ICLR 2025 Papers

In this work, we introduce the first unsupervised method that simultaneously predicts time-varying neural implicit surfaces and deformations between pairs of point clouds. We propose to model the point movement using an explicit velocity field and directly deform a time-varying implicit field using the modified level-set equation. This equation utilizes an iso-surface evolution with Eikonal constraints in a compact formulation, ensuring the integrity of the signed distance field. By applying a smooth, volume-preserving constraint to the velocity field, our method successfully recovers physically plausible intermediate shapes. Our method is able to handle both rigid and non-rigid deformations without any intermediate shape supervision. Our experimental results demonstrate that our method significantly outperforms existing works, delivering superior results in both quality and efficiency.

The Gromov-Wasserstein (GW) distance has gained increasing interest in the machine learning community in recent years, as it allows for the comparison of measures in different metric spaces. To overcome the limitations imposed by the equal mass requirements of the classical GW problem, researchers have begun exploring its application in unbalanced settings. However, Unbalanced GW (UGW) can only be regarded as a discrepancy rather than a rigorous metric/distance between two metric measure spaces (mm-spaces). In this paper, we propose a particular case of the UGW problem, termed Partial Gromov-Wasserstein (PGW). We establish that PGW is a well-defined metric between mm-spaces and discuss its theoretical properties, including the existence of a minimizer for the PGW problem and the relationship between PGW and GW, among others. We then propose two variants of the Frank-Wolfe algorithm for solving the PGW problem and show that they are mathematically and computationally equivalent. Moreover, based on our PGW metric, we introduce the analogous concept of barycenters for mm-spaces. Finally, we validate the effectiveness of our PGW metric and related solvers in applications such as shape matching, shape retrieval, and shape interpolation, comparing them against existing baselines. Our code is available at https://github.com/mint-vu/PGW_Metric.

Artificial Intelligence (AI) has demonstrated significant potential in healthcare, particularly in disease diagnosis and treatment planning. Recent progress in Medical Large Vision-Language Models (Med-LVLMs) has opened up new possibilities for interactive diagnostic tools. However, these models often suffer from factual hallucination, which can lead to incorrect diagnoses. Fine-tuning and retrieval-augmented generation (RAG) have emerged as methods to address these issues. However, the amount of high-quality data and distribution shifts between training data and deployment data limit the application of fine-tuning methods. Although RAG is lightweight and effective, existing RAG-based approaches are not sufficiently general to different medical domains and can potentially cause misalignment issues, both between modalities and between the model and the ground truth. In this paper, we propose a versatile multimodal RAG system, MMed-RAG, designed to enhance the factuality of Med-LVLMs. Our approach introduces a domain-aware retrieval mechanism, an adaptive retrieved contexts selection, and a provable RAG-based preference fine-tuning strategy. These innovations make the RAG process sufficiently general and reliable, significantly improving alignment when introducing retrieved contexts. Experimental results across five medical datasets (involving radiology, ophthalmology, pathology) on medical VQA and report generation demonstrate that MMed-RAG can achieve an average improvement of 43.8% in factual accuracy in the factual accuracy of Med-LVLMs.

Extensive experimental studies have shown that in lower mammals, neuronal orientation preference in the primary visual cortex is organized in disordered "salt-and-pepper" organizations. In contrast, higher-order mammals display a continuous variation in orientation preference, forming pinwheel-like structures. Despite these observations, the spiking mechanisms underlying the emergence of these distinct topological structures and their functional roles in visual processing remain poorly understood. To address this, we developed a self-evolving spiking neural network model with Hebbian plasticity, trained using physiological parameters characteristic of rodents, cats, and primates, including retinotopy, neuronal morphology, and connectivity patterns. Our results identify critical factors, such as the degree of input visual field overlap, neuronal connection range, and the balance between localized connectivity and long-range competition, that determine the emergence of either salt-and-pepper or pinwheel-like topologies. Furthermore, we demonstrate that pinwheel structures exhibit lower wiring costs and enhanced sparse coding capabilities compared to salt-and-pepper organizations. They also maintain greater coding robustness against noise in naturalistic visual stimuli. These findings suggest that such topological structures confer significant computational advantages in visual processing and highlight their potential application in the design of brain-inspired deep learning networks and algorithms.

