ICLR 2025 论文列表

Precipitation nowcasting plays a pivotal role in socioeconomic sectors, especially in severe convective weather warnings. Although notable progress has been achieved by approaches mining the spatiotemporal correlations with deep learning, these methods still suffer severe blurriness as the lead time increases, which hampers accurate predictions for extreme precipitation. To alleviate blurriness, researchers explore generative methods conditioned on blurry predictions. However, the pairs of blurry predictions and corresponding ground truth need to be given in advance, making the training pipeline cumbersome and limiting the generality of generative models within blurry modes that appear in training data. By rethinking the blurriness in precipitation nowcasting as a blur kernel acting on predictions, we propose an unsupervised postprocessing method to eliminate the blurriness without the requirement of training with the pairs of blurry predictions and corresponding ground truth. Specifically, we utilize blurry predictions to guide the generation process of a pre-trained unconditional denoising diffusion probabilistic model (DDPM) to obtain high-fidelity predictions with eliminated blurriness. A zero-shot blur kernel estimation mechanism and an auto-scale denoise guidance strategy are introduced to adapt the unconditional DDPM to any blurriness modes varying from datasets and lead times in precipitation nowcasting. Extensive experiments are conducted on 7 precipitation radar datasets, demonstrating the generality and superiority of our method.

Generative models see increasing use in computer-aided drug design. However, while performing well at capturing distributions of molecular motifs, they often produce synthetically inaccessible molecules. To address this, we introduce SynFlowNet, a GFlowNet model whose action space uses chemical reactions and buyable reactants to sequentially build new molecules. By incorporating forward synthesis as an explicit constraint of the generative mechanism, we aim at bridging the gap between in silico molecular generation and real world synthesis capabilities. We evaluate our approach using synthetic accessibility scores and an independent retrosynthesis tool to assess the synthesizability of our compounds, and motivate the choice of GFlowNets through considerable improvement in sample diversity compared to baselines. Additionally, we identify challenges with reaction encodings that can complicate traversal of the MDP in the backward direction. To address this, we introduce various strategies for learning the GFlowNet backward policy and thus demonstrate how additional constraints can be integrated into the GFlowNet MDP framework. This approach enables our model to successfully identify synthesis pathways for previously unseen molecules.

Data assimilation (DA) is an essential statistical technique for generating accurate estimates of a physical system's states by combining prior model predictions with observational data, especially in the realm of weather forecasting. Effectively modeling the prior distribution while adapting to diverse observational sources presents significant challenges for both traditional and neural network-based DA algorithms. This paper introduces VAE-Var, a novel neural network-based data assimilation algorithm aimed at 1) enhancing accuracy by capturing the non-Gaussian characteristics of the conditional background distribution $p(\mathbf{x}|\mathbf{x}_b)$, and 2) efficiently assimilating real-world observational data. VAE-Var utilizes a variational autoencoder to learn the background error distribution, with its decoder creating a variational cost function to optimize the analysis states. The advantages of VAE-Var include: 1) it maintains the framework of traditional variational assimilation, enabling it to accommodate various observation operators, particularly irregular observations; 2) it lessens the dependence on expert knowledge for constructing the background distribution, allowing for improved modeling of non-Gaussian structures; and 3) experimental results indicate that, when applied to the FengWu weather forecasting model, VAE-Var outperforms DiffDA and two traditional algorithms (interpolation and 3DVar) in terms of assimilation accuracy in sparse observational contexts, and is capable of assimilating real-world GDAS prepbufr observations over a year.

In traditional machine learning, models are defined by a set of parameters, which are optimized to perform specific tasks. In neural networks, these parameters correspond to the synaptic weights. However, in reality, it is often infeasible to control or update all weights. This challenge is not limited to artificial networks but extends to biological networks, such as the brain, where the extent of distributed synaptic weight modification during learning remains unclear. Motivated by these insights, we theoretically investigate how different allocations of a fixed number of learnable weights influence the capacity of neural networks. Using a teacher-student setup, we introduce a benchmark to quantify the expressivity associated with each allocation. We establish conditions under which allocations have \`maximal' or \`minimal' expressive power in linear recurrent neural networks and linear multi-layer feedforward networks. For suboptimal allocations, we propose heuristic principles to estimate their expressivity. These principles extend to shallow ReLU networks as well. Finally, we validate our theoretical findings with empirical experiments. Our results emphasize the critical role of strategically distributing learnable weights across the network, showing that a more widespread allocation generally enhances the network’s expressive power.

