ICLR 2025 Papers

The quest for robust and generalizable machine learning models has driven recent interest in exploiting symmetries through equivariant neural networks. In the context of PDE solvers, recent works have shown that Lie point symmetries can be a useful inductive bias for Physics-Informed Neural Networks (PINNs) through data and loss augmentation. Despite this, directly enforcing equivariance within the model architecture for these problems remains elusive. This is because many PDEs admit non-compact symmetry groups, oftentimes not studied beyond their infinitesimal generators, making them incompatible with most existing equivariant architectures. In this work, we propose Lie aLgebrA Canonicalization (LieLAC), a novel approach that exploits only the action of infinitesimal generators of the symmetry group, circumventing the need for knowledge of the full group structure. To achieve this, we address existing theoretical issues in the canonicalization literature, establishing connections with frame averaging in the case of continuous non-compact groups. Operating within the framework of canonicalization, LieLAC can easily be integrated with unconstrained pre-trained models, transforming inputs to a canonical form before feeding them into the existing model, effectively aligning the input for model inference according to allowed symmetries. LieLAC utilizes standard Lie group descent schemes, achieving equivariance in pre-trained models. Finally, we showcase LieLAC's efficacy on tasks of invariant image classification and Lie point symmetry equivariant neural PDE solvers using pre-trained models.

A rich line of recent works studies how participants in matching markets learn their unknown preferences through iterative interactions with each other. The two sides of participants in the market can be respectively formulated as players and arms in the bandit problem. To ensure market stability, the objective is to minimize the stable regret of each player. Though existing works provide significant theoretical upper bounds for players' stable regret, the results heavily rely on the assumption that each participant has a strict preference ranking. However, in real applications, multiple candidates (e.g., workers in the labor market and students in school admission) usually demonstrate comparable performance levels, making it challenging for participants (e.g., employers and schools) to differentiate and rank their preferences. To deal with the potential indifferent preferences, we propose an adaptive exploration algorithm based on arm-guided Gale-Shapley (AE-AGS). We show that its stable regret is of order $O(NK \log T / \Delta^2)$, where $N$ is the number of players, $K$ the number of arms, $T$ the total time horizon, and $\Delta$ the minimum non-zero preference gap. Extensive experiments demonstrate the algorithm's effectiveness in handling such complex situations and its consistent superiority over baselines.

Choice of training data distribution greatly influences model behavior. Yet, in large-scale settings, precisely characterizing *how* changes in training data affects predictions is often difficult due to model training costs. Current practice is to instead extrapolate from scaled down, inexpensive-to-train proxy models. However, changes in data do not influence smaller and larger models identically. Therefore, understanding how choice of data affects large-scale models raises the question: how does training data distribution influence model behavior across compute scale? We find that small- and large-scale language model predictions (generally) *do* highly correlate across choice of training data. Equipped with these findings, we characterize how proxy scale affects effectiveness in two downstream proxy model applications: data attribution and dataset selection.

The annotation (assigning structural chemical identities) of MS/MS spectra remains a significant challenge due to the enormous molecular diversity in biological samples and the limited scope of reference databases. Currently, the vast majority of spectral measurements remain in the "dark chemical space" without structural annotations. To improve annotation, we propose MADGEN (Mass-spec Attends to De Novo Molecular GENeration), a scaffold-based method for de novo molecular structure generation guided by mass spectrometry data. MADGEN operates in two stages: scaffold retrieval and spectra-conditioned molecular generation starting with the scaffold. In the first stage, given an MS/MS spectrum, we formulate scaffold retrieval as a ranking problem and employ contrastive learning to align mass spectra with candidate molecular scaffolds. In the second stage, starting from the retrieved scaffold, we employ the MS/MS spectrum to guide an attention-based generative model to generate the final molecule. Our approach constrains the molecular generation search space, reducing its complexity and improving generation accuracy. We evaluate MADGEN on three datasets (NIST23, CANOPUS, and MassSpecGym) and evaluate MADGEN's performance with a predictive scaffold retriever and with an oracle retriever. We demonstrate the effectiveness of using attention to integrate spectral information throughout the generation process to achieve strong results with the oracle retriever.