Weighted low rank approximation is a fundamental problem in numerical linear algebra, and it has many applications in machine learning. Given a matrix $M \in \mathbb{R}^{n \times n}$, a non-negative weight matrix $W \in \mathbb{R}_{\geq 0}^{n \times n}$, a parameter $k$, the goal is to output two matrices $X,Y\in \mathbb{R}^{n \times k}$ such that $\\| W \circ (M - X Y^\top) \\|_F$ is minimized, where $\circ$ denotes the Hadamard product. It naturally generalizes the well-studied low rank matrix completion problem. Such a problem is known to be NP-hard and even hard to approximate assuming the Exponential Time Hypothesis. Meanwhile, alternating minimization is a good heuristic solution for weighted low rank approximation. In particular, [Li, Liang and Risteski, ICML'16] shows that, under mild assumptions, alternating minimization does provide provable guarantees. In this work, we develop an efficient and robust framework for alternating minimization that allows the alternating updates to be computed approximately. For weighted low rank approximation, this improves the runtime of [Li, Liang and Risteski, ICML'16] from $\\|W\\|_0k^2$ to $\\|W\\|_0 k$ where $\\|W\\|_0$ denotes the number of nonzero entries of the weight matrix. At the heart of our framework is a high-accuracy multiple response regression solver together with a robust analysis of alternating minimization.

Observation-based trajectory prediction for systems with unknown dynamics is essential in fields such as physics and biology. Most existing approaches are limited to learning within a single system with fixed dynamics patterns. However, many real-world applications require learning across systems with evolving dynamics patterns, a challenge that has been largely overlooked. To address this, we systematically investigate the problem of Continual Dynamics Learning (CDL), examining task configurations and evaluating the applicability of existing techniques, while identifying key challenges. In response, we propose the Mode-switching Graph ODE (MS-GODE) model, which integrates the strengths LG-ODE and sub-network learning with a mode-switching module, enabling efficient learning over varying dynamics. Moreover, we construct a novel benchmark of biological dynamic systems for CDL, Bio-CDL, featuring diverse systems with disparate dynamics and significantly enriching the research field of machine learning for dynamic systems. Our code available at \url{https://github.com/QueuQ/MS-GODE}.

Artificial neural networks often struggle with _catastrophic forgetting_ when learning multiple tasks sequentially, as training on new tasks degrades the performance on previously learned tasks. Recent theoretical work has addressed this issue by analysing learning curves in synthetic frameworks under predefined training protocols. However, these protocols relied on heuristics and lacked a solid theoretical foundation assessing their optimality. In this paper, we fill this gap by combining exact equations for training dynamics, derived using statistical physics techniques, with optimal control methods. We apply this approach to teacher-student models for continual learning and multi-task problems, obtaining a theory for task-selection protocols maximising performance while minimising forgetting. Our theoretical analysis offers non-trivial yet interpretable strategies for mitigating catastrophic forgetting, shedding light on how optimal learning protocols modulate established effects, such as the influence of task similarity on forgetting. Finally, we validate our theoretical findings with experiments on real-world data.

Large language models (LLMs) have been increasingly employed for (interactive) decision-making, via the development of LLM-based autonomous agents. Despite their emerging successes, the performance of LLM agents in decision-making has not been fully investigated through quantitative metrics, especially in the multi-agent setting when they interact with each other, a typical scenario in real-world LLM-agent applications. To better understand the limits of LLM agents in these interactive environments, we propose to study their interactions in benchmark decision-making settings in online learning and game theory, through the performance metric of regret. We first empirically study the no-regret behaviors of LLMs in canonical non-stochastic online learning problems, as well as the emergence of equilibria when LLM agents interact through playing repeated games. We then provide some theoretical insights into the no-regret behaviors of LLM agents, under certain assumptions on the supervised pre-training and the rationality model of human decision-makers who generate the data. Notably, we also identify (simple) cases where advanced LLMs such as GPT-4 fail to be no-regret. To further promote the no-regret behaviors, we propose a novel unsupervised training loss of regret-loss, which, in contrast to the supervised pre-training loss, does not require the labels of (optimal) actions. Finally, we establish the statistical guarantee of generalization bound for regret-loss minimization, and more importantly, the optimization guarantee that minimizing such a loss may automatically lead to known no-regret learning algorithms, when single-layer self-attention models are used. Our further experiments demonstrate the effectiveness of our regret-loss, especially in addressing the above “regrettable” cases.

