ICLR 2025 Papers

We introduce a novel masked pre-training technique for graph neural networks (GNNs) applied to computational fluid dynamics (CFD) problems. By randomly masking up to 40\% of input mesh nodes during pre-training, we force the model to learn robust representations of complex fluid dynamics. We pair this masking strategy with an asymmetric encoder-decoder architecture and gated multi-layer perceptrons to further enhance performance. The proposed method achieves state-of-the-art results on seven CFD datasets, including a new challenging dataset of 3D intracranial aneurysm simulations with over 250,000 nodes per mesh. Moreover, it significantly improves model performance and training efficiency across such diverse range of fluid simulation tasks. We demonstrate improvements of up to 60\% in long-term prediction accuracy compared to previous best models, while maintaining similar computational costs. Notably, our approach enables effective pre-training on multiple datasets simultaneously, significantly reducing the time and data required to achieve high performance on new tasks. Through extensive ablation studies, we provide insights into the optimal masking ratio, architectural choices, and training strategies.

Molecular discovery, when formulated as an optimization problem, presents significant computational challenges because optimization objectives can be non-differentiable. Evolutionary Algorithms (EAs), often used to optimize black-box objectives in molecular discovery, traverse chemical space by performing random mutations and crossovers, leading to a large number of expensive objective evaluations. In this work, we ameliorate this shortcoming by incorporating chemistry-aware Large Language Models (LLMs) into EAs. Namely, we redesign crossover and mutation operations in EAs using LLMs trained on large corpora of chemical information. We perform extensive empirical studies on both commercial and open-source models on multiple tasks involving property optimization, molecular rediscovery, and structure-based drug design, demonstrating that the joint usage of LLMs with EAs yields superior performance over all baseline models across single- and multi-objective settings. We demonstrate that our algorithm improves both the quality of the final solution and convergence speed, thereby reducing the number of required objective evaluations.

Antibodies are essential proteins responsible for immune responses in organisms, capable of specifically recognizing antigen molecules of pathogens. Recent advances in generative models have significantly enhanced rational antibody design. However, existing methods mainly create antibodies from scratch without template constraints, leading to model optimization challenges and unnatural sequences. To address these issues, we propose a retrieval-augmented diffusion framework, termed RADAb, for efficient antibody design. Our method leverages a set of structural homologous motifs that align with query structural constraints to guide the generative model in inversely optimizing antibodies according to desired design criteria. Specifically, we introduce a structure-informed retrieval mechanism that integrates these exemplar motifs with the input backbone through a novel dual-branch denoising module, utilizing both structural and evolutionary information. Additionally, we develop a conditional diffusion model that iteratively refines the optimization process by incorporating both global context and local evolutionary conditions. Our approach is agnostic to the choice of generative models. Empirical experiments demonstrate that our method achieves state-of-the-art performance in multiple antibody inverse folding and optimization tasks, offering a new perspective on biomolecular generative models.

Contrastive Language-Image Pretraining (CLIP) stands out as a prominent method for image representation learning. Various architectures, from vision transformers~(ViTs) to convolutional networks (ResNets) have been trained with CLIP to serve as general solutions to diverse vision tasks. This paper explores the differences across various CLIP-trained vision backbones. Despite using the same data and training objective, we find that these architectures have notably different representations, different classification performance across datasets, and different robustness properties to certain types of image perturbations. Our findings indicate a remarkable possible synergy across backbones by leveraging their respective strengths. In principle, classification accuracy could be improved by over 40 percentage with an informed selection of the optimal backbone per test example. Using this insight, we develop a straightforward yet powerful approach to adaptively ensemble multiple backbones. The approach uses as few as one labeled example per class to tune the adaptive combination of backbones. On a large collection of datasets, the method achieves a remarkable increase in accuracy of up to 39.1\% over the best single backbone, well beyond traditional ensembles.

