respect to a group action. In this work, we study \emph{adaptive symmetry discovery} for dynamical system identification and address how a system can be identified from a single trajectory when it is equivariant with respect to an unknown symmetry group. To this end, we first show that for known symmetries, the system can be identified from a significantly shorter single trajectory than in the generic setting, and we precisely characterize this improvement. We then consider the automatic symmetry discovery setting, proposing a method to learn the symmetry group directly from a single trajectory and incorporate it into the identification procedure, achieving the same optimal trajectory length as in the known-symmetry case. Our analysis relies on tools from group representation theory and the expander properties of Cayley graphs, and may be of independent interest for the study of symmetries in dynamical systems.

We propose a modular, data-driven framework for jointly learning unknown functional mappings and discovering the underlying one-parameter symmetry subgroup governing the data. Unlike conventional geometric deep learning methods that assume known symmetries, our approach identifies the relevant continuous subgroup directly from data. Our framework focuses on three primary geometric components of one-parameter subgroup actions: elliptic, hyperbolic, and parabolic regimes. For the given regime, our framework instantiates a corresponding symmetry discovery architecture with invariant and equivariant representation layers structured according to the Lie algebra of the subgroup, and learns the exact generator parameters end-to-end from data. This yields models whose invariance or equivariance is guaranteed by construction and admits formal proofs, enabling symmetry to be explicitly traced to identifiable components of the architecture. The approach is applicable to one-parameter subgroups of a wide range of matrix Lie groups, including $SO(n)$, $SL(n)$, and the Lorentz group. Experiments on synthetic and real-world systems, including moment of inertia prediction, double-pendulum dynamics, and high-energy \textit{Top Quark Tagging}, demonstrate accurate subgroup recovery and strong predictive performance across both compact and non-compact regimes.

Structure-Based Drug Design (SBDD) aims to discover bioactive ligands. Conventional approaches construct probability paths separately in Euclidean and probabilistic spaces for continuous atomic coordinates and discrete chemical categories, leading to a mismatch with the underlying statistical manifolds. We address this issue by representing molecules using composite exponential-family distributions, where coordinates and categories are represented within a unified natural parameter space to evolve synchronously along exponential geodesics under the Fisher-Rao metric. To avoid the instantaneous trajectory collapse induced by geodesics directly targeting Dirac distributions, we propose Evolving Exponential Geodesic Flow for SBDD (EvoEGF-Mol), which replaces static Dirac targets with dynamically concentrating distributions and is trained with a progressive-parameter-refinement architecture. Our model approaches a reference-level PoseBusters passing rate (93.4%) on CrossDock, demonstrating remarkable geometric precision and interaction fidelity, while achieving superior performance over baseline methods on real-world MolGenBench tasks for bioactive scaffold recovery. Code is available at https://github.com/BLEACH366/EvoEGF-Mol.

False discovery rate (FDR) is a cornerstone of modern multiple testing. However, it often fails to guarantee the reliability of ``marginal" discoveries that lie at the boundary of the rejection set, which are often crucial in high-precision applications. While recent works (Soloff et al., 2024; Xiang et al., 2025) introduced the boundary false discovery rate (bFDR) to control the error probability at the marginal discovery, their method relies on restrictive assumptions such as independence or specific prior distributions. In this paper, we first propose $k$-bFDR, a novel generalization that controls the error probability of the $k$ least significant discoveries. We then provide a systematic investigation into the theoretical relationship between $k$-bFDR and existing error metrics. Furthermore, building upon the closure principle, we develop Domino, a unified framework that guarantees $k$-bFDR control under arbitrary dependence, applicable for both p-values and e-values. We prove the theoretical validity of the proposed Domino algorithm and demonstrate through extensive numerical experiments that it consistently achieves rigorous $k$-bFDR control while identifying trustworthy marginal discoveries. Analyses of real data reveal that $k$-bFDR control yields higher-quality rejection sets with greater practical significance.

Function-guided protein design is a crucial task with significant applications in drug discovery and enzyme engineering. However, the field lacks a unified and comprehensive evaluation framework. Current models are assessed using inconsistent and limited subsets of metrics, which prevents fair comparison and a clear understanding of the relationships between different evaluation criteria. To address this gap, we introduce **PDFBench**, the first comprehensive benchmark for function-guided de novo protein design. Our benchmark systematically evaluates eight state-of-the-art models on 16 metrics across two key settings: description-guided design, for which we repurpose the Mol-Instructions dataset, originally lacking quantitative benchmarking, and keyword-guided design, for which we introduce a new test set, SwissTest, created with a strict datetime cutoff to ensure data integrity. By benchmarking across a wide array of metrics and analyzing their correlations, **PDFBench** enables more reliable model comparisons and provides key insights to guide future research.