Recently, data-driven simulators based on graph neural networks have gained attention in modeling physical systems on unstructured meshes. However, they struggle with long-range dependencies in fluid flows, particularly in refined mesh regions. This challenge, known as the 'over-squashing' problem, hinders information propagation. While existing graph rewiring methods address this issue to some extent, they only consider graph topology, overlooking the underlying physical phenomena. We propose Physics-Informed Ollivier--Ricci Flow (PIORF), a novel rewiring method that combines physical correlations with graph topology. PIORF uses Ollivier--Ricci curvature (ORC) to identify bottleneck regions and connects these areas with nodes in high-velocity gradient nodes, enabling long-range interactions and mitigating over-squashing. Our approach is computationally efficient in rewiring edges and can scale to larger simulations. Experimental results on 3 fluid dynamics benchmark datasets show that PIORF consistently outperforms baseline models and existing rewiring methods, achieving up to 26.2\% improvement.

Quantifying model generalization to out-of-distribution data has been a longstanding challenge in machine learning. Addressing this issue is crucial for leveraging machine learning in scientific discovery, where models must generalize to new molecules or materials. Current methods typically split data into train and test sets using various criteria — temporal, sequence identity, scaffold, or random cross-validation — before evaluating model performance. However, with so many splitting criteria available, existing approaches offer limited guidance on selecting the most appropriate one, and they do not provide mechanisms for incorporating prior knowledge about the target deployment distribution(s). To tackle this problem, we have developed a novel metric, AU-GOOD, which quantifies expected model performance under conditions of increasing dissimilarity between train and test sets, while also accounting for prior knowledge about the target deployment distribution(s), when available. This metric is broadly applicable to biochemical entities, including proteins, small molecules, nucleic acids, or cells; as long as a relevant similarity function is defined for them. Recognizing the wide range of similarity functions used in biochemistry, we propose criteria to guide the selection of the most appropriate metric for partitioning. We also introduce a new partitioning algorithm that generates more challenging test sets, and we propose statistical methods for comparing models based on AU-GOOD. Finally, we demonstrate the insights that can be gained from this framework by applying it to two different use cases: developing predictors for pharmaceutical properties of small molecules, and using protein language models as embeddings to build biophysical property predictors.

Learning to sample from complex unnormalized distributions over discrete domains emerged as a promising research direction with applications in statistical physics, variational inference, and combinatorial optimization. Recent work has demonstrated the potential of diffusion models in this domain. However, existing methods face limitations in memory scaling and thus the number of attainable diffusion steps since they require backpropagation through the entire generative process. To overcome these limitations we introduce two novel training methods for discrete diffusion samplers, one grounded in the policy gradient theorem and the other one leveraging Self-Normalized Neural Importance Sampling (SN-NIS). These methods yield memory-efficient training and achieve state-of-the-art results in unsupervised combinatorial optimization. Numerous scientific applications additionally require the ability of unbiased sampling. We introduce adaptations of SN-NIS and Neural Markov Chain Monte Carlo that enable for the first time the application of discrete diffusion models to this problem. We validate our methods on Ising model benchmarks and find that they outperform popular autoregressive approaches. Our work opens new avenues for applying diffusion models to a wide range of scientific applications in discrete domains that were hitherto restricted to exact likelihood models.

Large vision and language assistants have enabled new capabilities for interpreting natural images. These approaches have recently been adapted to earth observation data, but they are only able to handle single image inputs, limiting their use for many real-world tasks. In this work, we develop a new vision and language assistant called TEOChat that can engage in conversations about temporal sequences of earth observation data. To train TEOChat, we curate an instruction-following dataset composed of many single image and temporal tasks including building change and damage assessment, semantic change detection, and temporal scene classification. We show that TEOChat can perform a wide variety of spatial and temporal reasoning tasks, substantially outperforming previous vision and language assistants, and even achieving comparable or better performance than several specialist models trained to perform specific tasks. Furthermore, TEOChat achieves impressive zero-shot performance on a change detection and change question answering dataset, outperforms GPT-4o and Gemini 1.5 Pro on multiple temporal tasks, and exhibits stronger single image capabilities than a comparable single image instruction-following model on scene classification, visual question answering, and captioning. We publicly release our data, models, and code at https://github.com/ermongroup/TEOChat .

