ICLR 2025 Papers

Message passing-based graph neural networks (GNNs) have achieved great success in many real-world applications. For a sampled mini-batch of target nodes, the message passing process is divided into two parts: message passing between nodes within the batch (MP-IB) and message passing from nodes outside the batch to those within it (MP-OB). However, MP-OB recursively relies on higher-order out-of-batch neighbors, leading to an exponentially growing computational cost with respect to the number of layers. Due to the neighbor explosion, the whole message passing stores most nodes and edges on the GPU such that many GNNs are infeasible to large-scale graphs. To address this challenge, we propose an accurate and fast mini-batch approach for large graph transductive learning, namely topological compensation (TOP), which obtains the outputs of the whole message passing solely through MP-IB, without the costly MP-OB. The major pillar of TOP is a novel concept of message invariance, which defines message-invariant transformations to convert costly MP-OB into fast MP-IB. This ensures that the modified MP-IB has the same output as the whole message passing. Experiments demonstrate that TOP is significantly faster than existing mini-batch methods by order of magnitude on vast graphs (millions of nodes and billions of edges) with limited accuracy degradation.

When learning an input-output mapping from very few examples, is it better to first infer a latent function that explains the examples, or is it better to directly predict new test outputs, e.g. using a neural network? We study this question on ARC by training neural models for \emph{induction} (inferring latent functions) and \emph{transduction} (directly predicting the test output for a given test input). We train on synthetically generated variations of Python programs that solve ARC training tasks. We find inductive and transductive models solve different kinds of test problems, despite having the same training problems and sharing the same neural architecture: Inductive program synthesis excels at precise computations, and at composing multiple concepts, while transduction succeeds on fuzzier perceptual concepts. Ensembling them approaches human-level performance on ARC.

In this work, we introduce a planning neural operator (PNO) for predicting the value function of a motion planning problem. We recast value function approximation as learning a single operator from the cost function space to the value function space, which is defined by an Eikonal partial differential equation (PDE). Therefore, our PNO model, despite being trained with a finite number of samples at coarse resolution, inherits the zero-shot super-resolution property of neural operators. We demonstrate accurate value function approximation at 16× the training resolution on the MovingAI lab’s 2D city dataset, compare with state-of-the-art neural value function predictors on 3D scenes from the iGibson building dataset and showcase optimal planning with 4-joint robotic manipulators. Lastly, we investigate employing the value function output of PNO as a heuristic function to accelerate motion planning. We show theoretically that the PNO heuristic is $\epsilon$-consistent by introducing an inductive bias layer that guarantees our value functions satisfy the triangle inequality. With our heuristic, we achieve a $30$% decrease in nodes visited while obtaining near optimal path lengths on the MovingAI lab 2D city dataset, compared to classical planning methods (A$^\ast$, RRT$^\ast$).

Physical properties derived from electronic distributions are essential information that determines molecular properties. However, the electron-level information is not accessible in most real-world complex molecules due to the extensive computational costs of determining uncertain electronic distributions. For this reason, existing methods for molecular property prediction have remained in regression models on simplified atom-level molecular descriptors, such as atomic structures and fingerprints. This paper proposes an efficient knowledge transfer method for electron-aware molecular representation learning. To this end, we devised a self-supervised diffusion method that estimates the electron-level information of real-world complex molecules without expensive quantum mechanical calculations. The proposed method achieved state-of-the-art prediction accuracy in the tasks of predicting molecular properties on extensive real-world molecular datasets.

Supervised fine-tuning (SFT) and alignment of large language models (LLMs) are key steps in providing a good user experience. However, the concept of an appropriate alignment is inherently application-dependent, and current methods often rely on heuristic choices to drive optimization. In this work, we formulate SFT and alignment as a constrained optimization problem: the LLM is fine-tuned on a task while being required to meet application-specific requirements, without resorting to heuristics. To solve this, we propose Lagrange Large Language Models (L3Ms), which employ logarithmic barriers to enforce the constraints. This approach allows for the customization of L3Ms across diverse applications while avoiding heuristic-driven processes. We experimentally demonstrate the versatility and efficacy of L3Ms in achieving tailored alignments for various applications.