The goal of protein design typically involves increasing fitness (extrapolating) beyond what is seen during training (e.g., towards higher stability, stronger binding affinity, etc.). State-of-the-art methods assume that one can safely steer proteins towards such extrapolated regions by learning from pairs alone. We hypothesize that noisy training pairs are not sufficiently informative to capture the fitness gradient and that models learned from pairs specifically may fail to capture three-way relations important for search, e.g., how two alternatives fair relative to a seed. Building on the success of preference alignment models in large language models, we introduce a progressive search method for extrapolative protein design by directly distilling into the model relevant triplet relations. We evaluated our model's performance in designing AAV and GFP proteins and demonstrated that the proposed framework significantly improves effectiveness in extrapolation tasks.

Proteomics is the large-scale study of proteins. Tandem mass spectrometry, as the only high-throughput technique for protein sequence identification, plays a pivotal role in proteomics research. One of the long-standing challenges in this field is peptide identification, which entails determining the specific peptide (sequence of amino acids) that corresponds to each observed mass spectrum. The conventional approach involves database searching, wherein the observed mass spectrum is scored against a pre-constructed peptide database. However, the reliance on pre-existing databases limits applicability in scenarios where the peptide is absent from existing databases. Such circumstances necessitate \emph{de novo} peptide sequencing, which derives peptide sequence solely from input mass spectrum, independent of any peptide database. Despite ongoing advancements in \emph{de novo} peptide sequencing, its performance still has considerable room for improvement, which limits its application in large-scale experiments. In this study, we introduce a novel \textbf{Re}trieval-based \emph{De \textbf{Novo}} peptide sequencing methodology, termed \textbf{ReNovo}, which draws inspiration from database search methods. Specifically, by constructing a datastore from training data, ReNovo can retrieve information from the datastore during the inference stage to conduct retrieval-based inference, thereby achieving improved performance. This innovative approach enables ReNovo to effectively combine the strengths of both methods: utilizing the assistance of the datastore while also being capable of predicting novel peptides that are not present in pre-existing databases. A series of experiments have confirmed that ReNovo outperforms state-of-the-art models across multiple widely-used datasets, incurring only minor storage and time consumption, representing a significant advancement in proteomics. Supplementary materials include the code.

Cryogenic electron tomography (Cryo-ET) is a powerful technique for visualizing subcellular structures in their native states. Nonetheless, its effectiveness is compromised by anisotropic resolution artifacts caused by the missing-wedge effect. To address this, IsoNet, a deep learning-based method, proposes iteratively reconstructing the missing-wedge information. While successful, IsoNet's dependence on recursive prediction updates often leads to training instability and model divergence. In this study, we introduce CryoGEN—an energy-based probabilistic model that not only mitigates resolution anisotropy but also removes the need for recursive subtomogram averaging, delivering an approximate *10*$\times$ speedup for training. Evaluations across various biological datasets, including immature HIV-1 virions and ribosomes, demonstrate that CryoGEN significantly enhances structural completeness and interpretability of the reconstructed samples.

We introduce a new framework for 2D molecular graph generation using 3D molecule generative models. Our Synthetic Coordinate Embedding (SyCo) framework maps 2D molecular graphs to 3D Euclidean point clouds via synthetic coordinates and learns the inverse map using an E($n$)-Equivariant Graph Neural Network (EGNN). The induced point cloud-structured latent space is well-suited to apply existing 3D molecule generative models. This approach simplifies the graph generation problem into a point cloud generation problem followed by node and edge classification tasks, without relying on molecular fragments nor autoregressive decoding. Further, we propose a novel similarity-constrained optimization scheme for 3D diffusion models based on inpainting and guidance. As a concrete implementation of our framework, we develop EDM-SyCo based on the E(3) Equivariant Diffusion Model (EDM). EDM-SyCo achieves state-of-the-art performance in distribution learning of molecular graphs, outperforming the best non-autoregressive methods by more than 26\% on ZINC250K and 16\% on the GuacaMol dataset while improving conditional generation by up to 3.9 times.

