The Graph Edit Distance (GED) problem, which aims to compute the minimum number of edit operations required to transform one graph into another, is a fundamental challenge in graph analysis with wide-ranging applications. However, due to its NP-hard nature, traditional A* approaches often suffer from scalability issue, making them computationally intractable for large graphs. Many recent deep learning frameworks address GED by formulating it as a regression task, which, while efficient, fails to recover the edit path -- a central interest in GED. Furthermore, recent hybrid approaches that combine deep learning with traditional methods to recover the edit path often yield poor solution quality. These methods also struggle to generate candidate solutions in parallel, resulting in increased running times.In this paper, we present a novel approach, DiffGED, that leverages generative diffusion model to solve GED and recover the corresponding edit path. Specifically, we first generate multiple diverse node matching matrices in parallel through a diffusion-based graph matching model. Next, node mappings are extracted from each generated matching matrices in parallel, and each extracted node mapping can be simply transformed into an edit path. Benefiting from the generative diversity provided by the diffusion model, DiffGED is less likely to fall into local sub-optimal solutions, thereby achieving superior overall solution quality close to the exact solution. Experimental results on real-world datasets demonstrate that DiffGED can generate multiple diverse edit paths with exceptionally high accuracy comparable to exact solutions while maintaining a running time shorter than most of hybrid approaches.

Molecular relational learning (MRL) focuses on understanding the interaction dynamics between molecules and has gained significant attention from researchers thanks to its diverse applications [20]. For instance, understanding how a medication dissolves in different solvents (medication-solvent interaction) is vital in pharmacy [30, 26, 3], while predicting the optical and photophysical properties of chromophores in various solvents (chromophore-solvent interaction) is essential for material discovery [16]. Because of the expensive time and financial costs associated with conducting wet lab experiments to test the interaction behavior of all possible molecular pairs [31], machine learning methods have been quickly embraced for MRL. Despite recent advancements in MRL, previous works tend to ignore molecules' 3D geometric information and instead focus solely on their 2D topological structures. However, in molecular science, the 3D geometric information of molecules (Figure 1 (a)) is crucial for understanding and predicting molecular behavior across various contexts, ranging from physical properties [1] to biological functions [10, 46]. This is particularly important in MRL, as geometric information plays a key role in molecular interactions by determining how molecules recognize, interact, and bind with one another in their interaction environment [34]. In traditional molecular dynamics simulations, explicit solvent models, which directly consider the detailed environment of molecular interaction, have demonstrated superior performance compared to implicit solvent models, which simplify the solvent as a continuous medium, highlighting the significance of explicitly modeling the complex geometries of interaction environments [47]. However, acquiring stereochemical structures of molecules is often very costly, resulting in limited availability of such 3D geometric information for downstream tasks [23].

Recent studies have demonstrated the strong empirical performance of diffusion models on discrete sequences (i.e., discrete diffusion models) across domains from natural language to biological sequence generation. For example, in the protein inverse folding task, where the goal is to generate a protein sequence from a given backbone structure, conditional diffusion models have achieved impressive results in generating natural-like sequences that fold back into the original structure. However, practical design tasks often require not only modeling a conditional distribution but also optimizing specific task objectives. For instance, in the inverse folding task, we may prefer protein sequences with high stability. To address this, we consider the scenario where we have pre-trained discrete diffusion models that can generate natural-like sequences, as well as reward models that map sequences to task objectives. We then formulate the reward maximization problem within discrete diffusion models, analogous to reinforcement learning (RL), while minimizing the KL divergence against pretrained diffusion models to preserve naturalness. To solve this RL problem, we propose a novel algorithm, DRAKES, that enables direct backpropagation of rewards through entire trajectories generated by diffusion models, by making the originally nondifferentiable trajectories differentiable using the Gumbel-Softmax trick. Our theoretical analysis indicates that our approach can generate sequences that are both natural-like (i.e., have a high probability under a pretrained model) and yield high rewards. While similar tasks have been recently explored in diffusion models for continuous domains, our work addresses unique algorithmic and theoretical challenges specific to discrete diffusion models, which arise from their foundation in continuous-time Markov chains rather than Brownian motion. Finally, we demonstrate the effectiveness of our algorithm in generating DNA and protein sequences that optimize enhancer activity and protein stability, respectively, important tasks for gene therapies and protein-based therapeutics. Diffusion models have gained widespread recognition as effective generative models in continuous spaces, such as image and video generation (Song et al., 2020; Ho et al., 2022). Inspired by seminal works (e.g., Austin et al. (2021); Campbell et al. (2022); Sun et al. (2022)), recent studies (Lou et al., 2023; Shi et al., 2024; Sahoo et al., 2024) have shown that diffusion models are also highly effective in discrete spaces, including natural language and biological sequence generation (DNA, RNA, proteins). Work mainly done during an internship at Genentech.