A popular approach to neurosymbolic AI involves mapping logic formulas to arithmetic circuits (computation graphs consisting of sums and products) and passing the outputs of a neural network through these circuits. This approach enforces symbolic constraints onto a neural network in a principled and end-to-end differentiable way. Unfortunately, arithmetic circuits are challenging to run on modern tensor accelerators as they exhibit a high degree of irregular sparsity. To address this limitation, we introduce knowledge layers (KLay), a new data structure to represent arithmetic circuits that can be efficiently parallelized on GPUs. Moreover, we contribute two algorithms used in the translation of traditional circuit representations to KLay and a further algorithm that exploits parallelization opportunities during circuit evaluations. We empirically show that KLay achieves speedups of multiple orders of magnitude over the state of the art, thereby paving the way towards scaling neurosymbolic AI to larger real-world applications.

Learning informative representations of phylogenetic tree structures is essential for analyzing evolutionary relationships. Classical distance-based methods have been widely used to project phylogenetic trees into Euclidean space, but they are often sensitive to the choice of distance metric and may lack sufficient resolution. In this paper, we introduce *phylogenetic variational autoencoders* (PhyloVAEs), an unsupervised learning framework designed for representation learning and generative modeling of tree topologies. Leveraging an efficient encoding mechanism inspired by autoregressive tree topology generation, we develop a deep latent-variable generative model that facilitates fast, parallelized topology generation. PhyloVAE combines this generative model with a collaborative inference model based on learnable topological features, allowing for high-resolution representations of phylogenetic tree samples. Extensive experiments demonstrate PhyloVAE's robust representation learning capabilities and fast generation of phylogenetic tree topologies.

Generative models on discrete state-spaces have a wide range of potential applications, particularly in the domain of natural sciences. In continuous state-spaces, controllable and flexible generation of samples with desired properties has been realized using guidance on diffusion and flow models. However, these guidance approaches are not readily amenable to discrete state-space models. Consequently, we introduce a general and principled method for applying guidance on such models. Our method depends on leveraging continuous-time Markov processes on discrete state-spaces, which unlocks computational tractability for sampling from a desired guided distribution. We demonstrate the utility of our approach, Discrete Guidance, on a range of applications including guided generation of small-molecules, DNA sequences and protein sequences.

Despite the progress in quantum computing, one major bottleneck against the practical utility is its susceptibility to noise, which frequently occurs in current quantum systems. Existing quantum error mitigation (QEM) methods either lack generality to noise and circuit types or fail to capture the global dependencies of entire systems in addition to circuit structure. In this work, we first propose a unique circuit-to-graph encoding scheme with qubit-wise noisy measurement aggregated. Then, we introduce GTranQEM, a non-message passing graph transformer designed to mitigate errors in expected circuit measurement outcomes effectively. GTranQEM is equipped with a quantum-specific positional encoding, a structure matrix as attention bias guiding nonlocal aggregation, and a virtual quantum-representative node to further grasp graph representations, which guarantees to model the long-range entanglement. Experimental evaluations demonstrate that GTranQEM outperforms state-of-the-art QEM methods on both random and structured quantum circuits across noise types and scales among diverse settings.

Many applications in traffic, civil engineering, or electrical engineering revolve around edge-level signals. Such signals can be categorized as inherently directed, for example, the water flow in a pipe network, and undirected, like the diameter of a pipe. Topological methods model edge signals with inherent direction by representing them relative to a so-called *orientation* assigned to each edge. They can neither model undirected edge signals nor distinguish if an edge itself is directed or undirected. We address these shortcomings by (i) revising the notion of *orientation equivariance* to enable edge direction-aware topological models, (ii) proposing *orientation invariance* as an additional requirement to describe signals without inherent direction, and (iii) developing EIGN, an architecture composed of novel direction-aware edge-level graph shift operators, that provably fulfils the aforementioned desiderata. It is the first work that discusses modeling directed and undirected signals while distinguishing between directed and undirected edges. A comprehensive evaluation shows that EIGN outperforms prior work in edge-level tasks, improving in RMSE on flow simulation tasks by up to 23.5%.