Plug-and-play diffusion priors (PnPDP) have emerged as a promising research direction for solving inverse problems. However, current studies primarily focus on natural image restoration, leaving the performance of these algorithms in scientific inverse problems largely unexplored. To address this gap, we introduce \textsc{InverseBench}, a framework that evaluates diffusion models across five distinct scientific inverse problems. These problems present unique structural challenges that differ from existing benchmarks, arising from critical scientific applications such as optical tomography, medical imaging, black hole imaging, seismology, and fluid dynamics. With \textsc{InverseBench}, we benchmark 14 inverse problem algorithms that use plug-and-play diffusion priors against strong, domain-specific baselines, offering valuable new insights into the strengths and weaknesses of existing algorithms. To facilitate further research and development, we open-source the codebase, along with datasets and pre-trained models, at [https://devzhk.github.io/InverseBench/](https://devzhk.github.io/InverseBench/).

Models of Virtual Cells and Virtual Tissues at single-cell resolution would allow us to test perturbations in silico and accelerate progress in tissue and cell engineering. However, most such models are not rooted in causal inference and as a result, could mistake correlation for causation. We introduce Celcomen, a novel generative graph neural network grounded in mathematical causality to disentangle intra- and inter-cellular gene regulation in spatial transcriptomics and single-cell data. Celcomen can also be prompted by perturbations to generate spatial counterfactuals, thus offering insights into experimentally inaccessible states, with potential applications in human health. We validate the model's disentanglement and identifiability through simulations, and demonstrate its counterfactual predictions in clinically relevant settings, including human glioblastoma and fetal spleen, recovering inflammation-related gene programs post immune system perturbation. Moreover, it supports mechanistic interpretability, as its parameters can be reverse-engineered from observed behavior, making it an accessible model for understanding both neural networks and complex biological systems.

Time-series forecasting is a challenging problem that traditionally requires specialized models custom-trained for the specific task at hand. Recently, inspired by the success of large language models, foundation models pre-trained on vast amounts of time-series data from diverse domains have emerged as a promising candidate for general-purpose time-series forecasting. The defining characteristic of these foundation models is their ability to perform zero-shot learning, that is, forecasting a new system from limited context data without explicit re-training or fine-tuning. Here, we evaluate whether the zero-shot learning paradigm extends to the challenging task of forecasting chaotic systems. Across 135 distinct chaotic dynamical systems and $10^8$ timepoints, we find that foundation models produce competitive forecasts compared to custom-trained models (including NBEATS, TiDE, etc.), particularly when training data is limited. Interestingly, even after point forecasts fail, large foundation models are able to preserve the geometric and statistical properties of the chaotic attractors. We attribute this success to foundation models' ability to perform in-context learning and identify context parroting as a simple mechanism used by these models to capture the long-term behavior of chaotic dynamical systems. Our results highlight the potential of foundation models as a tool for probing nonlinear and complex systems.

Designing mechanically efficient geometry for architectural structures like shells, towers, and bridges, is an expensive iterative process. Existing techniques for solving such inverse problems rely on traditional optimization methods, which are slow and computationally expensive, limiting iteration speed and design exploration. Neural networks would seem to offer a solution via data-driven amortized optimization, but they often require extensive fine-tuning and cannot ensure that important design criteria, such as mechanical integrity, are met. In this work, we combine neural networks with a differentiable mechanics simulator to develop a model that accelerates the solution of shape approximation problems for architectural structures represented as bar systems. This model explicitly guarantees compliance with mechanical constraints while generating designs that closely match target geometries. We validate our approach in two tasks, the design of masonry shells and cable-net towers. Our model achieves better accuracy and generalization than fully neural alternatives, and comparable accuracy to direct optimization but in real time, enabling fast and reliable design exploration. We further demonstrate its advantages by integrating it into 3D modeling software and fabricating a physical prototype. Our work opens up new opportunities for accelerated mechanical design enhanced by neural networks for the built environment.

The observed similarities in the behavior of humans and Large Language Models (LLMs) have prompted researchers to consider the potential of using LLMs as models of human cognition. However, several significant challenges must be addressed before LLMs can be legitimately regarded as cognitive models. For instance, LLMs are trained on far more data than humans typically encounter, and may have been directly trained on human data in specific cognitive tasks or aligned with human preferences. Consequently, the origins of these behavioral similarities are not well understood. In this paper, we propose a novel way to enhance the utility of language models as cognitive models. This approach involves (i) leveraging computationally equivalent tasks that both a language model and a rational agent need to master for solving a cognitive problem and (ii) examining the specific task distributions required for a language model to exhibit human-like behaviors. We apply this approach to decision-making -- specifically risky and intertemporal choice -- where the key computationally equivalent task is the arithmetic of expected value calculations. We show that a small language model pretrained on an ecologically valid arithmetic dataset, which we call Arithmetic-GPT, predicts human behavior better than many traditional cognitive models. Pretraining language models on ecologically valid arithmetic datasets is sufficient to produce a strong correspondence between these models and human decision-making. Our results also suggest that language models used as cognitive models should be carefully investigated via ablation studies of the pretraining data.