Discrete diffusion models have gained increasing attention for their ability to model complex distributions with tractable sampling and inference. However, the error analysis for discrete diffusion models remains less well-understood. In this work, we propose a comprehensive framework for the error analysis of discrete diffusion models based on Lévy-type stochastic integrals. By generalizing the Poisson random measure to that with a time-independent and state-dependent intensity, we rigorously establish a stochastic integral formulation of discrete diffusion models and provide the corresponding change of measure theorems that are intriguingly analogous to Itô integrals and Girsanov's theorem for their continuous counterparts. Our framework unifies and strengthens the current theoretical results on discrete diffusion models and obtains the first error bound for the $\tau$-leaping scheme in KL divergence. With error sources clearly identified, our analysis gives new insight into the mathematical properties of discrete diffusion models and offers guidance for the design of efficient and accurate algorithms for real-world discrete diffusion model applications.

For vision-language models (VLMs), understanding the dynamic properties of objects and their interactions in 3D scenes from videos is crucial for effective reasoning about high-level temporal and action semantics. Although humans are adept at understanding these properties by constructing 3D and temporal (4D) representations of the world, current video understanding models struggle to extract these dynamic semantics, arguably because these models use cross-frame reasoning without underlying knowledge of the 3D/4D scenes. In this work, we introduce **DynSuperCLEVR**, the first video question answering dataset that focuses on language understanding of the dynamic properties of 3D objects. We concentrate on three physical concepts—*velocity*, *acceleration*, and *collisions*—within 4D scenes. We further generate three types of questions, including factual queries, future predictions, and counterfactual reasoning that involve different aspects of reasoning on these 4D dynamic properties. To further demonstrate the importance of explicit scene representations in answering these 4D dynamics questions, we propose **NS-4DPhysics**, a **N**eural-**S**ymbolic VideoQA model integrating **Physics** prior for **4D** dynamic properties with explicit scene representation of videos. Instead of answering the questions directly from the video text input, our method first estimates the 4D world states with a 3D generative model powered by a physical prior, and then uses neural symbolic reasoning to answer the questions based on the 4D world states. Our evaluation on all three types of questions in DynSuperCLEVR shows that previous video question answering models and large multimodal models struggle with questions about 4D dynamics, while our NS-4DPhysics significantly outperforms previous state-of-the-art models.

Accurate nutrition estimation helps people make informed dietary choices and is essential in the prevention of serious health complications. We present NutriBench, the first publicly available natural language meal description nutrition benchmark. NutriBench consists of 11,857 meal descriptions generated from real-world global dietary intake data. The data is human-verified and annotated with macro-nutrient labels, including carbohydrates, proteins, fats, and calories. We conduct an extensive evaluation of Nutribench on the task of carbohydrate estimation, testing twelve leading Large Language Models (LLMs), including GPT-4o, Llama3.1, Qwen2, Gemma2, and OpenBioLLM models, using standard, Chain-of-Thought and Retrieval-Augmented Generation strategies. Additionally, we present a study involving professional nutritionists, finding that LLMs can provide comparable but significantly faster estimates. Finally, we perform a real-world risk assessment by simulating the effect of carbohydrate predictions on the blood glucose levels of individuals with type 1 diabetes. Our work highlights the opportunities and challenges of using LLMs for nutrition estimation, demonstrating their potential to aid professionals and laypersons and improve health outcomes. Our benchmark is publicly available at: https://mehak126.github.io/nutribench.html

Foundation models are transforming machine learning across many modalities, with in-context learning replacing classical model training. Recent work on tabular data hints at a similar opportunity to build foundation models for classification for numerical data. However, existing meta-learning approaches can not compete with tree-based methods in terms of inference time. In this paper, we propose MotherNet, a hypernetwork architecture trained on synthetic classification tasks that, once prompted with a never-seen-before training set generates the weights of a trained ``child'' neural-network by in-context learning using a single forward pass. In contrast to most existing hypernetworks that are usually trained for relatively constrained multi-task settings, MotherNet can create models for multiclass classification on arbitrary tabular datasets without any dataset specific gradient descent. The child network generated by MotherNet outperforms neural networks trained using gradient descent on small datasets, and is competitive with predictions by TabPFN and standard ML methods like Gradient Boosting. Unlike a direct application of TabPFN, MotherNet generated networks are highly efficient at inference time.