Scientific discovery contributes largely to the prosperity of human society, and recent progress shows that LLMs could potentially catalyst the process. However, it is still unclear whether LLMs can discover novel and valid hypotheses in chemistry. In this work, we investigate this main research question: whether LLMs can automatically discover novel and valid chemistry research hypotheses, given only a research question? With extensive discussions with chemistry experts, we adopt the assumption that a majority of chemistry hypotheses can be resulted from a research background question and several inspirations. With this key insight, we break the main question into three smaller fundamental questions. In brief, they are: (1) given a background question, whether LLMs can retrieve good inspirations; (2) with background and inspirations, whether LLMs can lead to hypothesis; and (3) whether LLMs can identify good hypotheses to rank them higher. To investigate these questions, we construct a benchmark consisting of 51 chemistry papers published in Nature or a similar level in 2024 (all papers are only available online since 2024). Every paper is divided by chemistry PhD students into three components: background, inspirations, and hypothesis. The goal is to rediscover the hypothesis given only the background and a large chemistry literature corpus consisting the ground truth inspiration papers, with LLMs trained with data up to 2023. We also develop an LLM-based multi-agent framework that leverages the assumption, consisting of three stages reflecting the more smaller questions. The proposed method can rediscover many hypotheses with very high similarity with the ground truth ones, covering the main innovations.

Effective treatment of cancer is a major challenge faced by healthcare providers, due to the highly individualized nature of patient responses to treatment. This is caused by the heterogeneity seen in cancer-causing alterations (mutations) across patient genomes. Limited availability of response data in patients makes it difficult to train personalized treatment recommendation models on mutations from clinical genomic sequencing reports. Prior methods tackle this by utilising larger, labelled pre-clinical laboratory datasets (‘cell lines’), via transfer learning. These methods augment patient data by learning a shared, domain-invariant representation, between the cell line and patient domains, which is then used to train a downstream drug response prediction (DRP) model. This approach augments data in the shared space but fails to model patient-specific characteristics, which have a strong influence on their drug response. We propose a novel generative attention-based data augmentation and predictive modeling framework, GANDALF, to tackle this crucial shortcoming of prior methods. GANDALF not only augments patient genomic data directly, but also accounts for its domain-specific characteristics. GANDALF outperforms state-of-the-art DRP models on publicly available patient datasets and emerges as the front-runner amongst SOTA cancer DRP models.

Understanding transition pathways between two meta-stable states of a molecular system is crucial to advance drug discovery and material design. However, unbiased molecular dynamics (MD) simulations are computationally infeasible because of the high energy barriers that separate these states. Although recent machine learning techniques are proposed to sample rare events, they are often limited to simple systems and rely on collective variables (CVs) derived from costly domain expertise. In this paper, we introduce a novel approach that trains diffusion path samplers (DPS) to address the transition path sampling (TPS) problem without requiring CVs. We reformulate the problem as an amortized sampling from the transition path distribution by minimizing the log-variance divergence between the path distribution induced by DPS and the transition path distribution. Based on the log-variance divergence, we propose learnable control variates to reduce the variance of gradient estimators and the off-policy training objective with replay buffers and simulated annealing techniques to improve sample efficiency and diversity. We also propose a scale-based equivariant parameterization of the bias forces to ensure scalability for large systems. We extensively evaluate our approach, termed TPS-DPS, on a synthetic system, small peptide, and challenging fast-folding proteins, demonstrating that it produces more realistic and diverse transition pathways than existing baselines. We also provide links to [project page](https://kiyoung98.github.io/tps-dps/) and [code](https://github.com/kiyoung98/tps-dps).

