ICML 2025 Papers

Diffusion models are the standard toolkit for generative modelling of 3D atomic systems. However, for different types of atomic systems -- such as molecules and materials -- the generative processes are usually highly specific to the target system despite the underlying physics being the same. We introduce the All-atom Diffusion Transformer (ADiT), a unified latent diffusion framework for jointly generating both periodic materials and non-periodic molecular systems using the same model: (1) An autoencoder maps a unified, all-atom representations of molecules and materials to a shared latent embedding space; and (2) A diffusion model is trained to generate new latent embeddings that the autoencoder can decode to sample new molecules or materials. Experiments on MP20, QM9 and GEOM-DRUGS datasets demonstrate that jointly trained ADiT generates realistic and valid molecules as well as materials, obtaining state-of-the-art results on par with molecule and crystal-specific models. ADiT uses standard Transformers with minimal inductive biases for both the autoencoder and diffusion model, resulting in significant speedups during training and inference compared to equivariant diffusion models. Scaling ADiT up to half a billion parameters predictably improves performance, representing a step towards broadly generalizable foundation models for generative chemistry. Open source code: https://github.com/facebookresearch/all-atom-diffusion-transformer

We present Mechanistic PDE Networks -- a model for discovery of governing *partial differential equations* from data. Mechanistic PDE Networks represent spatiotemporal data as space-time dependent *linear* partial differential equations in neural network hidden representations. The represented PDEs are then solved and decoded for specific tasks. The learned PDE representations naturally express the spatiotemporal dynamics in data in neural network hidden space, enabling increased modeling power. Solving the PDE representations in a compute and memory-efficient way, however, is a significant challenge. We develop a native, GPU-capable, parallel, sparse and differentiable multigrid solver specialized for linear partial differential equations that acts as a module in Mechanistic PDE Networks. Leveraging the PDE solver we propose a discovery architecture that can discovers nonlinear PDEs in complex settings, while being robust to noise. We validate PDE discovery on a number of PDEs including reaction-diffusion and Navier-Stokes equations.

Neural PDE surrogates can improve the cost-accuracy tradeoff of classical solvers, but often generalize poorly to new initial conditions and accumulate errors over time. Physical and symmetry constraints have shown promise in closing this performance gap, but existing techniques for imposing these inductive biases are incompatible with the staggered grids commonly used in computational fluid dynamics. Here we introduce novel input and output layers that respect physical laws and symmetries on the staggered grids, and for the first time systematically investigate how these constraints, individually and in combination, affect the accuracy of PDE surrogates. We focus on two challenging problems: shallow water equations with closed boundaries and decaying incompressible turbulence. Compared to strong baselines, symmetries and physical constraints consistently improve performance across tasks, architectures, autoregressive prediction steps, accuracy measures, and network sizes. Symmetries are more effective than physical constraints, but surrogates with both performed best, even compared to baselines with data augmentation or pushforward training, while themselves benefiting from the pushforward trick. Doubly-constrained surrogates also generalize better to initial conditions and durations beyond the range of the training data, and more accurately predict real-world ocean currents.

Hierarchical clustering is a widely used method for unsupervised learning with numerous applications. However, in the application of modern algorithms, the datasets studied are usually large and dynamic. If the hierarchical clustering is sensitive to small perturbations of the dataset, the usability of the algorithm will be greatly reduced. In this paper, we focus on the hierarchical $k$ -median clustering problem, which bridges hierarchical and centroid-based clustering while offering theoretical appeal, practical utility, and improved interpretability. We analyze the average sensitivity of algorithms for this problem by measuring the expected change in the output when a random data point is deleted. We propose an efficient algorithm for hierarchical $k$-median clustering and theoretically prove its low average sensitivity and high clustering quality. Additionally, we show that single linkage clustering and a deterministic variant of the CLNSS algorithm exhibit high average sensitivity, making them less stable. Finally, we validate the robustness and effectiveness of our algorithm through experiments.

Physics-informed neural networks (PINNs) aim to constrain the outputs and gradients of deep learning models to satisfy specified governing physics equations, which have demonstrated significant potential for solving partial differential equations (PDEs). Although existing PINN methods have achieved pleasing performance, they always treat both easy and hard sample points indiscriminately, especially ones in the physical boundaries. This easily causes the PINN model to fall into undesirable local minima and unstable learning, thereby resulting in an Unbalanced Prediction Problem (UPP). To deal with this daunting problem, we propose a novel framework named Cognitive Physical Informed Neural Network (CoPINN) that imitates the human cognitive learning manner from easy to hard. Specifically, we first employ separable subnetworks to encode independent one-dimensional coordinates and apply an aggregation scheme to generate multi-dimensional predicted physical variables. Then, during the training phase, we dynamically evaluate the difficulty of each sample according to the gradient of the PDE residuals. Finally, we propose a cognitive training scheduler to progressively optimize the entire sampling regions from easy to hard, thereby embracing robustness and generalization against predicting physical boundary regions. Extensive experiments demonstrate that our CoPINN achieves state-of-the-art performance, particularly significantly reducing prediction errors in stubborn regions.