Graph representation learning, involving both node features and graph structures, is crucial for real-world applications but often encounters pervasive noise. State-of-the-art methods typically address noise by focusing separately on node features with large language models (LLMs) and on graph structures with graph structure learning models (GSLMs). In this paper, we introduce LangGSL, a robust framework that integrates the complementary strengths of pre-trained language models and GSLMs to jointly enhance both node feature and graph structure learning. In LangGSL, we first leverage LLMs to filter noise in the raw data and extract valuable cleaned information as features, enhancing the synergy of downstream models. During the mutual learning phase in LangGSL, the core idea is to leverage the relatively small language model (LM) to process local attributes and generate reliable pseudo-labels and informative node embeddings, which are then integrated into the GSLM's prediction phase. This approach enriches the global context and enhances overall performance. Meanwhile, GSLM refines the evolving graph structure constructed from the LM's output, offering updated labels back to the LM as additional guidance, thus facilitating a more effective mutual learning process. The LM and GSLM work synergistically, complementing each other's strengths and offsetting weaknesses within a variational information-maximizing framework, resulting in enhanced node features and a more robust graph structure. Extensive experiments on diverse graph datasets of varying scales and across different task scenarios demonstrate the scalability and effectiveness of the proposed approach.

Spatial-Temporal Graph (STG) data is characterized as dynamic, heterogenous, and non-stationary, leading to the continuous challenge of spatial-temporal graph learning. In the past few years, various GNN-based methods have been proposed to solely focus on mimicking the relationships among node individuals of the STG network, ignoring the significance of modeling the intrinsic features that exist in STG system over time. In contrast, modern Selective State Space Models (SSSMs) present a new approach which treat STG Network as a system, and meticulously explore the STG system's dynamic state evolution across temporal dimension. In this work, we introduce Spatial-Temporal Graph Mamba (STG-Mamba) as the first exploration of leveraging the powerful selective state space models for STG learning by treating STG Network as a system, and employing the Spatial-Temporal Selective State Space Module (ST-S3M) to precisely focus on the selected STG latent features. Furthermore, to strengthen GNN's ability of modeling STG data under the setting of selective state space models, we propose Kalman Filtering Graph Neural Networks (KFGN) for dynamically integrate and upgrade the STG embeddings from different temporal granularities through a learnable Kalman Filtering statistical theory-based approach. Extensive empirical studies are conducted on three benchmark STG forecasting datasets, demonstrating the performance superiority and computational efficiency of STG-Mamba. It not only surpasses existing state-of-the-art methods in terms of STG forecasting performance, but also effectively alleviate the computational bottleneck of large-scale graph networks in reducing the computational cost of FLOPs and test inference time. The implementation code is available at: \url{https://github.com/LincanLi98/STG-Mamba}.

Deep generative models (DGMs) have been widely developed for graph data. However, much less investigation has been carried out on understanding the latent space of such pretrained graph DGMs. These understandings possess the potential to provide constructive guidelines for crucial tasks, such as graph controllable generation. Thus in this work, we are interested in studying this problem and propose GraphCG, a method for the unsupervised discovery of steerable factors in the latent space of pretrained graph DGMs. We first examine the representation space of three pretrained graph DGMs with six disentanglement metrics, and we observe that the pretrained representation space is entangled. Motivated by this observation, GraphCG learns the steerable factors via maximizing the mutual information between semantic-rich directions, where the controlled graph moving along the same direction will share the same steerable factors. We quantitatively verify that GraphCG outperforms four competitive baselines on two graph DGMs pretrained on two molecule datasets. Additionally, we qualitatively illustrate seven steerable factors learned by GraphCG on five pretrained DGMs over five graph datasets, including two for molecules and three for point clouds.

