ICML 2025 Papers

Determining the direction of relationships between variables is fundamental for understanding complex systems across scientific domains. While observational data can uncover relationships between variables, it cannot distinguish between cause and effect without experimental interventions. To effectively uncover causality, previous works have proposed intervention strategies that sequentially optimize the intervention values. However, most of these approaches primarily maximized information-theoretic gains that may not effectively measure the reliability of direction determination. In this paper, we formulate the causal direction identification as a hypothesis-testing problem, and propose a Bayes factor-based intervention strategy, which can quantify the evidence strength of one hypothesis (*e.g.*, causal) over the other (*e.g.*, non-causal). To balance the immediate and future gains of testing strength, we propose a sequential intervention objective over intervention values in multiple steps. By analyzing the objective function, we develop a dynamic programming algorithm that reduces the complexity from non-polynomial to polynomial. Experimental results on bivariate systems, tree-structured graphs, and an embodied AI environment demonstrate the effectiveness of our framework in direction determination and its extensibility to both multivariate settings and real-world applications.

Generalized Category Discovery (GCD) aims to identify unlabeled samples by leveraging the base knowledge from labeled ones, where the unlabeled set consists of both base and novel classes. Since clustering methods are time-consuming at inference, parametric-based approaches have become more popular. However, recent parametric-based methods suffer from inferior base discrimination due to unreliable self-supervision. To address this issue, we propose a Reciprocal Learning Framework (RLF) that introduces an auxiliary branch devoted to base classification. During training, the main branch filters the pseudo-base samples to the auxiliary branch. In response, the auxiliary branch provides more reliable soft labels for the main branch, leading to a virtuous cycle. Furthermore, we introduce Class-wise Distribution Regularization (CDR) to mitigate the learning bias towards base classes. CDR essentially increases the prediction confidence of the unlabeled data and boosts the novel class performance. Combined with both components, our proposed method, RLCD, achieves superior performance in all classes with negligible extra computation. Comprehensive experiments across seven GCD datasets validate its superiority. Our codes are available at https://github.com/APORduo/RLCD.

Symmetry is widely applied in problems such as the design of equivariant networks and the discovery of governing equations, but in complex scenarios, it is not known in advance. Most previous symmetry discovery methods are limited to linear symmetries, and recent attempts to discover nonlinear symmetries fail to explicitly get the Lie algebra subspace. In this paper, we propose LieNLSD, which is, to our knowledge, the first method capable of determining the number of infinitesimal generators with nonlinear terms and their explicit expressions. We specify a function library for the infinitesimal group action and aim to solve for its coefficient matrix, proving that its prolongation formula for differential equations, which governs dynamic data, is also linear with respect to the coefficient matrix. By substituting the central differences of the data and the Jacobian matrix of the trained neural network into the infinitesimal criterion, we get a system of linear equations for the coefficient matrix, which can then be solved using SVD. On top quark tagging and a series of dynamic systems, LieNLSD shows qualitative advantages over existing methods and improves the long rollout accuracy of neural PDE solvers by over $20\\%$ while applying to guide data augmentation. Code and data are available at [https://github.com/hulx2002/LieNLSD](https://github.com/hulx2002/LieNLSD).

The discovery of new materials is essential for enabling technological advancements. Computational approaches for predicting novel materials must effectively learn the manifold of stable crystal structures within an infinite design space. We introduce Open Materials Generation (OMatG), a unifying framework for the generative design and discovery of inorganic crystalline materials. OMatG employs stochastic interpolants (SI) to bridge an arbitrary base distribution to the target distribution of inorganic crystals via a broad class of tunable stochastic processes, encompassing both diffusion models and flow matching as special cases. In this work, we adapt the SI framework by integrating an equivariant graph representation of crystal structures and extending it to account for periodic boundary conditions in unit cell representations. Additionally, we couple the SI flow over spatial coordinates and lattice vectors with discrete flow matching for atomic species. We benchmark OMatG's performance on two tasks: Crystal Structure Prediction (CSP) for specified compositions, and de novo generation (DNG) aimed at discovering stable, novel, and unique structures. In our ground-up implementation of OMatG, we refine and extend both CSP and DNG metrics compared to previous works. OMatG establishes a new state of the art in generative modeling for materials discovery, outperforming purely flow-based and diffusion-based implementations. These results underscore the importance of designing flexible deep learning frameworks to accelerate progress in materials science. The OMatG code is available at https://github.com/FERMat-ML/OMatG.

Combinatorial CRISPR screening enables large-scale identification of synergistic gene pairs for combination therapies, but exhaustive experimentation is infeasible. We introduce NAIAD, an active learning framework that efficiently discovers optimal gene pairs by leveraging single-gene perturbation effects and adaptive gene embeddings that scale with the training data size, mitigating overfitting in small-sample learning while capturing complex gene interactions as more data is collected. Evaluated on four CRISPR datasets with over 350,000 interactions, NAIAD trained on small datasets outperforms existing models by up to 40\%. Its recommendation system prioritizes gene pairs with maximum predicted effects, accelerating discovery with fewer experiments. We also extend NAIAD to optimal drug combination identification among 2,000 candidates. Overall, NAIAD enhances combinatorial perturbation design and drives advances in genomics research and therapeutic development in combination therapy. Our code is publicly available at: https://github.com/NeptuneBio/NAIAD

Existing symmetry discovery methods predominantly focus on global transformations across the entire system or space, but they fail to consider the symmetries in local neighborhoods. This may result in the reported symmetry group being a misrepresentation of the true symmetry. In this paper, we formalize the notion of local symmetry as atlas equivariance. Our proposed pipeline, automatic local symmetry discovery (AtlasD), recovers the local symmetries of a function by training local predictor networks and then learning a Lie group basis to which the predictors are equivariant. We demonstrate AtlasD is capable of discovering local symmetry groups with multiple connected components in top-quark tagging and partial differential equation experiments. The discovered local symmetry is shown to be a useful inductive bias that improves the performance of downstream tasks in climate segmentation and vision tasks. Our code is publicly available at https://github.com/Rose-STL-Lab/AtlasD.