Accurate prediction of thermodynamic properties is essential in drug discovery and materials science. Molecular dynamics (MD) simulations provide a principled approach to this task, yet they typically rely on prohibitively long sequential simulations. Implicit Transfer Operator (ITO) Learning offers a promising approach to address this limitation by enabling stable simulation with time steps orders of magnitude larger than MD. However, to train ITOs, we need extensive, unbiased MD data, limiting the scope of this framework. Here, we introduce Boltzmann Priors for ITO (BoPITO) to enhance ITO learning in two ways. First, BoPITO enables more efficient data generation, and second, it embeds inductive biases for long-term dynamical behavior, simultaneously improving sample efficiency by one order of magnitude and guaranteeing asymptotically unbiased equilibrium statistics. Furthermore, we showcase the use of BoPITO in a new tunable sampling protocol interpolating between ITOs trained on off-equilibrium simulations and an equilibrium model by incorporating unbiased correlation functions. Code is available at https://github.com/olsson-group/bopito.

Graph unlearning has emerged as a pivotal research area for ensuring privacy protection, given the widespread adoption of Graph Neural Networks (GNNs) in applications involving sensitive user data. Among existing studies, certified graph unlearning is distinguished by providing robust privacy guarantees. However, current certified graph unlearning methods are impractical for large-scale graphs because they necessitate the costly re-computation of graph propagation for each unlearning request. Although numerous scalable techniques have been developed to accelerate graph propagation for GNNs, their integration into certified graph unlearning remains uncertain as these scalable approaches introduce approximation errors into node embeddings. In contrast, certified graph unlearning demands bounded model error on exact node embeddings to maintain its certified guarantee. To address this challenge, we present ScaleGUN, the first approach to scale certified graph unlearning to billion-edge graphs. ScaleGUN integrates the approximate graph propagation technique into certified graph unlearning, offering certified guarantees for three unlearning scenarios: node feature, edge and node unlearning. Extensive experiments on real-world datasets demonstrate the efficiency and unlearning efficacy of ScaleGUN. Remarkably, ScaleGUN accomplishes $(\epsilon,\delta)=(1,10^{-4})$ certified unlearning on the billion-edge graph ogbn-papers100M in 20 seconds for a 5,000 random edge removal request -- of which only 5 seconds are required for updating the node embeddings -- compared to 1.91 hours for retraining and 1.89 hours for re-propagation. Our code is available at https://github.com/luyi256/ScaleGUN.

Generative models in drug discovery have recently gained attention as efficient alternatives to brute-force virtual screening. However, most existing models do not account for synthesizability, limiting their practical use in real-world scenarios. In this paper, we propose RxnFlow, which sequentially assembles molecules using predefined molecular building blocks and chemical reaction templates to constrain the synthetic chemical pathway. We then train on this sequential generating process with the objective of generative flow networks (GFlowNets) to generate both highly rewarded and diverse molecules. To mitigate the large action space of synthetic pathways in GFlowNets, we implement a novel action space subsampling method. This enables RxnFlow to learn generative flows over extensive action spaces comprising combinations of 1.2 million building blocks and 71 reaction templates without significant computational overhead. Additionally, RxnFlow can employ modified or expanded action spaces for generation without retraining, allowing for the introduction of additional objectives or the incorporation of newly discovered building blocks. We experimentally demonstrate that RxnFlow outperforms existing reaction-based and fragment-based models in pocket-specific optimization across various target pockets. Furthermore, RxnFlow achieves state-of-the-art performance on CrossDocked2020 for pocket-conditional generation, with an average Vina score of –8.85 kcal/mol and 34.8% synthesizability. Code is available at https://github.com/SeonghwanSeo/RxnFlow.