Despite their wide application across various fields, current molecular property prediction models struggle with the challenge of activity cliff, which refers to the situation where molecules with similar chemical structures display remarkable different properties. This phenomenon hinders existing models' ability to learn distinctive representations for molecules with similar chemical structures, and results in inaccurate predictions on molecules with activity cliff. To address this limitation, we first present empirical evidence demonstrating the ineffectiveness of standard training pipelines on molecules with activity cliff. We propose a novel approach that reformulates molecular property prediction as a node classification problem, introducing two innovative tasks at both the node and edge levels to improve learning outcomes for these challenging molecules with activity cliff. Our method is versatile, allowing seamless integration with a variety of base models, whether pre-trained or randomly initialized. Extensive evaluation across different molecular property prediction datasets validate the effectiveness of our approach.

Efficient physics simulations are essential for numerous applications, ranging from realistic cloth animations in video games, to analyzing pollutant dispersion in environmental sciences, to calculating vehicle drag coefficients in engineering applications. Unfortunately, analytical solutions to the underlying physical equations are rarely available, and numerical solutions are computationally demanding. Latest developments in the field of physics-based Deep Learning have led to promising efficiency gains but still suffer from limited generalization capabilities across multiple different PDEs. Thus, in this work, we introduce **Metamizer**, a novel neural optimizer that iteratively solves a wide range of physical systems without retraining by minimizing a physics-based loss function. To this end, our approach leverages a scale-invariant architecture that enhances gradient descent updates to accelerate convergence. Since the neural network itself acts as an optimizer, training this neural optimizer falls into the category of meta-optimization approaches. We demonstrate that Metamizer achieves high accuracy across multiple PDEs after training on the Laplace, advection-diffusion and incompressible Navier-Stokes equation as well as on cloth simulations. Remarkably, the model also generalizes to PDEs that were not covered during training such as the Poisson, wave and Burgers equation.

Proteins are essential macromolecules defined by their amino acid sequences, which determine their three-dimensional structures and, consequently, their functions in all living organisms. Therefore, generative protein modeling necessitates a multimodal approach to simultaneously model, understand, and generate both sequences and structures. However, existing methods typically use separate models for each modality, limiting their ability to capture the intricate relationships between sequence and structure. This results in suboptimal performance in tasks that requires joint understanding and generation of both modalities. In this paper, we introduce DPLM-2, a multimodal protein foundation model that extends discrete diffusion protein language model (DPLM) to accommodate both sequences and structures. To enable structural learning with the language model, 3D coordinates are converted to discrete tokens using a lookup-free quantization-based tokenizer. By training on both experimental and high-quality synthetic structures, DPLM-2 learns the joint distribution of sequence and structure, as well as their marginals and conditionals. We also implement an efficient warm-up strategy to exploit the connection between large-scale evolutionary data and structural inductive biases from pre-trained sequence-based protein language models. Empirical evaluation shows that DPLM-2 can simultaneously generate highly compatible amino acid sequences and their corresponding 3D structures eliminating the need for a two-stage generation approach. Moreover, DPLM-2 demonstrates competitive performance in various conditional generation tasks, including folding, inverse folding, and scaffolding with multimodal motif inputs.

Landmark universal function approximation results for neural networks with trained weights and biases provided the impetus for the ubiquitous use of neural networks as learning models in neuroscience and Artificial Intelligence (AI). Recent work has extended these results to networks in which a smaller subset of weights (e.g., output weights) are tuned, leaving other parameters random. However, it remains an open question whether universal approximation holds when only biases are learned, despite evidence from neuroscience and AI that biases significantly shape neural responses. The current paper answers this question. We provide theoretical and numerical evidence demonstrating that feedforward neural networks with fixed random weights can approximate any continuous function on compact sets. We further show an analogous result for the approximation of dynamical systems with recurrent neural networks. Our findings are relevant to neuroscience, where they demonstrate the potential for behaviourally relevant changes in dynamics without modifying synaptic weights, as well as for AI, where they shed light on recent fine-tuning methods for large language models, like bias and prefix-based approaches.