Graph neural networks (GNNs) have shown promise in learning the ground-state electronic properties of materials, subverting *ab initio* density functional theory (DFT) calculations when the underlying lattices can be represented as small and/or repeatable unit cells (i.e., molecules and periodic crystals). Realistic systems are, however, non-ideal and generally characterized by higher structural complexity. As such, they require large (10+ Å) unit cells and thousands of atoms to be accurately described. At these scales, DFT becomes computationally prohibitive, making GNNs especially attractive. In this work, we present a strictly local equivariant GNN capable of learning the electronic Hamiltonian (**H**) of realistically extended materials. It incorporates an *augmented partitioning* approach that enables training on arbitrarily large structures while preserving local atomic environments beyond boundaries. We demonstrate its capabilities by predicting the electronic Hamiltonian of various systems with up to 3,000 nodes (atoms), 500,000+ edges, ~ 28 million orbital interactions (nonzero entries of **H**), and $\leq$0.53\% error in the eigenvalue spectra. Our work expands the applicability of current electronic property prediction methods to some of the most challenging cases encountered in computational materials science, namely systems with disorder, interfaces, and defects.

Addressing selection bias in latent variable causal discovery is important yet underexplored, largely due to a lack of suitable statistical tools: While various tools beyond basic conditional independencies have been developed to handle latent variables, none have been adapted for selection bias. We make an attempt by studying rank constraints, which, as a generalization to conditional independence constraints, exploits the ranks of covariance submatrices in linear Gaussian models. We show that although selection can significantly complicate the joint distribution, interestingly, the ranks in the biased covariance matrices still preserve meaningful information about both causal structures and selection mechanisms. We provide a graph-theoretic characterization of such rank constraints. Using this tool, we demonstrate that the one-factor model, a classical latent variable model, can be identified under selection bias. Simulations and real-world experiments confirm the effectiveness of using our rank constraints.

We demonstrate how neural networks can drive mathematical discovery through a case study of the Hadwiger-Nelson problem, a long-standing open problem at the intersection of discrete geometry and extremal combinatorics that is concerned with coloring the plane while avoiding monochromatic unit-distance pairs. Using neural networks as approximators, we reformulate this mixed discrete-continuous geometric coloring problem with hard constraints as an optimization task with a probabilistic, differentiable loss function. This enables gradient-based exploration of admissible configurations that most significantly led to the discovery of two novel six-colorings, providing the first improvement in thirty years to the off-diagonal variant of the original problem (Mundinger et al., 2024a). Here, we establish the underlying machine learning approach used to obtain these results and demonstrate its broader applicability through additional numerical insights.

Generative modeling of crystalline materials using diffusion models presents a series of challenges: the data distribution is characterized by inherent symmetries and involves multiple modalities, with some defined on specific manifolds. Notably, the treatment of fractional coordinates representing atomic positions in the unit cell requires careful consideration, as they lie on a hypertorus. In this work, we introduce Kinetic Langevin Diffusion for Materials (KLDM), a novel diffusion model for crystalline materials generation, where the key innovation resides in the modeling of the coordinates. Instead of resorting to Riemannian diffusion on the hypertorus directly, we generalize Trivialized Diffusion Model (TDM) to account for the symmetries inherent to crystals. By coupling coordinates with auxiliary Euclidean variables representing velocities, the diffusion process is now offset to a flat space. This allows us to effectively perform diffusion on the hypertorus while providing a training objective that accounts for the periodic translation symmetry of the true data distribution. We evaluate KLDM on both Crystal Structure Prediction (CSP) and De-novo Generation (DNG) tasks, demonstrating its competitive performance with current state-of-the-art models.

For researchers and practitioners in finance, finding synergistic formulaic alphas is very important but challenging. In this paper, we reconsider the discovery of synergistic formulaic alphas from the viewpoint of sequential decision-making, and conceptualize the entire alpha discovery process as a non-stationary and reward-sparse Markov decision process. To overcome the challenges of non-stationarity and reward-sparsity, we propose the AlphaQCM method, a novel distributional reinforcement learning method designed to search for synergistic formulaic alphas efficiently. The AlphaQCM method first learns the Q function and quantiles via a Q network and a quantile network, respectively. Then, the AlphaQCM method applies the quantiled conditional moment method to learn unbiased variance from the potentially biased quantiles. Guided by the learned Q function and variance, the AlphaQCM method navigates the non-stationarity and reward-sparsity to explore the vast search space of formulaic alphas with high efficacy. Empirical applications to real-world datasets demonstrate that our AlphaQCM method significantly outperforms its competitors, particularly when dealing with large datasets comprising numerous stocks.

Neural causal discovery methods have recently improved in terms of scalability and computational efficiency. However, our systematic evaluation highlights significant room for improvement in their accuracy when uncovering causal structures. We identify a fundamental limitation: \textit{unavoidable likelihood score estimation errors disallow distinguishing the true structure}, even for small graphs and relatively large sample sizes. Furthermore, we identify the faithfulness property as a critical bottleneck: (i) it is likely to be violated across any reasonable dataset size range, and (ii) its violation directly undermines the performance of neural penalized-likelihood discovery methods. These findings lead us to conclude that progress within the current paradigm is fundamentally constrained, necessitating a paradigm shift in this domain.