Predicting the ground-state 3D molecular conformations from 2D molecular graphs is critical in computational chemistry due to its profound impact on molecular properties. Deep learning (DL) approaches have recently emerged as promising alternatives to computationally-heavy classical methods such as density functional theory (DFT). However, we discover that existing DL methods inadequately model inter-atomic forces, particularly for non-bonded atomic pairs, due to their naive usage of bonds and pairwise distances. Consequently, significant prediction errors occur for atoms with low degree (ie., low coordination numbers) whose conformations are primarily influenced by non-bonded interactions. To address this, we propose ReBIND, a novel framework that rewires molecular graphs by adding edges based on the Lennard-Jones potential to capture non-bonded interactions for low-degree atoms. Experimental results demonstrate that ReBIND significantly outperforms state-of-the-art methods across various molecular sizes, achieving up to a 20% reduction in prediction error. The code is available in: https://github.com/holymollyhao/ReBIND

The phenomenon of knowledge hallucinations has raised substantial concerns about the security and reliability of deployed large language models (LLMs). Current methods for detecting hallucinations primarily depend on manually designed individual metrics, such as prediction uncertainty and consistency, and fall short in effectively calibrating model predictions, thus constraining their detection accuracy and applicability in practical applications. In response, we propose an advanced framework, termed HaDeMiF, for detecting and mitigating hallucinations in LLMs. Specifically, hallucinations within the output and semantic spaces of LLMs are comprehensively captured through two compact networks—a novel, interpretable tree model known as the Deep Dynamic Decision Tree (D3T) and a Multilayer Perceptron (MLP)—which take as input a set of prediction characteristics and the hidden states of tokens, respectively. The predictions of LLMs are subsequently calibrated using the outputs from the D3T and MLP networks, aiming to mitigate hallucinations and enhance model calibration. HaDeMiF can be applied during both the inference and fine-tuning phases of LLMs, introducing less than 2% of the parameters relative to the LLMs through the training of two small-scale networks. Extensive experiments conclusively demonstrate the effectiveness of our framework in hallucination detection and model calibration across text generation tasks with responses of varying lengths.

We introduce Fengbo, a pipeline entirely in Clifford Algebra to solve 3D partial differential equations (PDEs) specifically for computational fluid dynamics (CFD). Fengbo is an architecture composed of only 3D convolutional and Fourier Neural Operator (FNO) layers, all working in 3D Clifford Algebra. It models the PDE solution problem as an interpretable mapping from the geometry to the physics of the problem. Despite having just few layers, Fengbo achieves competitive accuracy, superior to 5 out of 6 proposed models reported in \cite{li2024geometry} for the $\emph{ShapeNet Car}$ dataset, and it does so with only 42 million trainable parameters, at a reduced computational complexity compared to graph-based methods, and estimating jointly pressure \emph{and} velocity fields. In addition, the output of each layer in Fengbo can be clearly visualised as objects and physical quantities in 3D space, making it a whitebox model. By leveraging Clifford Algebra and establishing a direct mapping from the geometry to the physics of the PDEs, Fengbo provides an efficient, geometry- and physics-aware approach to solving complex PDEs.

Recent advancements in neural theorem proving integrate large language models with tree search algorithms like Monte Carlo Tree Search (MCTS), where the language model suggests tactics and the tree search finds the complete proof path. However, many tactics proposed by the language model converge to semantically or strategically similar, reducing diversity and increasing search costs by expanding redundant proof paths. This issue exacerbates as computation scales and more tactics are explored per state. Furthermore, the trained value function suffers from false negatives, label imbalance, and domain gaps due to biased data construction. To address these challenges, we propose CARTS (diversified tactic CAlibration and bias-Resistant Tree Search), which balances tactic diversity and importance while calibrating model confidence. CARTS also introduce preference modeling and an adjustment term related to the ratio of valid tactics to improve the bias-resistance of the value function. Experimental results demonstrate that CARTS consistently outperforms previous methods achieving a pass@l rate of 49.6\% on the miniF2F-test benchmark. Further analysis confirms that CARTS improves tactic diversity and leads to a more balanced tree search.

