ICLR 2026 论文列表

A central goal in systems biology and drug discovery is to predict the transcriptional response of cells to perturbations. This task is challenging due to the noisy, sparse nature of single-cell measurements and the fact that perturbations often induce population-level shifts rather than changes in individual cells. Existing deep learning methods typically assume cell-level correspondences, limiting their ability to capture such global effects. We present **scDFM**, a generative framework based on conditional flow matching that models the full distribution of perturbed cells conditioned on control states. By incorporating an MMD objective, our method aligns perturbed and control populations beyond cell-level correspondences. To further improve robustness to sparsity and noise, we propose the Perturbation-Aware Differential Transformer architecture (PAD-Transformer), a backbone that leverages gene interaction graphs and differential attention to capture context-specific expression changes. **scDFM** outperforms prior methods across multiple genetic and drug perturbation benchmarks, excelling in both unseen and combinatorial settings. In the combinatorial setting, it reduces MSE by 19.6\% over the strongest baseline. These results highlight the importance of distribution-level generative modeling for robust $\textit{in silico}$ perturbation prediction. The code is available at https://github.com/AI4Science-WestlakeU/scDFM.

Uncertainty Quantification (UQ) is paramount for inference in engineering applications. A common inference task is to recover full-field information of physical systems from a small number of noisy observations, a usually highly ill-posed problem. Critically, engineering systems often have complicated and variable geometries prohibiting the use of standard Bayesian UQ. In this work, we introduce Geometric Autoencoders for Bayesian Inversion (GABI), a framework for learning geometry-aware generative models of physical responses that serve as highly informative geometry-conditioned priors for Bayesian inversion. Following a “learn first, observe later” paradigm, GABI distills information from large datasets of systems with varying geometries, without requiring knowledge of governing PDEs, boundary conditions, or observation processes, into a rich latent prior. At inference time, this prior is seamlessly combined with the likelihood of the specific observation process, yielding a geometry-adapted posterior distribution. Our proposed framework is architecture agnostic. A creative use of Approximate Bayesian Computation (ABC) sampling yields an efficient implementation that utilizes modern GPU hardware. We test our method on: steady-state heat over rectangular domains; Reynold-Averaged Navier-Stokes (RANS) flow around airfoils; Helmholtz resonance and source localization on 3D car bodies; RANS airflow over terrain. We find: the predictive accuracy to be comparable to deterministic supervised learning approaches in the restricted setting where supervised learning is applicable; UQ to be well calibrated and robust on challenging problems with complex geometries. The method provides a flexible geometry-aware train-once-use-anywhere foundation model which is independent of any particular observation process.

Hybrid neural ordinary differential equations (neural ODEs) integrate mechanistic models with neural ODEs, offering strong inductive bias and flexibility, and are particularly advantageous in data-scarce healthcare settings. However, excessive latent states and interactions from mechanistic models can lead to training inefficiency and over-fitting, limiting practical effectiveness of hybrid neural ODEs. In response, we propose a new hybrid pipeline for automatic state selection and structure optimization in mechanistic neural ODEs, combining domain-informed graph modifications with data-driven regularization to sparsify the model for improving predictive performance and stability while retaining mechanistic plausibility. Experiments on synthetic and real-world data show improved predictive performance and robustness with desired sparsity, establishing an effective solution for hybrid model reduction in healthcare applications.

Gaussian Probability Path based Generative Models (GPPGMs) generate data by reversing a stochastic process that progressively corrupts samples with Gaussian noise. Despite state-of-the-art results in 3D molecular generation, their deployment is hindered by the high cost of long generative trajectories, often requiring hundreds to thousands of steps during training and sampling. In this work, we propose a principled method, named GAGA, to improve generation efficiency without sacrificing training granularity or inference fidelity of GPPGMs. Our key insight is that different data modalities obtain sufficient Gaussianity at markedly different steps during the forward process. Based on this observation, we analytically identify a characteristic step at which molecular data attains sufficient Gaussianity, after which the trajectory can be replaced by a closed-form Gaussian approximation. Unlike existing accelerators that coarsen or reformulate trajectories, our approach preserves full-resolution learning dynamics while avoiding redundant transport through truncated distributional states. Experiments on 3D molecular generation benchmarks demonstrate that our GAGA achieves substantial improvement on both generation quality and computational efficiency.