Understanding complex three-dimensional (3D) structures of graphs is essential for accurately modeling various properties, yet many existing approaches struggle with fully capturing the intricate spatial relationships and symmetries inherent in such systems, especially in large-scale, dynamic molecular datasets. These methods often must balance trade-offs between expressiveness and computational efficiency, limiting their scalability. To address this gap, we propose a novel Geometric Tensor Network (GotenNet) that effectively models the geometric intricacies of 3D graphs while ensuring strict equivariance under the Euclidean group E(3). Our approach directly tackles the expressiveness-efficiency trade-off by leveraging effective geometric tensor representations without relying on irreducible representations or Clebsch-Gordan transforms, thereby reducing computational overhead. We introduce a unified structural embedding, incorporating geometry-aware tensor attention and hierarchical tensor refinement that iteratively updates edge representations through inner product operations on high-degree steerable features, allowing for flexible and efficient representations for various tasks. We evaluated models on QM9, rMD17, MD22, and Molecule3D datasets, where the proposed model consistently outperforms state-of-the-art methods in both scalar and high-degree property predictions, demonstrating exceptional robustness across diverse datasets, and establishes GotenNet as a versatile and scalable framework for 3D equivariant Graph Neural Networks.

Deep learning methods incorporate PDE residuals as the loss function for solving Fokker-Planck equations, and usually impose the proper normalization condition to avoid a trivial solution. However, soft constraints require careful balancing of multi-objective loss functions, and specific network architectures may limit representation capacity under hard constraints. In this paper, we propose a novel framework: Fokker-Planck neural network (FPNN) that adopts a score PDE loss to decouple the score learning and the density normalization into two stages. Our method allows free-form network architectures to model the unnormalized density and strictly satisfy normalization constraints by post-processing. We demonstrate the effectiveness on various high-dimensional steady-state Fokker-Planck (SFP) equations, achieving superior accuracy and over a 20$\times$ speedup compared to state-of-the-art methods. Without any labeled data, FPNNs achieve the mean absolute percentage error (MAPE) of 11.36%, 13.87% and 12.72% for 4D Ring, 6D Unimodal and 6D Multi-modal problems respectively, requiring only 256, 980, and 980 parameters. Experimental results highlights the potential as a universal fast solver for handling more than 20-dimensional SFP equations, with great gains in efficiency, accuracy, memory and computational resource usage.

High-content perturbation experiments allow scientists to probe biomolecular systems at unprecedented resolution, but experimental and analysis costs pose significant barriers to widespread adoption. Machine learning has the potential to guide efficient exploration of the perturbation space and extract novel insights from these data. However, current approaches neglect the semantic richness of the relevant biology, and their objectives are misaligned with downstream biological analyses. In this paper, we hypothesize that large language models (LLMs) present a natural medium for representing complex biological relationships and rationalizing experimental outcomes. We propose PerturbQA, a benchmark for structured reasoning over perturbation experiments. Unlike current benchmarks that primarily interrogate existing knowledge, PerturbQA is inspired by open problems in perturbation modeling: prediction of differential expression and change of direction for unseen perturbations, and gene set enrichment. We evaluate state-of-the-art machine learning and statistical approaches for modeling perturbations, as well as standard LLM reasoning strategies, and we find that current methods perform poorly on PerturbQA. As a proof of feasibility, we introduce Summer (SUMMarize, retrievE, and answeR, a simple, domain-informed LLM framework that matches or exceeds the current state-of-the-art. Our code and data are publicly available at https://github.com/genentech/PerturbQA.