Recent advances in language models have demonstrated their capability to solve mathematical reasoning problems, achieving near-perfect accuracy on grade-school level math benchmarks like GSM8K. In this paper, we formally study how language models solve these problems. We design a series of controlled experiments to address several fundamental questions: (1) Can language models truly develop reasoning skills, or do they simply memorize templates? (2) What is the model's hidden (mental) reasoning process? (3) Do models solve math questions using skills similar to or different from humans? (4) Do models trained on GSM8K-like datasets develop reasoning skills beyond those necessary for solving GSM8K problems? (5) What mental process causes models to make reasoning mistakes? (6) How large or deep must a model be to effectively solve GSM8K-level math questions? Our study uncovers many hidden mechanisms by which language models solve mathematical questions, providing insights that extend beyond current understandings of LLMs.

Preconditioning is at the heart of iterative solutions of large, sparse linear systems of equations in scientific disciplines. Several algebraic approaches, which access no information beyond the matrix itself, are widely studied and used, but ill-conditioned matrices remain very challenging. We take a machine learning approach and propose using graph neural networks as a general-purpose preconditioner. They show attractive performance for many problems and can be used when the mainstream preconditioners perform poorly. Empirical evaluation on over 800 matrices suggests that the construction time of these graph neural preconditioners (GNPs) is more predictable and can be much shorter than that of other widely used ones, such as ILU and AMG, while the execution time is faster than using a Krylov method as the preconditioner, such as in inner-outer GMRES. GNPs have a strong potential for solving large-scale, challenging algebraic problems arising from not only partial differential equations, but also economics, statistics, graph, and optimization, to name a few.

Solving high wavenumber Helmholtz equations is notoriously challenging. Traditional solvers have yet to yield satisfactory results, and most neural network methods struggle to accurately solve cases with extremely high wavenumbers within heterogeneous media. This paper presents an advanced multigrid-hierarchical AI solver, tailored specifically for high wavenumber Helmholtz equations. We adapt the MGCNN architecture to align with the problem setting and incorporate a novel Fourier neural network (FNN) to match the characteristics of Helmholtz equations. FNN, mathematically akin to the convolutional neural network (CNN), enables faster propagation of source influence during the solve phase, making it particularly suitable for handling large size, high wavenumber problems. We conduct supervised learning tests against numerous neural operator learning methods to demonstrate the superior learning capabilities of our solvers. Additionally, we perform scalability tests using an unsupervised strategy to highlight our solvers' significant speedup over the most recent specialized AI solver and AI-enhanced traditional solver for high wavenumber Helmholtz equations. We also carry out an ablation study to underscore the effectiveness of the multigrid hierarchy and the benefits of introducing FNN. Notably, our solvers exhibit optimal convergence of $\mathcal{O}(k)$ up to $k \approx 2000$.

Recently, diffusion- and flow-based generative models of protein structures have emerged as a powerful tool for de novo protein design. Here, we develop *Proteina*, a new large-scale flow-based protein backbone generator that utilizes hierarchical fold class labels for conditioning and relies on a tailored scalable transformer architecture with up to $5\times$ as many parameters as previous models. To meaningfully quantify performance, we introduce a new set of metrics that directly measure the distributional similarity of generated proteins with reference sets, complementing existing metrics. We further explore scaling training data to millions of synthetic protein structures and explore improved training and sampling recipes adapted to protein backbone generation. This includes fine-tuning strategies like LoRA for protein backbones, new guidance methods like classifier-free guidance and autoguidance for protein backbones, and new adjusted training objectives. Proteina achieves state-of-the-art performance on de novo protein backbone design and produces diverse and designable proteins at unprecedented length, up to 800 residues. The hierarchical conditioning offers novel control, enabling high-level secondary-structure guidance as well as low-level fold-specific generation.

The motion planning problem involves finding a collision-free path from a robot's starting to its target configuration. Recently, self-supervised learning methods have emerged to tackle motion planning problems without requiring expensive expert demonstrations. They solve the Eikonal equation for training neural networks and lead to efficient solutions. However, these methods struggle in complex environments because they fail to maintain key properties of the Eikonal equation, such as optimal value functions and geodesic distances. To overcome these limitations, we propose a novel self-supervised temporal difference metric learning approach that solves the Eikonal equation more accurately and enhances performance in solving complex and unseen planning tasks. Our method enforces Bellman's principle of optimality over finite regions, using temporal difference learning to avoid spurious local minima while incorporating metric learning to preserve the Eikonal equation's essential geodesic properties. We demonstrate that our approach significantly outperforms existing self-supervised learning methods in handling complex environments and generalizing to unseen environments, with robot configurations ranging from 2 to 12 degrees of freedom (DOF).