Multistate mechanisms underlie many of the complex functions observed in natural proteins. The ability to rationally design multistate proteins would have transformative implications for many areas of biotechnology, yet lies beyond the capabilities of existing deep learning frameworks for protein design. To address this gap, we introduce SwitchCraft, a versatile and programmatic framework for designing state-switching proteins based on backpropagation through compositional design constraints parameterized by structure prediction models. In silico evaluations demonstrate success on a wide range of state-switching functional primitives, from allosteric regulation of motifs to discrimination of bound ligand identities. Using these primitives, we demonstrate an in silico strategy for de novo design of fluorescent biosensors to arbitrary small molecule analytes. These results position SwitchCraft at the inception of a powerful paradigm for higher-order functional protein design. Code is available at https://github.com/bjing2016/switchcraft.

Structure-based and ligand-based computational drug design have traditionally relied on disjoint data sources and modeling assumptions, limiting their joint use at scale. In this work, we introduce **Con**trastive **G**eometric **L**earning for **U**nified Computational **D**rug D**e**sign (ConGLUDe), a single contrastive geometric model that unifies structure- and ligand-based training. ConGLUDe couples a geometric protein encoder that produces whole-protein representations and implicit embeddings of predicted binding sites with a fast ligand encoder, removing the need for pre-defined pockets. By aligning ligands with both global protein representations and multiple candidate binding sites through contrastive learning, ConGLUDe supports ligand-conditioned pocket prediction in addition to virtual screening and target fishing, while being trained jointly on protein-ligand complexes and large-scale bioactivity data. Across diverse benchmarks, ConGLUDe achieves competitive zero-shot virtual screening performance, substantially outperforms existing methods on a challenging target fishing task, and demonstrates state-of-the-art ligand-conditioned pocket selection. These results highlight the advantages of unified structure-ligand training and position ConGLUDe as a step toward general-purpose foundation models for drug discovery.

Most causal discovery methods recover a completed partially directed acyclic graph (CPDAG) representing a Markov equivalence class from observational data. Recent work has extended these methods to federated settings to address data decentralization and privacy constraints, but often under idealized assumptions that all clients share the same causal model. Such assumptions are unrealistic in practice, as client-specific policies, for instance, across hospitals, naturally induce heterogeneous and unknown interventions. In this work, we address federated causal discovery under unknown client-level interventions. We propose I-PERI, a novel federated algorithm that first recovers the CPDAG common to all clients and then orients additional edges by exploiting structural differences induced by interventions across clients. This yields a tighter equivalence class, which we call the $\mathbf{\Phi}$-Markov Equivalence Class, represented by an augmented version of the CPDAG, namely, a $\mathbf{\Phi}$-CPDAG. We provide theoretical guarantees on the convergence of I-PERI, as well as on its privacy-preserving properties, and present empirical evaluations demonstrating the effectiveness of the proposed algorithm.

We consider the problem of unsupervised skill segmentation and hierarchical structure discovery in reinforcement learning. While recent approaches have sought to segment trajectories into reusable skills or options, most rely on action labels, rewards, or handcrafted annotations, limiting their applicability. We propose a method that segments unlabelled trajectories into skills and induces a hierarchical structure over them using a grammar-based approach. The resulting hierarchy captures both low-level behaviours and their composition into higher-level skills. We evaluate our approach in high-dimensional, pixel-based environments, including Craftax and the full, unmodified version of Minecraft. Using metrics for skill segmentation, reuse, and hierarchy quality, we find that our method consistently produces more structured and semantically meaningful hierarchies than existing baselines. Furthermore, as a proof of concept, we demonstrate that these discovered hierarchies accelerate and stabilise learning on downstream reinforcement learning tasks.

Causal discovery is essential for advancing data-driven fields such as scientific AI and data analysis, yet existing approaches face significant time- and space-efficiency bottlenecks when scaling to large graphs. To address this challenge, we present CauScale, a neural architecture designed for efficient causal discovery that scales inference to graphs with up to 1000 nodes. CauScale improves time efficiency via a reduction unit that compresses data embeddings and improves space efficiency by adopting tied attention weights to avoid maintaining axis-specific attention maps. To keep high causal discovery accuracy, CauScale adopts a two-stream design: a data stream extracts relational evidence from high-dimensional observations, while a graph stream integrates statistical graph priors and preserves key structural signals. CauScale successfully scales to 500-node graphs during training, where prior work fails due to space limitations. Across testing data with varying graph scales and causal mechanisms, CauScale achieves 99.6\% mAP on in-distribution data and 84.4\% on out-of-distribution data, while delivering 4$\times$–13,000$\times$ inference speedups over prior methods.