Molecular dynamics (MD) simulations remain the gold standard for studying protein dynamics, but their computational cost limits access to biologically relevant timescales. Recent generative models have shown promise in accelerating simulations, yet they struggle with long-horizon generation due to architectural constraints, error accumulation, and inadequate modeling of spatiotemporal dynamics. We present STAR-MD (Spatio-Temporal Autoregressive Rollout for Molecular Dynamics), a scalable SE(3)-equivariant diffusion model that generates physically plausible protein trajectories over microsecond timescales. Our key innovation is a causal diffusion transformer with joint spatiotemporal attention that efficiently captures complex space-time dependencies while avoiding the memory bottlenecks of existing methods. On the standard ATLAS benchmark, STAR-MD achieves state-of-the-art performance across all metrics--substantially improving conformational coverage, structural validity, and dynamic fidelity compared to previous methods. STAR-MD successfully extrapolates to generate stable microsecond-scale trajectories where baseline methods fail catastrophically, maintaining high structural quality throughout the extended rollout. Our comprehensive evaluation reveals severe limitations in current models for long-horizon generation, while demonstrating that STAR-MD's joint spatiotemporal modeling enables robust dynamics simulation at biologically relevant timescales, paving the way for accelerated exploration of protein function.

As large language models (LLMs) continue to revolutionize AI research, there is a growing interest in building large-scale brain foundation models to advance neuroscience. While most existing brain foundation models are pre-trained on time-series signals or connectome features, we propose a novel graph-based pre-training paradigm for constructing a brain graph foundation model. In this paper, we introduce the Brain Graph Foundation Model, termed BrainGFM, a unified framework that leverages graph contrastive learning and graph masked autoencoders for large-scale fMRI-based pre-training. BrainGFM is pre-trained on a diverse mixture of brain atlases with varying parcellations, significantly expanding the pre-training corpus and enhancing the model’s ability to generalize across heterogeneous fMRI-derived brain representations. To support efficient and versatile downstream transfer, we integrate both graph prompts and language prompts into the model design, enabling BrainGFM to flexibly adapt to a wide range of atlases, neurological and psychiatric disorders, and task settings. Furthermore, we employ meta-learning to optimize the graph prompts, facilitating strong generalization to previously unseen disorders under both few-shot and zero-shot learning conditions via language-guided prompting. BrainGFM is established on 27 neuroimaging datasets spanning 25 common neurological and psychiatric disorders, encompassing 2 types of brain atlases (functional and anatomical) across 8 widely used parcellations, and covering over 25,000 subjects, 60,000 fMRI scans, and a total of 400,000 graph samples aggregated across all atlases and parcellations. The code is available at https://github.com/weixinxu666/BrainGFM.

Machine-Learned Interatomic Potentials (MLIPs) require vast amounts of atomic structure data to learn forces and energies, and their performance continues to improve with training set size. Meanwhile, the even greater quantities of accompanying data in the Hamiltonian matrix $\mathbf{H}$ behind these datasets has so far gone unused for this purpose. Here, we provide a recipe for integrating the orbital interaction data within $\mathbf{H}$ towards training pipelines for atomic-level properties. We first introduce HELM ('Hamiltonian-trained Electronic-structure Learning for Molecules'), a state-of-the-art Hamiltonian prediction model which bridges the gap between Hamiltonian prediction and universal MLIPs by scaling to $\mathbf{H}$ of structures with 100+ atoms, high elemental diversity, and large basis sets including diffuse functions. To accompany HELM, we release a curated Hamiltonian matrix dataset, 'OMol\_CSH\_58k', with unprecedented elemental diversity (58 elements), molecular size (up to 150 atoms), and basis set (def2-TZVPD). Finally, we introduce 'Hamiltonian pretraining' as a method to extract meaningful descriptors of atomic environments even from a limited number atomic structures, and repurpose this shared embedding space to improve performance on energy-prediction in low-data regimes. Our results highlight the use of electronic interactions as a rich and transferable data source for representing chemical space.