Cryo-electron microscopy (cryo-EM) is a powerful technique in structural biology and drug discovery, enabling the study of biomolecules at high resolution. Significant advancements by structural biologists using cryo-EM have led to the production of around 40k protein density maps at various resolutions. However, cryo-EM data processing algorithms have yet to fully benefit from our knowledge of biomolecular density maps, with only a few recent models being data-driven but limited to specific tasks. In this study, we present CryoFM, a foundation model designed as a generative model, learning the distribution of high-quality density maps and generalizing effectively to downstream tasks. Built on flow matching, CryoFM is trained to accurately capture the prior distribution of biomolecular density maps. Furthermore, we introduce a flow posterior sampling method that leverages CryoFM as a flexible prior for several downstream tasks in cryo-EM and cryo-electron tomography (cryo-ET) without the need for fine-tuning, achieving state-of-the-art performance on most tasks and demonstrating its potential as a foundational model for broader applications in these fields.

This paper explores alternative formulations of the Kolmogorov Superposition Theorem (KST) as a foundation for neural network design. The original KST formulation, while mathematically elegant, presents practical challenges due to its limited insight into the structure of inner and outer functions and the large number of unknown variables it introduces. Kolmogorov-Arnold Networks (KANs) leverage KST for function approximation, but they have faced scrutiny due to mixed results compared to traditional multilayer perceptrons (MLPs) and practical limitations imposed by the original KST formulation. To address these issues, we introduce ActNet, a scalable deep learning model that builds on the KST and overcomes some of the drawbacks of Kolmogorov's original formulation. We evaluate ActNet in the context of Physics-Informed Neural Networks (PINNs), a framework well-suited for leveraging KST's strengths in low-dimensional function approximation, particularly for simulating partial differential equations (PDEs). In this challenging setting, where models must learn latent functions without direct measurements, ActNet consistently outperforms KANs across multiple benchmarks and is competitive against the current best MLP-based approaches. These results present ActNet as a promising new direction for KST-based deep learning applications, particularly in scientific computing and PDE simulation tasks.

Accurate protein identification from mass spectrometry (MS) data is fundamental to unraveling the complex roles of proteins in biological systems, with peptide sequencing being a pivotal step in this process. The two main paradigms for peptide sequencing are database search, which matches experimental spectra with peptide sequences from databases, and \emph{de novo} sequencing, which infers peptide sequences directly from MS without relying on pre-constructed database. Although database search methods are highly accurate, they are limited by their inability to identify novel, modified, or mutated peptides absent from the database. In contrast, \emph{de novo} sequencing is adept at discovering novel peptides but often struggles with missing peaks issue, further leading to lower precision. We introduce SearchNovo, a novel framework that synergistically integrates the strengths of database search and \emph{de novo} sequencing to enhance peptide sequencing. SearchNovo employs an efficient search mechanism to retrieve the most similar peptide spectrum match (PSM) from a database for each query spectrum, followed by a fusion module that utilizes the reference peptide sequence to guide the generation of the target sequence. Furthermore, we observed that dissimilar (noisy) reference peptides negatively affect model performance. To mitigate this, we constructed pseudo reference PSMs to minimize their impact. Comprehensive evaluations on multiple datasets reveal that SearchNovo significantly outperforms state-of-the-art models. Also, analysis indicates that many retrieved spectra contain missing peaks absent in the query spectra, and the retrieved reference peptides often share common fragments with the target peptides. These are key elements in the recipe for SearchNovo’s success. The code is available at: \textcolor{magenta}{\url{https://github.com/junxia97/SearchNovo}}.

By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally increases with the system dimensionality, requiring larger datasets, more complex deep networks, and significant computational effort. We propose a novel geometric network architecture to learn physically-consistent reduced-order dynamic parameters that accurately describe the original high-dimensional system behavior. This is achieved by building on recent advances in model-order reduction and by adopting a Riemannian perspective to jointly learn a non-linear structure-preserving latent space and the associated low-dimensional dynamics. Our approach enables accurate long-term predictions of the high-dimensional dynamics of rigid and deformable systems with increased data efficiency by inferring interpretable and physically-plausible reduced Lagrangian models.