We describe HypotheSAEs, a general method to hypothesize interpretable relationships between text data (e.g., headlines) and a target variable (e.g., clicks). HypotheSAEs has three steps: (1) train a sparse autoencoder on text embeddings to produce interpretable features describing the data distribution, (2) select features that predict the target variable, and (3) generate a natural language interpretation of each feature (e.g., *mentions being surprised or shocked*) using an LLM. Each interpretation serves as a hypothesis about what predicts the target variable. Compared to baselines, our method better identifies reference hypotheses on synthetic datasets (at least +0.06 in F1) and produces more predictive hypotheses on real datasets (~twice as many significant findings), despite requiring 1-2 orders of magnitude less compute than recent LLM-based methods. HypotheSAEs also produces novel discoveries on two well-studied tasks: explaining partisan differences in Congressional speeches and identifying drivers of engagement with online headlines.

The cellular Potts model (CPM) is a powerful computational method for simulating collective spatiotemporal dynamics of biological cells. To drive the dynamics, CPMs rely on physics-inspired Hamiltonians. However, as first principles remain elusive in biology, these Hamiltonians only approximate the full complexity of real multicellular systems. To address this limitation, we propose NeuralCPM, a more expressive cellular Potts model that can be trained directly on observational data. At the core of NeuralCPM lies the Neural Hamiltonian, a neural network architecture that respects universal symmetries in collective cellular dynamics. Moreover, this approach enables seamless integration of domain knowledge by combining known biological mechanisms and the expressive Neural Hamiltonian into a hybrid model. Our evaluation with synthetic and real-world multicellular systems demonstrates that NeuralCPM is able to model cellular dynamics that cannot be accounted for by traditional analytical Hamiltonians.

Large language model (LLM) agents are increasingly capable of autonomously conducting cyberattacks, posing significant threats to existing applications. This growing risk highlights the urgent need for a real-world benchmark to evaluate the ability of LLM agents to exploit web application vulnerabilities. However, existing benchmarks fall short as they are limited to abstracted Capture-the-Flag competitions or lack comprehensive coverage. Building a benchmark for real-world vulnerabilities involves both specialized exper- tise to reproduce exploits and a systematic approach to evaluating unpredictable attacks. To address this challenge, we introduce CVE-Bench, a real-world cybersecurity benchmark based on critical-severity Common Vulnerabilities and Exposures. In CVE-Bench, we design a sandbox framework that enables LLM agents to exploit vulnerable web applications in scenarios that mimic real-world conditions, while also providing effective evaluation of their exploits. Our experiments show that the state-of-the-art agent framework can exploit up to 13% of the vulnerabilities.

We introduce PDE-Transformer, an improved transformer-based architecture for surrogate modeling of physics simulations on regular grids. We combine recent architectural improvements of diffusion transformers with adjustments specific for large-scale simulations to yield a more scalable and versatile general-purpose transformer architecture, which can be used as the backbone for building large-scale foundation models in physical sciences. We demonstrate that our proposed architecture outperforms state-of-the-art transformer architectures for computer vision on a large dataset of 16 different types of PDEs. We propose to embed different physical channels individually as spatio-temporal tokens, which interact via channel-wise self-attention. This helps to maintain a consistent information density of tokens when learning multiple types of PDEs simultaneously. We demonstrate that our pre-trained models achieve improved performance on several challenging downstream tasks compared to training from scratch and also beat other foundation model architectures for physics simulations. Our source code is available at https://github.com/tum-pbs/pde-transformer.

The measurement tasks involved in evaluating generative AI (GenAI) systems lack sufficient scientific rigor, leading to what has been described as "a tangle of sloppy tests [and] apples-to-oranges comparisons" (Roose, 2024). In this position paper, we argue that the ML community would benefit from learning from and drawing on the social sciences when developing and using measurement instruments for evaluating GenAI systems. Specifically, our position is that evaluating GenAI systems is a social science measurement challenge. We present a four-level framework, grounded in measurement theory from the social sciences, for measuring concepts related to the capabilities, behaviors, and impacts of GenAI systems. This framework has two important implications: First, it can broaden the expertise involved in evaluating GenAI systems by enabling stakeholders with different perspectives to participate in conceptual debates. Second, it brings rigor to both conceptual and operational debates by offering a set of lenses for interrogating validity.