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which relevant statistics (e.g., RMS and two-point correlations) can be derived. Here, we propose a graph-based latent diffusion model that enables direct sampling of states from their equilibrium distribution, given a mesh discretization of the system and its physical parameters. This allows for the efficient computation of flow statistics without running long and expensive numerical simulations. The graph-based structure enables operations on unstructured meshes, which is critical for representing complex geometries with spatially localized high gradients, while latent-space diffusion modeling with a multi-scale GNN allows for efficient learning and inference of entire distributions of solutions. A key finding of our work is that the proposed networks can accurately learn full distributions even when trained on incomplete data from relatively short simulations. We apply this method to a range of fluid dynamics tasks, such as predicting pressure distributions on 3D wing models in turbulent flow, demonstrating both accuracy and computational efficiency in challenging scenarios. The ability to directly sample accurate solutions, and capturing their diversity from short ground-truth simulations, is highly promising for complex scientific modeling tasks.

Density Functional Theory (DFT) is a pivotal method within quantum chemistry and materials science, with its core involving the construction and solution of the Kohn-Sham Hamiltonian. Despite its importance, the application of DFT is frequently limited by the substantial computational resources required to construct the Kohn-Sham Hamiltonian. In response to these limitations, current research has employed deep-learning models to efficiently predict molecular and solid Hamiltonians, with roto-translational symmetries encoded in their neural networks. However, the scalability of prior models may be problematic when applied to large molecules, resulting in non-physical predictions of ground-state properties. In this study, we generate a substantially larger training set (PubChemQH) than used previously and use it to create a scalable model for DFT calculations with physical accuracy. For our model, we introduce a loss function derived from physical principles, which we call Wavefunction Alignment Loss (WALoss). WALoss involves performing a basis change on the predicted Hamiltonian to align it with the observed one; thus, the resulting differences can serve as a surrogate for orbital energy differences, allowing models to make better predictions for molecular orbitals and total energies than previously possible. WALoss also substantially accelerates self-consistent-field (SCF) DFT calculations. Here, we show it achieves a reduction in total energy prediction error by a factor of 1347 and an SCF calculation speed-up by a factor of 18\%. These substantial improvements set new benchmarks for achieving accurate and applicable predictions in larger molecular systems.

Neural Ordinary Differential Equations (Neural ODEs or NODEs) excel at modeling continuous dynamical systems from observational data, especially when the data is irregularly sampled. However, existing training methods predominantly rely on numerical ODE solvers, which are time-consuming and prone to accumulating numerical errors over time due to autoregression. In this work, we propose VF-NODE, a novel approach based on the variational formulation (VF) to accelerate the training of NODEs. Unlike existing training methods, the proposed VF-NODEs implement a series of global integrals, thus evaluating Deep Neural Network (DNN)--based vector fields only at specific observed data points. This strategy drastically reduces the number of function evaluations (NFEs). Moreover, our method eliminates the use of autoregression, thereby reducing error accumulations for modeling dynamical systems. Nevertheless, the VF loss introduces oscillatory terms into the integrals when using the Fourier basis. We incorporate Filon's method to address this issue. To further enhance the performance for noisy and incomplete data, we employ the natural cubic spline regression to estimate a closed-form approximation. We provide a fundamental analysis of how our approach minimizes computational costs. Extensive experiments demonstrate that our approach accelerates NODE training by 10 to 1000 times compared to existing NODE-based methods, while achieving higher or comparable accuracy in dynamical systems. The code is available at https://github.com/ZhaoHongjue/VF-NODE-ICLR2025.

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied data distribution are expected to adhere to specific governing equations. We present a framework that unifies generative modeling and partial differential equation fulfillment by introducing a first-principle-based loss term that enforces generated samples to fulfill the underlying physical constraints. Our approach reduces the residual error by up to two orders of magnitudes compared to previous work in a fluid flow case study and outperforms task-specific frameworks in relevant metrics for structural topology optimization. We also present numerical evidence that our extended training objective acts as a natural regularization mechanism against overfitting. Our framework is simple to implement and versatile in its applicability for imposing equality and inequality constraints as well as auxiliary optimization objectives. Code is available at https://github.com/jhbastek/PhysicsInformedDiffusionModels.