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable solutions, their accuracy is often tied to the use of computationally intensive fine meshes. Moreover, they do not naturally account for measurements or prior solutions, and any change in the problem parameters requires results to be fully recomputed. Neural network-based approaches, such as physics-informed neural networks and neural operators, offer a mesh-free alternative by directly fitting those models to the PDE solution. They can also integrate prior knowledge and tackle entire families of PDEs by simply aggregating additional training losses. Nevertheless, they are highly sensitive to hyperparameters such as collocation points and the weights associated with each loss. This paper addresses these challenges by developing a science-constrained learning (SCL) framework. It demonstrates that finding a (weak) solution of a PDE is equivalent to solving a constrained learning problem with worst-case losses. This explains the limitations of previous methods that minimize the expected value of aggregated losses. SCL also organically integrates structural constraints (e.g., invariances) and (partial) measurements or known solutions. The resulting constrained learning problems can be tackled using a practical algorithm that yields accurate solutions across a variety of PDEs, neural network architectures, and prior knowledge levels without extensive hyperparameter tuning and sometimes even at a lower computational cost.

Recent advances in machine learning for molecules exhibit great potential for facilitating drug discovery from in silico predictions. Most models for molecule generation rely on the decomposition of molecules into frequently occurring substructures (motifs), from which they generate novel compounds. While motif representations greatly aid in learning molecular distributions, such methods fail to represent substructures beyond their known motif set, posing a fundamental limitation for discovering novel compounds. To address this limitation and enhance structural expressivity, we propose to separate structure from features by abstracting motifs to scaffolds and, subsequently, allocating atom and bond types. To this end, we introduce a novel factorisation of the molecules' data distribution that considers the entire molecular context and facilitates learning adequate assignments of atoms and bonds to scaffolds. Complementary to this, we propose MAGNet, the first model to freely learn motifs. Importantly, we demonstrate that MAGNet's improved expressivity leads to molecules with more structural diversity and, at the same time, diverse atom and bond assignments.

We present a new family of mobile hybrid vision networks, called iFormer, with a focus on optimizing latency and accuracy on mobile applications. iFormer effectively integrates the fast local representation capacity of convolution with the efficient global modeling ability of self-attention. The local interactions are derived from transforming a standard convolutional network, \textit{i.e.}, ConvNeXt, to design a more lightweight mobile network. Our newly introduced mobile modulation attention removes memory-intensive operations in MHA and employs an efficient modulation mechanism to boost dynamic global representational capacity. We conduct comprehensive experiments demonstrating that iFormer outperforms existing lightweight networks across various tasks. Notably, iFormer achieves an impressive Top-1 accuracy of 80.4% on ImageNet-1k with a latency of only 1.10 ms on an iPhone 13, surpassing the recently proposed MobileNetV4 under similar latency constraints. Additionally, our method shows significant improvements in downstream tasks, including COCO object detection, instance segmentation, and ADE20k semantic segmentation, while still maintaining low latency on mobile devices for high-resolution inputs in these scenarios. Code and models are available at: https://github.com/ChuanyangZheng/iFormer.

A grand challenge in biology is to discover evolutionary traits---features of organisms common to a group of species with a shared ancestor in the tree of life (also referred to as phylogenetic tree). With the growing availability of image repositories in biology, there is a tremendous opportunity to discover evolutionary traits directly from images in the form of a hierarchy of prototypes. However, current prototype-based methods are mostly designed to operate over a flat structure of classes and face several challenges in discovering hierarchical prototypes, including the issue of learning over-specific prototypes at internal nodes. To overcome these challenges, we introduce the framework of Hierarchy aligned Commonality through Prototypical Networks (HComP-Net). The key novelties in HComP-Net include a novel over-specificity loss to avoid learning over-specific prototypes, a novel discriminative loss to ensure prototypes at an internal node are absent in the contrasting set of species with different ancestry, and a novel masking module to allow for the exclusion of over-specific prototypes at higher levels of the tree without hampering classification performance. We empirically show that HComP-Net learns prototypes that are accurate, semantically consistent, and generalizable to unseen species in comparison to baselines. Our code is publicly accessible at Imageomics Institute Github site: https://github.com/Imageomics/HComPNet.