Mechanical meta-materials are solids whose geometric structure results in exotic nonlinear behaviors that are not typically achievable via homogeneous materials. We show how to drastically expand the design space of a class of mechanical meta-materials known as $\textit{cellular solids}$, by generalizing beyond translational symmetry. This is made possible by transforming a reference geometry according to a divergence free flow that is parameterized by a neural network and equivariant under the relevant symmetry group. We show how to construct flows equivariant to the space groups, despite the fact that these groups are not compact. Coupling this flow with a differentiable nonlinear mechanics simulator allows us to represent a much richer set of cellular solids than was previously possible. These materials can be optimized to exhibit desirable mechanical properties such as negative Poisson's ratios or to match target stress-strain curves. We validate these new designs in simulation and by fabricating real-world prototypes. We find that designs with higher-order symmetries can exhibit a wider range of behaviors.

This paper proposes a new 3D molecule generation framework, called GOAT, for fast and effective 3D molecule generation based on the flow-matching optimal transport objective. Specifically, we formulate a geometric transport formula for measuring the cost of mapping multi-modal features (e.g., continuous atom coordinates and categorical atom types) between a base distribution and a target data distribution. Our formula is solved within a joint, equivariant, and smooth representation space. This is achieved by transforming the multi-modal features into a continuous latent space with equivariant networks. In addition, we find that identifying optimal distributional coupling is necessary for fast and effective transport between any two distributions. We further propose a mechanism for estimating and purifying optimal coupling to train the flow model with optimal transport. By doing so, GOAT can turn arbitrary distribution couplings into new deterministic couplings, leading to an estimated optimal transport plan for fast 3D molecule generation. The purification filters out the subpar molecules to ensure the ultimate generation quality. We theoretically and empirically prove that the proposed optimal coupling estimation and purification yield transport plan with non-increasing cost. Finally, extensive experiments show that GOAT enjoys the efficiency of solving geometric optimal transport, leading to a double speedup compared to the sub-optimal method while achieving the best generation quality regarding validity, uniqueness, and novelty.

The brain's ability to transform sensory inputs into motor functions is central to neuroscience and crucial for the development of embodied intelligence. Sensory-motor integration involves complex neural circuits, diverse neuronal types, and intricate intercellular connections. Bridging the gap between biological realism and behavioral functionality presents a formidable challenge. In this study, we focus on the columnar structure of the superficial layers of mouse barrel cortex as a model system. We constructed a model comprising 4,218 neurons across 13 neuronal subtypes, with neural distribution and connection strengths constrained by anatomical experimental findings. A key innovation of our work is the development of an effective construction and training pipeline tailored for this biologically constrained model. Additionally, we converted an existing simulated whisker sweep dataset into a spiking-based format, enabling our network to be trained and tested on neural signals that more closely mimic those observed in biological systems. The results of object discrimination utilizing whisker signals demonstrate that our barrel cortex model, grounded in biological constraints, achieves a classification accuracy exceeds classical convolutional neural networks (CNNs), recurrent neural networks (RNNs), and long short-term memory networks (LSTMs), by an average of 8.6%, and is on par with recent spiking neural networks (SNNs) in performance. Interestingly, a whisker deprivation experiment, designed in accordance with neuroscience practices, further validates the perceptual capabilities of our model in behavioral tasks. Critically, it offers significant biological interpretability: post-training analysis reveals that neurons within our model exhibit firing characteristics and distribution patterns similar to those observed in the actual neuronal systems of the barrel cortex. This study advances our understanding of neural processing in the barrel cortex and exemplifies how integrating detailed biological structures into neural network models can enhance both scientific inquiry and artificial intelligence applications. The code is available at https://github.com/fun0515/RSNN_bfd.