Biomedical reasoning integrates structured, codified knowledge with tacit, experience-driven insights. Depending on the context, quantity, and nature of available evidence, researchers and clinicians use diverse strategies, including rule-based, prototype-based, and case-based reasoning. Effective medical AI models must handle this complexity while ensuring reliability and adaptability. We introduce KGARevion, a knowledge graph-based agent that answers knowledge-intensive questions. Upon receiving a query, KGARevion generates relevant triplets by leveraging the latent knowledge embedded in a large language model. It then verifies these triplets against a grounded knowledge graph, filtering out errors and retaining only accurate, contextually relevant information for the final answer. This multi-step process strengthens reasoning, adapts to different models of medical inference, and outperforms retrieval-augmented generation-based approaches that lack effective verification mechanisms. Evaluations on medical QA benchmarks show that KGARevion improves accuracy by over 5.2% over 15 models in handling complex medical queries. To further assess its effectiveness, we curated three new medical QA datasets with varying levels of semantic complexity, where KGARevion improved accuracy by 10.4%. The agent integrates with different LLMs and biomedical knowledge graphs for broad applicability across knowledge-intensive tasks. We evaluated KGARevion on AfriMed-QA, a newly introduced dataset focused on African healthcare, demonstrating its strong zero-shot generalization to underrepresented medical contexts.

Quantifying the complexity of quantum states is a longstanding key problem in various subfields of science, ranging from quantum computing to the black-hole theory. The lower bound on quantum pure state complexity has been shown to grow linearly with system size [J. Haferkamp et al., 2022, *Nat. Phys.*]. However, extending this result to noisy circuit environments, which better reflect real quantum devices, remains an open challenge. In this paper, we explore the complexity of weakly noisy quantum states via the quantum learning method. We present an efficient learning algorithm, that leverages the classical shadow representation of target quantum states, to predict the circuit complexity of weakly noisy quantum states. Our algorithm is proved to be optimal in terms of sample complexity accompanied with polynomial classical processing time. Our result builds a bridge between the learning algorithm and quantum state complexity, meanwhile highlighting the power of learning algorithm in characterizing intrinsic properties of quantum states.

Graph data augmentation (GDA) has shown significant promise in enhancing the performance, generalization, and robustness of graph neural networks (GNNs). However, contemporary methodologies are often limited to static graphs, whose applicability on dynamic graphs—more prevalent in real-world applications—remains unexamined. In this paper, we empirically highlight the challenges faced by static GDA methods when applied to dynamic graphs, particularly their inability to maintain temporal consistency. In light of this limitation, we propose a dedicated augmentation framework for dynamic graphs, termed $\texttt{DyAug}$, which adaptively augments the evolving graph structure with temporal consistency awareness. Specifically, we introduce the paradigm of graph rationalization for dynamic GNNs, progressively distinguishing between causal subgraphs (\textit{rationale}) and the non-causal complement (\textit{environment}) across snapshots. We develop three types of environment replacement, including, spatial, temporal, and spatial-temporal, to facilitate data augmentation in the latent representation space, thereby improving the performance, generalization, and robustness of dynamic GNNs. Extensive experiments on six benchmarks and three GNN backbones demonstrate that $\texttt{DyAug}$ can \textbf{(I)} improve the performance of dynamic GNNs by $0.89\\%\sim3.13\\%\uparrow$; \textbf{(II)} effectively counter targeted and non-targeted adversarial attacks with $6.2\\%\sim12.2\\%\\uparrow$ performance boost; \textbf{(III)} make stable predictions under temporal distribution shifts.

Generative models that satisfy hard constraints are critical in many scientific and engineering applications, where physical laws or system requirements must be strictly respected. Many existing constrained generative models, especially those developed for computer vision, rely heavily on gradient information, which is often sparse or computationally expensive in some fields, e.g., partial differential equations (PDEs). In this work, we introduce a novel framework for adapting pre-trained, unconstrained flow-matching models to satisfy constraints exactly in a zero-shot manner without requiring expensive gradient computations or fine-tuning. Our framework, *ECI sampling*, alternates between extrapolation (E), correction (C), and interpolation (I) stages during each iterative sampling step of flow matching sampling to ensure accurate integration of constraint information while preserving the validity of the generation. We demonstrate the effectiveness of our approach across various PDE systems, showing that ECI-guided generation strictly adheres to physical constraints and accurately captures complex distribution shifts induced by these constraints. Empirical results demonstrate that our framework consistently outperforms baseline approaches in various zero-shot constrained generation tasks and also achieves competitive results in the regression tasks without additional fine-tuning.

