Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks

Graph Neural Networks (GNNs) and differential equations (DEs) are two rapidly advancing areas of research that have shown remarkable synergy in recent years. GNNs have emerged as powerful tools for learning on graph-structured data, while differential equations provide a principled framework for modeling continuous dynamics across time and space. The intersection of these fields has led to innovative approaches that leverage the strengths of both, enabling applications in physics-informed learning, spatiotemporal modeling, and scientific computing. This survey aims to provide a comprehensive overview of the burgeoning research at the intersection of GNNs and DEs. We will categorize existing methods, discuss their underlying principles, and highlight their applications across domains such as molecular modeling, traffic prediction, and epidemic spreading. Furthermore, we identify open challenges and outline future research directions to advance this interdisciplinary field. A comprehensive paper list is provided at https://github.com/Emory-Melody/Awesome-Graph-NDEs. This survey serves as a resource for researchers and practitioners seeking to understand and contribute to the fusion of GNNs and DEs

Scalable Graph Condensation with Evolving Capabilities

Graph data has become a pivotal modality due to its unique ability to model relational datasets. However, real-world graph data continues to grow exponentially, resulting in a quadratic increase in the complexity of most graph algorithms as graph sizes expand. Although graph condensation (GC) methods have been proposed to address these scalability issues, existing approaches often treat the training set as static, overlooking the evolving nature of real-world graph data. This limitation leads to inefficiencies when condensing growing training sets. In this paper, we introduce GECC (Graph Evolving Clustering Condensation), a scalable graph condensation method designed to handle large-scale and evolving graph data. GECC employs a traceable and efficient approach by performing class-wise clustering on aggregated features. Furthermore, it can inherits previous condensation results as clustering centroids when the condensed graph expands, thereby attaining an evolving capability. This methodology is supported by robust theoretical foundations and demonstrates superior empirical performance. Comprehensive experiments show that GECC achieves better performance than most state-of-the-art graph condensation methods while delivering an around 1,000x speedup on large datasets.

TimeDistill: Efficient Long-Term Time Series Forecasting with MLP via Cross-Architecture Distillation

Transformer-based and CNN-based methods demonstrate strong performance in long-term time series forecasting. However, their high computational and storage requirements can hinder large-scale deployment. To address this limitation, we propose integrating lightweight MLP with advanced architectures using knowledge distillation (KD). Our preliminary study reveals different models can capture complementary patterns, particularly multi-scale and multi-period patterns in the temporal and frequency domains. Based on this observation, we introduce TimeDistill, a cross-architecture KD framework that transfers these patterns from teacher models (e.g., Transformers, CNNs) to MLP. Additionally, we provide a theoretical analysis, demonstrating that our KD approach can be interpreted as a specialized form of mixup data augmentation. TimeDistill improves MLP performance by up to 18.6%, surpassing teacher models on eight datasets. It also achieves up to 7X faster inference and requires 130X fewer parameters. Furthermore, we conduct extensive evaluations to highlight the versatility and effectiveness of TimeDistill.

CAPE: Covariate-Adjusted Pre-Training for Epidemic Time Series Forecasting

Accurate forecasting of epidemic infection trajectories is crucial for safeguarding public health. However, limited data availability during emerging outbreaks and the complex interaction between environmental factors and disease dynamics present significant challenges for effective forecasting. In response, we introduce CAPE, a novel epidemic pre-training framework designed to harness extensive disease datasets from diverse regions and integrate environmental factors directly into the modeling process for more informed decision-making on downstream diseases. Based on a covariate adjustment framework, CAPE utilizes pre-training combined with hierarchical environment contrasting to identify universal patterns across diseases while estimating latent environmental influences. We have compiled a diverse collection of epidemic time series datasets and validated the effectiveness of CAPE under various evaluation scenarios, including full-shot, few-shot, zero-shot, cross-location, and cross-disease settings, where it outperforms the leading baseline by an average of 9.9% in full-shot and 14.3% in zero-shot settings. The code will be released upon acceptance.

STRUX: An LLM for Decision-Making with Structured Explanations

Countless decisions shape our daily lives, and it is paramount to understand the how and why behind these choices. In this paper, we introduce a new LLM decision-making framework called STRUX, which enhances LLM decision-making by providing structured explanations. These include favorable and adverse facts related to the decision, along with their respective strengths. STRUX begins by distilling lengthy information into a concise table of key facts. It then employs a series of self-reflection steps to determine which of these facts are pivotal, categorizing them as either favorable or adverse in relation to a specific decision. Lastly, we fine-tune an LLM to identify and prioritize these key facts to optimize decision-making. STRUX has been evaluated on the challenging task of forecasting stock investment decisions based on earnings call transcripts and demonstrated superior performance against strong baselines. It enhances decision transparency by allowing users to understand the impact of different factors, representing a meaningful step towards practical decision-making with LLMs.