Brain decoding aims to reconstruct visual perception of human subject from fMRI signals, which is crucial for understanding brain's perception mechanisms. Existing methods are confined to the single-subject paradigm due to substantial brain variability, which leads to weak generalization across individuals and incurs high training costs, exacerbated by limited availability of fMRI data. To address these challenges, we propose MindAligner, an explicit functional alignment framework for cross-subject brain decoding from limited fMRI data. The proposed MindAligner enjoys several merits. First, we learn a Brain Transfer Matrix (BTM) that projects the brain signals of an arbitrary new subject to one of the known subjects, enabling seamless use of pre-trained decoding models. Second, to facilitate reliable BTM learning, a Brain Functional Alignment module is proposed to perform soft cross-subject brain alignment under different visual stimuli with a multi-level brain alignment loss, uncovering fine-grained functional correspondences with high interpretability. Experiments indicate that MindAligner not only outperforms existing methods in visual decoding under data-limited conditions, but also provides valuable neuroscience insights in cross-subject functional analysis. The code will be made publicly available.

Natural data is often organized as a hierarchical composition of features. How many samples do generative models need in order to learn the composition rules, so as to produce a combinatorially large number of novel data? What signal in the data is exploited to learn those rules? We investigate these questions in the context of diffusion models both theoretically and empirically. Theoretically, we consider a simple probabilistic context-free grammar - a tree-like graphical model used to represent the hierarchical and compositional structure of data such as language and images. We demonstrate that diffusion models learn the grammar's composition rules with the sample complexity required for clustering features with statistically similar context, a process similar to the word2vec algorithm. However, this clustering emerges hierarchically: higher-level features associated with longer contexts require more data to be identified. This mechanism leads to a sample complexity that scales polynomially with the said context size. As a result, diffusion models trained on an intermediate dataset size generate data coherent up to a certain scale, but lacking global coherence. We test these predictions across different domains and find remarkable agreement: both generated texts and images achieve progressively larger coherence lengths as the training time or dataset size grows. We discuss connections between the hierarchical clustering mechanism we introduce here and the renormalization group in physics.

In this paper, we provide the first practical algorithms with provable guarantees for the problem of inferring the topics assigned to each document in an LDA topic model. This is the primary inference problem for many applications of topic models in social science, data exploration, and causal inference settings. We obtain this result by showing a novel non-gradient-based, combinatorial approach to estimating topic models. This yields algorithms that converge to near-optimal posterior probability in logarithmic parallel computation time (adaptivity)---exponentially faster than any known LDA algorithm. We also show that our approach can provide interpretability guarantees such that each learned topic is formally associated with a known keyword. Finally, we show that unlike alternatives, our approach can maintain the independence assumptions necessary to use the learned topic model for downstream causal inference methods that allow researchers to study topics as treatments. In terms of practical performance, our approach consistently returns solutions of higher semantic quality than solutions from state-of-the-art LDA algorithms, neural topic models, and LLM-based topic models across a diverse range of text datasets and evaluation parameters.

Traditional machine societies rely on data-driven learning, overlooking interactions and limiting knowledge acquisition from model interplay. To address these issues, we revisit the development of machine societies by drawing inspiration from the evolutionary processes of human societies. Motivated by Social Learning (SL), this paper introduces a practical paradigm of Socialized Coevolution (SC). Compared to most existing methods focused on knowledge distillation and multi-task learning, our work addresses a more challenging problem: not only enhancing the capacity to solve new downstream tasks but also improving the performance of existing tasks through inter-model interactions. Inspired by cognitive science, we propose Dynamic Information Socialized Collaboration (DISC), which achieves SC through interactions between models specialized in different downstream tasks. Specifically, we introduce the dynamic hierarchical collaboration and dynamic selective collaboration modules to enable dynamic and effective interactions among models, allowing them to acquire knowledge from these interactions. Finally, we explore potential future applications of combining SL and SC, discuss open questions, and propose directions for future research, aiming to spark interest in this emerging and exciting interdisciplinary field. Our code will be publicly available at https://github.com/yxjdarren/SC.

Advancements in generative models have promoted text- and image-based multi-context image generation. Brain signals, offering a direct representation of user intent, present new opportunities for image customization. However, it faces challenges in brain interpretation, cross-modal context fusion and retention. In this paper, we present MindCustomer to explore the blending of visual brain signals in multi-context image generation. We first design shared neural data augmentation for stable cross-subject brain embedding by introducing the Image-Brain Translator (IBT) to generate brain responses from visual images. Then, we propose an effective cross-modal information fusion pipeline that mask-freely adapts distinct semantics from image and brain contexts within a diffusion model. It resolves semantic conflicts for context preservation and enables harmonious context integration. During the fusion pipeline, we further utilize the IBT to transfer image context to the brain representation to mitigate the cross-modal disparity. MindCustomer enables cross-subject generation, delivering unified, high-quality, and natural image outputs. Moreover, it exhibits strong generalization for new subjects via few-shot learning, indicating the potential for practical application. As the first work for multi-context blending with brain signal, MindCustomer lays a foundational exploration and inspiration for future brain-controlled generative technologies.