$D^2$-sampling is a fundamental component of sampling-based clustering algorithms such as $k$-means++. Given a dataset $V \subset \mathbb{R}^d$ with $N$ points and a center set $C \subset \mathbb{R}^d$, $D^2$-sampling refers to picking a point from $V$ where the sampling probability of a point is proportional to its squared distance from the nearest center in $C$. The popular $k$-means++ algorithm is simply a $k$-round $D^2$-sampling process, which runs in $O(Nkd)$ time and gives $O(\log{k})$-approximation in expectation for the $k$-means problem. In this work, we give a quantum algorithm for (approximate) $D^2$-sampling in the QRAM model that results in a quantum implementation of $k$-means++ with a running time $\tilde{O}(\zeta^2 k^2)$. Here $\zeta$ is the aspect ratio ( i.e., largest to smallest interpoint distance) and $\tilde{O}$ hides polylogarithmic factors in $N, d, k$. It can be shown through a robust approximation analysis of $k$-means++ that the quantum version preserves its $O(\log{k})$ approximation guarantee. Further, we show that our quantum algorithm for $D^2$-sampling can be dequantized using the sample-query access model of Tang (PhD Thesis, Ewin Tang, University of Washington, 2023). This results in a fast quantum-inspired classical implementation of $k$-means++, which we call QI-$k$-means++, with a running time $O(Nd) + \tilde{O}(\zeta^2k^2d)$, where the $O(Nd)$ term is for setting up the sample-query access data structure. Experimental investigations show promising results for QI-$k$-means++ on large datasets with bounded aspect ratio. Finally, we use our quantum $D^2$-sampling with the known $ D^2$-sampling-based classical approximation scheme to obtain the first quantum approximation scheme for the $k$-means problem with polylogarithmic running time dependence on $N$.

Machine Learning Force Fields (MLFFs) are of great importance for chemistry, physics, materials science, and many other related fields. The Clebsch–Gordan transform (CG transform) effectively encodes many-body interactions and is thus an important building block for many models of MLFFs. However, the permutation-equivariance requirement of MLFFs limits the design space of CG transform, that is, intensive CG transform has to be conducted for each neighboring edge and the operations should be performed in the same manner for all edges. Freeing up the design space can greatly improve the model's expressiveness while simultaneously decreasing computational demands. To reach this goal, we utilize a mathematical proposition, invariance transitivity, to show that implementing the CG transform layer on the permutation-invariant abstract edges allows complete freedom in the design of the layer without compromising the overall permutation equivariance. Developing on this free design space, we further propose group CG transform with sparse path, abstract edges shuffling, and attention enhancer to form a powerful and efficient CG transform layer. Our method, known as FreeCG, achieves state-of-the-art (SOTA) results in force prediction for MD17, rMD17, MD22, and is well extended to property prediction in QM9 datasets with several improvements greater than 15% and the maximum beyond 20%. The extensive real-world applications showcase high practicality. FreeCG introduces a novel paradigm for carrying out efficient and expressive CG transform in future geometric network designs. To demonstrate this, the recent SOTA, QuinNet, is also enhanced under our paradigm. Code: https://github.com/ShihaoShao-GH/FreeCG.

The dominant paradigm for learning on graphs is message passing. Despite being a strong inductive bias, the local message passing mechanism faces challenges such as over-smoothing, over-squashing, and limited expressivity. To address these issues, we introduce Bundle Neural Networks (BuNNs), a novel graph neural network architecture that operates via *message diffusion* on *flat vector bundles* — geometrically inspired structures that assign to each node a vector space and an orthogonal map. A BuNN layer evolves node features through a diffusion-type partial differential equation, where its discrete form acts as a special case of the recently introduced Sheaf Neural Network (SNN), effectively alleviating over-smoothing. The continuous nature of message diffusion enables BuNNs to operate at larger scales, reducing over-squashing. We establish the universality of BuNNs in approximating feature transformations on infinite families of graphs with injective positional encodings, marking the first positive expressivity result of its kind. We support our claims with formal analysis and synthetic experiments. Empirically, BuNNs perform strongly on heterophilic and long-range tasks, which demonstrates their robustness on a diverse range of challenging real-world tasks.