The problem of physical dynamics, which involves predicting the 3D trajectories of particles, is a fundamental task with wide-ranging applications across science and engineering. However, accurately forecasting long-horizon trajectories from initial states remains challenging, due to complex particle interactions and entangled multi-scale dynamics involving both low- and high-frequency components. To address this, we propose a novel knowledge-distillation-based framework, SGDD (Spectral-Guided Dynamics Distillation), which integrates a spectral-guided enhancement to adaptively prioritize key frequency components within a unified spatio-temporal representation. Through knowledge distillation, SGDD leverages future trajectories as privileged information during training, guiding a teacher encoder to generate comprehensive dynamics representations while a student encoder approximates them using only the initial state. This enables the student to generate effective dynamics representations at inference, even without privileged information, thereby enabling accurate long-horizon trajectory prediction. Experimental results on molecule, protein, and human motion datasets demonstrate that our method achieves more accurate and stable long-term predictions than previous physical dynamics models, successfully capturing the complex spatio-temporal structures of real-world systems.

Fibring of modal logics is a well-established formalism for combining countable families of modal logics into a single fibred language with common semantics, characterized by fibred models. Inspired by this formalism, fibring of neural networks was introduced as a neurosymbolic framework for combining learning and reasoning in neural networks. Fibring of neural networks uses the (pre-)activations of a trained network to evaluate a fibring function computing the weights of another network whose outputs are injected back into the original network. However, the exact correspondence between fibring of neural networks and fibring of modal logics was never formally established. In this paper, we close this gap by formalizing the idea of fibred models compatible with fibred neural networks. Using this correspondence, we then derive non-uniform logical expressiveness results for Graph Neural Networks (GNNs), Graph Attention Networks (GATs) and Transformer encoders. Longer-term, the goal of this paper is to open the way for the use of fibring as a formalism for interpreting the logical theories learnt by neural networks with the tools of computational logic.

Chromosomes are the carriers of genetic information. Further understanding their 3D structure can help reveal gene-regulatory mechanisms and cellular functions. A standard pipeline for reconstructing the chromosome 3D structure first applies the single-cell Hi-C high-throughput screening method to measure pairwise interactions between DNA fragments at different resolutions; then it adopts computational methods to reconstruct the 3D structures from these contacts. These include traditional numerical methods and deep learning models, which struggle with limited model expressiveness and poor generalization across resolutions. To solve this issue, we propose InertialGenome, a novel transformer-based framework for robust and resolution-agnostic chromosome reconstruction. InertialGenome first adopts the inertial frame for the pose canonicalization. Then, based on such an invariant frame, it proposes a Transformer with geometry-aware positional encoding, leveraging Nyström estimation. To verify the effect of InertialGenome, we evaluate our model on two single-cell 3D reconstruction datasets with four resolutions, reaching superior performance over all four computational baselines. In addition to the structure metrics, we observe that InertialGenome outperforms when analyzing the function of reconstructed structures on two validation tasks. Finally, we leverage InertialGenome for cross-resolution transfer learning, yielding up to a 5\% improvement from low to high resolution.

Inspired by the effectiveness of genetic algorithms and the importance of synthesizability in molecular design, we present SynGA, a simple genetic algorithm that operates directly over synthesis routes. Our method features custom crossover and mutation operators that explicitly constrain it to synthesizable molecular space. By modifying the fitness function, we demonstrate the effectiveness of SynGA on a variety of design tasks, including synthesizable analog search and sample-efficient property optimization, for both 2D and 3D objectives. Furthermore, by coupling SynGA with a machine learning-based filter that focuses the building block set, we boost SynGA to state-of-the-art performance. For property optimization, this manifests as a model-based variant SynGBO, which employs SynGA and block filtering in the inner loop of Bayesian optimization. Since SynGA is lightweight and enforces synthesizability by construction, our hope is that SynGA can not only serve as a strong standalone baseline but also as a versatile module that can be incorporated into larger synthesis-aware workflows in the future.