Generalized Category Discovery (GCD) aims to identify both known and novel categories within unlabeled data by leveraging a set of labeled examples from known categories. Existing GCD methods primarily depend on semantic labels and global image representations, often overlooking the detailed part-level cues that are crucial for distinguishing closely related categories. In this paper, we introduce PartCo, short for Part-Level Correspondence Prior, a novel framework that enhances category discovery by incorporating part-level visual feature correspondences. By leveraging part-level relationships, PartCo captures finer-grained semantic structures, enabling a more nuanced understanding of category relationships. Importantly, PartCo seamlessly integrates with existing GCD methods without requiring significant modifications. Our extensive experiments on multiple benchmark datasets demonstrate that PartCo significantly improves the performance of current GCD approaches, outperforming most existing methods by bridging the gap between semantic labels and part-level visual compositions, thereby setting new benchmarks for GCD.

Efficiently designing high-quality molecules targeting disease-relevant targets is a critical challenge. Most existing methods can capture pairwise amino acid relations, neglecting the higher-order relations among multiple amino acids. This paper proposes a target-specific molecule generation framework, namely TSMGen, to comprehensively capture the local and global structural information of the protein pocket by modeling higher-order spatial dependencies both at the atomic and the amino acid levels. Furthermore, we design a context-aware bidirectional fusion module to learn the more detailed structural information about the protein pocket. This module simultaneously attends to features from both the protein pocket and the molecule, fully leveraging the structural information from both to optimize the generation process of targeted molecules, thereby enhancing the quality of generated molecules. Experiments show that TSMGen outperforms state-of-the-art methods in terms of Vina Score, High Affinity, QED, SA and Diversity, and a case study on $\beta$-secretase enzyme further confirms its ability to generate molecules with stronger binding affinity.

Biomolecules such as proteins and small-molecule ligands play a central role in biological systems, arising from the tight interplay between sequence and three-dimensional structure. Recent generative models for biomolecular co-design aim to capture this interplay by jointly modeling coupled modalities. However, existing approaches largely adopt a parallel execution of marginal generative processes, implicitly enforcing fixed synchronous coupling. We argue that a critical but overlooked degree of freedom lies in how these marginal processes are \emph{temporally coupled} during training and generation, where inappropriate coupling can introduce high-variance supervision and inconsistent intermediate states, affecting modality consistency. To address this, we introduce GeoCoupling, a systematic framework that optimizes for temporal couplings between heterogeneous modalities. Empirical results across structure-based drug design and unconditional protein design demonstrate the learned couplings consistently outperform synchronous and randomly coupled baselines, yielding biomolecules with improved physical validity and diversity.

Large language models (LLMs) have achieved remarkable performance on a wide range of tasks, hindering real-world deployment due to their massive size. Existing pruning methods (e.g., Wanda) tailored for LLMs rely heavily on manual design pruning algorithms, thereby leading to $\textit{huge labor costs}$ and $\textit{requires expert knowledge}$. Furthermore, we are the first to identify the serious \textit{outlier value issue} behind dramatic performance degradation under high pruning ratios that are caused by uniform sparsity, raising an additional concern about how to design adaptive pruning sparsity ideal for LLMs. Can LLMs prune by themselves? In this work, we introduce an affirmative answer by proposing a novel pruning method called $\textbf{AutoPrune}$, which first overcomes expert knowledge limits by leveraging LLMs to design optimal pruning algorithms for themselves automatically without any expert knowledge. Specifically, to mitigate the black-box nature of LLMs, we propose a Graph-driven Chain-of-Thought (GCoT) to optimize prompts, significantly enhancing the reasoning process in learning the pruning algorithm and enabling us to generate pruning algorithms with superior performance and interpretability in the next generation. Finally, grounded in insights of outlier value issue, we introduce Skew-aware Dynamic Sparsity Allocation (SDSA) to overcome the outlier value issue, mitigating performance degradation under high pruning ratios. We conduct extensive experiments on mainstream LLMs benchmarks, demonstrating the superiority of AutoPrune, which consistently excels state-of-the-art competitors. The code is available at: \url{https://anonymous.4open.science/r/AutoPrune}.