3D molecule generation is crucial for drug discovery and material design. While prior efforts focus on 3D diffusion models for their benefits in modeling continuous 3D conformers, they overlook the advantages of 1D SELFIES-based Language Models (LMs), which can generate 100\% valid molecules and leverage the billion-scale 1D molecule datasets. To combine these advantages for 3D molecule generation, we propose a foundation model -- NExT-Mol: 3D Diffusion Meets 1D Language Modeling for 3D Molecule Generation. NExT-Mol uses an extensively pretrained molecule LM for 1D molecule generation, and subsequently predicts the generated molecule's 3D conformers with a 3D diffusion model. We enhance NExT-Mol's performance by scaling up the LM's model size, refining the diffusion neural architecture, and applying 1D to 3D transfer learning. Notably, our 1D molecule LM significantly outperforms baselines in distributional similarity while ensuring validity, and our 3D diffusion model achieves leading performances in conformer prediction. Given these improvements in 1D and 3D modeling, NExT-Mol achieves a 26\% relative improvement in 3D FCD for de novo 3D generation on GEOM-DRUGS, and a 13\% average relative gain for conditional 3D generation on QM9-2014. Our codes and pretrained checkpoints are available at https://github.com/acharkq/NExT-Mol.

Does learning of task-relevant representations stop when behavior stops changing? Motivated by recent work in machine learning and the intuitive observation that human experts continue to learn after mastery, we hypothesize that task-specific representation learning in cortex can continue, even when behavior saturates. In a novel reanalysis of recently published neural data, we find evidence for such learning in posterior piriform cortex of mice following continued training on a task, long after behavior saturates at near-ceiling performance ("overtraining"). We demonstrate that class representations in cortex continue to separate during overtraining, so that examples that were incorrectly classified at the beginning of overtraining can abruptly be correctly classified later on, despite no changes in behavior during that time. We hypothesize this hidden learning takes the form of approximate margin maximization; we validate this and other predictions in the neural data, as well as build and interpret a simple synthetic model that recapitulates these phenomena. We conclude by demonstrating how this model of late-time feature learning implies an explanation for the empirical puzzle of overtraining reversal in animal learning, where task-specific representations are more robust to particular task changes because the learned features can be reused.

Language models can store vast factual knowledge, yet their ability to flexibly use this knowledge for downstream tasks (e.g., via instruction finetuning) remains questionable. This paper investigates four fundamental knowledge manipulation tasks: \textbf{retrieval} (e.g., "What is person A's attribute X?"), \textbf{classification} (e.g., "Is A's attribute X even or odd?"), \textbf{comparison} (e.g., "Is A greater than B in attribute X?"), and \textbf{inverse search} (e.g., "Which person's attribute X equals T?"). We show that language models excel in knowledge retrieval but struggle even in the simplest classification or comparison tasks unless Chain of Thoughts (CoTs) are employed during both training and inference. Moreover, their performance in inverse knowledge search is virtually 0\%, regardless of the prompts. Our primary contribution is a \emph{controlled, synthetic experiment} that confirms these weaknesses are \emph{inherent} to language models: they cannot efficiently manipulate knowledge from pre-training data, even when such knowledge is perfectly stored in the models, despite adequate training and sufficient model size. Our findings also apply to modern pretrained language models such as GPT-4, thus giving rise to many Turing tests to distinguish Humans from contemporary AIs.

Data-driven techniques have emerged as a promising alternative to traditional numerical methods for solving PDEs. For time-dependent PDEs, many approaches are Markovian---the evolution of the trained system only depends on the current state, and not the past states. In this work, we investigate the benefits of using memory for modeling time-dependent PDEs: that is, when past states are explicitly used to predict the future. Motivated by the Mori-Zwanzig theory of model reduction, we theoretically exhibit examples of simple (even linear) PDEs, in which a solution that uses memory is arbitrarily better than a Markovian solution. Additionally, we introduce Memory Neural Operator (MemNO), a neural operator architecture that combines recent state space models (specifically, S4) and Fourier Neural Operators (FNOs) to effectively model memory. We empirically demonstrate that when the PDEs are supplied in low resolution or contain observation noise at train and test time, MemNO significantly outperforms the baselines without memory---with up to $6 \times$ reduction in test error. Furthermore, we show that this benefit is particularly pronounced when the PDE solutions have significant high-frequency Fourier modes (e.g., low-viscosity fluid dynamics) and we construct a challenging benchmark dataset consisting of such PDEs.