Full-waveform inversion (FWI) plays a vital role in geoscience to explore the subsurface. It utilizes the seismic wave to image the subsurface velocity map. As the machine learning (ML) technique evolves, the data-driven approaches using ML for FWI tasks have emerged, offering enhanced accuracy and reduced computational cost compared to traditional physics-based methods. However, a common challenge in geoscience, the unprivileged data, severely limits ML effectiveness. The issue becomes even worse during model pruning, a step essential in geoscience due to environmental complexities. To tackle this, we introduce the EdGeo toolkit, which employs a diffusion-based model guided by physics principles to generate high-fidelity velocity maps. The toolkit uses the acoustic wave equation to generate corresponding seismic waveform data, facilitating the fine-tuning of pruned ML models. Our results demonstrate significant improvements in SSIM scores and reduction in both MAE and MSE across various pruning ratios. Notably, the ML model fine-tuned using data generated by EdGeo yields superior quality of velocity maps, especially in representing unprivileged features, outperforming other existing methods.

Graph Self-Supervised Learning (GSSL) provides a robust pathway for acquiring embeddings without expert labelling, a capability that carries profound implications for molecular graphs due to the staggering number of potential molecules and the high cost of obtaining labels. However, GSSL methods are designed not for optimisation within a specific domain but rather for transferability across a variety of downstream tasks. This broad applicability complicates their evaluation. Addressing this challenge, we present "Molecular Graph Representation Evaluation" (MOLGRAPHEVAL), generating detailed profiles of molecular graph embeddings with interpretable and diversified attributes. MOLGRAPHEVAL offers a suite of probing tasks grouped into three categories: (i) generic graph, (ii) molecular substructure, and (iii) embedding space properties. By leveraging MOLGRAPHEVAL to benchmark existing GSSL methods against both current downstream datasets and our suite of tasks, we uncover significant inconsistencies between inferences drawn solely from existing datasets and those derived from more nuanced probing. These findings suggest that current evaluation methodologies fail to capture the entirety of the landscape.

Graph Neural Networks (GNNs) are effective tools for graph representation learning. Most GNNs rely on a recursive neighborhood aggregation scheme, named message passing, thereby their theoretical expressive power is limited to the first-order Weisfeiler-Lehman test (1-WL). An effective approach to this challenge is to explicitly retrieve some annotated examples used to enhance GNN models. While retrieval-enhanced models have been proved to be effective in many language and vision domains, it remains an open question how effective retrieval-enhanced GNNs are when applied to graph datasets. Motivated by this, we want to explore how the retrieval idea can help augment the useful information learned in the graph neural networks, and we design a retrieval-enhanced scheme called GRAPHRETRIEVAL, which is agnostic to the choice of graph neural network models. In GRAPHRETRIEVAL, for each input graph, similar graphs together with their ground-true labels are retrieved from an existing database. Thus they can act as a potential enhancement to complete various graph property predictive tasks. We conduct comprehensive experiments over 13 datasets, and we observe that GRAPHRETRIEVAL is able to reach substantial improvements over existing GNNs. Moreover, our empirical study also illustrates that retrieval enhancement is a promising remedy for alleviating the long-tailed label distribution problem.

Elastic geophysical properties (such as P- and S-wave velocities) are of great importance to various subsurface applications like CO$_2$ sequestration and energy exploration (e.g., hydrogen and geothermal). Elastic full waveform inversion (FWI) is widely applied for characterizing reservoir properties. In this paper, we introduce $\mathbf{\mathbb{E}^{FWI}}$, a comprehensive benchmark dataset that is specifically designed for elastic FWI. $\mathbf{\mathbb{E}^{FWI}}$ encompasses 8 distinct datasets that cover diverse subsurface geologic structures (flat, curve, faults, etc). The benchmark results produced by three different deep learning methods are provided. In contrast to our previously presented dataset (pressure recordings) for acoustic FWI (referred to as OpenFWI), the seismic dataset in $\mathbf{\mathbb{E}^{FWI}}$ has both vertical and horizontal components. Moreover, the velocity maps in $\mathbf{\mathbb{E}^{FWI}}$ incorporate both P- and S-wave velocities. While the multicomponent data and the added S-wave velocity make the data more realistic, more challenges are introduced regarding the convergence and computational cost of the inversion. We conduct comprehensive numerical experiments to explore the relationship between P-wave and S-wave velocities in seismic data. The relation between P- and S-wave velocities provides crucial insights into the subsurface properties such as lithology, porosity, fluid content, etc. We anticipate that $\mathbf{\mathbb{E}^{FWI}}$ will facilitate future research on multiparameter inversions and stimulate endeavors in several critical research topics of carbon-zero and new energy exploration. All datasets, codes and relevant information can be accessed through our website at https://efwi-lanl.github.io/