Sub-graph Based Diffusion Model for Link Prediction

Denoising Diffusion Probabilistic Models (DDPMs) represent a contemporary class of generative models with exceptional qualities in both synthesis and maximizing the data likelihood. These models work by traversing a forward Markov Chain where data is perturbed, followed by a reverse process where a neural network learns to undo the perturbations and recover the original data. There have been increasing efforts exploring the applications of DDPMs in the graph domain. However, most of them have focused on the generative perspective. In this paper, we aim to build a novel generative model for link prediction. In particular, we treat link prediction between a pair of nodes as a conditional likelihood estimation of its enclosing sub-graph. With a dedicated design to decompose the likelihood estimation process via the Bayesian formula, we are able to separate the estimation of sub-graph structure and its node features. Such designs allow our model to simultaneously enjoy the advantages of inductive learning and the strong generalization capability. Remarkably, comprehensive experiments across various datasets validate that our proposed method presents numerous advantages: (1) transferability across datasets without retraining, (2) promising generalization on limited training data, and (3) robustness against graph adversarial attacks.

Threshold Filtering Packing for Supervised Fine-Tuning: Training Related Samples within Packs

Packing for Supervised Fine-Tuning (SFT) in autoregressive models involves concatenating data points of varying lengths until reaching the designed maximum length to facilitate GPU processing. However, randomly concatenating data points and feeding them into an autoregressive transformer can lead to cross-contamination of sequences due to the significant difference in their subject matter. The mainstream approaches in SFT ensure that each token in the attention calculation phase only focuses on tokens within its own short sequence, without providing additional learning signals for the preceding context. To address these challenges, we introduce Threshold Filtering Packing (TFP), a method that selects samples with related context while maintaining sufficient diversity within the same pack. Our experiments show that TFP offers a simple-to-implement and scalable approach that significantly enhances SFT performance, with observed improvements of up to 7\% on GSM8K, 4\% on HumanEval, and 15\% on the adult-census-income dataset.

RIS-based Over-the-air Diffractional Channel Coding

Reconfigurable Intelligent Surfaces (RIS) are programmable metasurfaces utilizing sub-wavelength meta-atoms and a controller for precise electromagnetic wave manipulation. This work introduces an innovative channel coding scheme, termed RIS-based diffractional channel coding (DCC), which capitalizes on diffraction between two RIS layers for signal-level encoding. Contrary to traditional methods, DCC expands signal dimensions through diffraction, presenting a novel countermeasure to channel effects. This paper focuses on the operational principles of DCC, including encoder and decoder designs, and explores its possibilities to construct block and trellis codes, demonstrating its potential as both an alternative and a supplementary conventional coding scheme. Key advantages of DCC include eliminating extra power requirements for encoding, achieving computation at the speed of light, and enabling adjustable code distance, making it a progressive solution for efficient wireless communication, particularly in systems with large-scale data or massive MIMO.

Learning on Graphs with Large Language Models(LLMs): A Deep Dive into Model Robustness

Large Language Models (LLMs) have demonstrated remarkable performance across various natural language processing tasks. Recently, several LLMs-based pipelines have been developed to enhance learning on graphs with text attributes, showcasing promising performance. However, graphs are well-known to be susceptible to adversarial attacks and it remains unclear whether LLMs exhibit robustness in learning on graphs. To address this gap, our work aims to explore the potential of LLMs in the context of adversarial attacks on graphs. Specifically, we investigate the robustness against graph structural and textual perturbations in terms of two dimensions: LLMs-as-Enhancers and LLMs-as-Predictors. Through extensive experiments, we find that, compared to shallow models, both LLMs-as-Enhancers and LLMs-as-Predictors offer superior robustness against structural and textual attacks.Based on these findings, we carried out additional analyses to investigate the underlying causes. Furthermore, we have made our benchmark library openly available to facilitate quick and fair evaluations, and to encourage ongoing innovative research in this field.

GC-Bench: A Benchmark Framework for Graph Condensation with New Insights

Graph condensation (GC) is an emerging technique designed to learn a significantly smaller graph that retains the essential information of the original graph. This condensed graph has shown promise in accelerating graph neural networks while preserving performance comparable to those achieved with the original, larger graphs. Additionally, this technique facilitates downstream applications such as neural architecture search and enhances our understanding of redundancy in large graphs. Despite the rapid development of GC methods, a systematic evaluation framework remains absent, which is necessary to clarify the critical designs for particular evaluative aspects. Furthermore, several meaningful questions have not been investigated, such as whether GC inherently preserves certain graph properties and offers robustness even without targeted design efforts. In this paper, we introduce GC-Bench, a comprehensive framework to evaluate recent GC methods across multiple dimensions and to generate new insights. Our experimental findings provide a deeper insights into the GC process and the characteristics of condensed graphs, guiding future efforts in enhancing performance and exploring new applications. Our code is available at \url{https://github.com/Emory-Melody/GraphSlim/tree/main/benchmark}.