We introduce *Einstein Fields*, a neural representation designed to compress computationally intensive *four-dimensional* numerical relativity simulations into compact implicit neural network weights. By modeling the *metric*, the core tensor field of general relativity, Einstein Fields enable the derivation of physical quantities via automatic differentiation. Unlike conventional neural fields (e.g., signed distance, occupancy, or radiance fields), Einstein Fields fall into the class of *Neural Tensor Fields* with the key difference that, when encoding the spacetime geometry into neural field representations, dynamics emerge naturally as a byproduct. Our novel implicit approach demonstrates remarkable potential, including continuum modeling of four-dimensional spacetime, mesh-agnosticity, storage efficiency, derivative accuracy, and ease of use. It achieves up to a $\mathtt{4,000}$-fold reduction in storage memory compared to discrete representations while retaining a numerical accuracy of five to seven decimal places. Moreover, in single precision, differentiation of the Einstein Fields-parameterized metric tensor is up to five orders of magnitude more accurate compared to naive finite differencing methods. We demonstrate these properties on several canonical test beds of general relativity and numerical relativity simulation data, while also releasing an open-source $\mathtt{JAX}$-based library: https://github.com/AndreiB137/EinFields, taking the first steps to studying the potential of machine learning in numerical relativity.

Crystal property prediction, governed by quantum mechanical principles, is computationally prohibitive to solve exactly for large many-body systems using traditional density functional theory. While machine learning models have emerged as efficient approximations for large-scale applications, their performance is strongly influenced by the choice of atomic representation. Although modern graph-based approaches have progressively incorporated more structural information, they often fail to capture long-range atomic interactions due to finite receptive fields and local encoding schemes. This limitation leads to distinct crystals being mapped to identical representations, hindering accurate property prediction. To address this, we introduce PRDNet that leverages unique reciprocal-space diffraction besides graph representations. To enhance sensitivity to elemental and environmental variations, we employ a data-driven pseudo-particle to generate a synthetic diffraction pattern. PRDNet ensures full invariance to crystallographic symmetries. Extensive experiments are conducted on Materials Project, JARVIS-DFT, and MatBench, demonstrating that the proposed model achieves state-of-the-art performance. The code is openly available at \url{https://github.com/Bin-Cao/PRDNet}.

Accurately solving partial differential equations (PDEs) on arbitrary geometries and a variety of meshes is an important task in science and engineering applications. In this paper, we propose Adaptive Fourier Mamba Operators (AFMO), which integrates reproducing kernels for state-space models (SSMs) rather than the kernel integral formulation of SSMs. This is achieved by constructing Takenaka-Malmquist systems for the PDEs. AFMO offers new representations that align well with the adaptive Fourier decomposition (AFD) theory and can approximate the solution manifold of PDEs on a wide range of geometries and meshes. In several challenging benchmark PDE problems in the field of fluid physics, solid physics, and finance on point clouds, structured meshes, regular grids, and irregular domains, AFMO consistently outperforms state-of-the-art solvers in terms of relative $L^2$ error. Overall, this work presents a new paradigm for designing explainable neural operator frameworks.

Generating molecular dynamics (MD) trajectories using deep generative models has attracted increasing attention, yet remains inherently challenging due to the limited availability of MD data and the complexities involved in modeling high-dimensional MD distributions. To overcome these challenges, we propose a novel framework that leverages structure pre-training for MD trajectory generation. Specifically, we first train a diffusion-based structure generation model on a large-scale conformer dataset, on top of which we introduce an interpolator module trained on MD trajectory data, designed to enforce temporal consistency among generated structures. Our approach effectively harnesses abundant structural data to mitigate the scarcity of MD trajectory data and effectively decomposes the intricate MD modeling task into two manageable subproblems: structural generation and temporal alignment. We comprehensively evaluate our method on the QM9 and DRUGS small-molecule datasets across unconditional generation, forward simulation, and interpolation tasks, and further extend our framework and analysis to tetrapeptide and protein monomer systems. Experimental results confirm that our approach excels in generating chemically realistic MD trajectories, as evidenced by remarkable improvements of accuracy in geometric, dynamical, and energetic measurements.

High-resolution structure determination by cryo-electron microscopy (cryo-EM) requires the accurate fitting of an atomic model into an experimental density map. Traditional refinement pipelines like Phenix.real_space_refine and Rosetta are computationally expensive, demand extensive manual tuning, and present a significant bottleneck for researchers. We present CryoNet.Refine, an end-to-end, deep learning framework that automates and accelerates molecular structure refinement. Our approach utilizes a one-step diffusion model that integrates a density-aware loss function with robust stereochemical restraints, enabling it to rapidly optimize a structure against the experimental data. CryoNet.Refine stands as a unified and versatile solution capable of refining not only protein complexes but also nucleic acids (DNA/RNA) and their assemblies. In benchmarks against Phenix.real_space_refine, CryoNet.Refine consistently yields substantial improvements in both model–map correlation and overall model geometric quality. By offering a scalable, automated, and powerful alternative, CryoNet.Refine is poised to become an essential tool for next-generation cryo-EM structure refinement.

Autoformalization, the task of translating informal mathematics into formal machine-verifiable languages, has long been challenging, even for individual statements. Beyond the statement level, mathematicians invest substantial effort in formalizing reusable abstractions such as common definitions and relations, based on which a large corpus of statements can be easily formalized. While previous work focuses on fine-tuning models for single statement autoformalization, we introduce $\textit{Divide and Abstract (DNA)}$, an end-to-end framework that not only improves the models' test-time performance at formalizing a corpus of statements, but also learns a library of reusable formal abstractions, which scales to statements outside of the corpus. First, $\textit{DNA}$ extracts common mathematical concepts from the entire informal corpus and formalizes them as reusable abstractions. Conditioned on these learned abstractions, $\textit{DNA}$ decomposes each informal statement in the corpus into a structured collection of informal clauses, translates each clause into its formal correspondents, composes the formal clauses back together, and refines the final formalization given feedback from a symbolic validator. The entire framework requires zero training and thus scales to any formal language, particularly low-resource Domain-Specific Languages (DSL). $\textit{DNA}$ significantly improves performance by up to $\textbf{8.6}\times$, and advances the SOTA by $\textbf{57.8}$\% from $\textbf{40.8}$ to $\textbf{64.4}$.

Spiking Neural Networks (SNNs), inspired by biological neurons, are attractive for their event-driven energy efficiency but still fall short of Artificial Neural Networks (ANNs) in accuracy. Knowledge distillation (KD) has emerged as a promising approach to narrow this gap by transferring ANN knowledge into SNNs. Temporal-wise distillation (TWD) leverages the temporal dynamics of SNNs by providing supervision across timesteps, but it applies a constant teacher output to all timesteps, mismatching the inherently evolving temporal process of SNNs. Moreover, while TWD improves per-timestep accuracy, truncated inference still suffers from full-length temporal information loss due to the progressive accumulation process. We propose **MEOM** (**M**any **E**yes, **O**ne **M**ind), a unified KD framework that enriches supervision with diverse temporal perspectives through mask-weighted teacher features and progressively aligns truncated predictions with the full-length prediction, thereby enabling more reliable inference across all timesteps. Extensive experiments and theoretical analyses demonstrate that MEOM achieves state-of-the-art performance on multiple benchmarks. Code is available at https://github.com/KaiSUN1/MEOM.

Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges for existing data-driven approaches. In this work, we propose a principled diffusion-based framework for learning physical systems from incomplete training samples. To this end, our method strategically partitions each such sample into observed context and unobserved query components through a carefully designed splitting strategy, then trains a conditional diffusion model to reconstruct the missing query portions given available contexts. This formulation enables accurate imputation across arbitrary observation patterns without requiring complete data supervision. Specifically, we provide theoretical analysis demonstrating that our diffusion training paradigm on incomplete data achieves asymptotic convergence to the true complete generative process under mild regularity conditions. Empirically, we show that our method significantly outperforms existing baselines on synthetic and real-world physical dynamics benchmarks, including fluid flows and weather systems, with particularly strong performance in limited and irregular observation regimes. These results demonstrate the effectiveness of our theoretically principled approach for learning and imputing partially observed dynamics.