Neural Message Passing Induced by Energy-Constrained Diffusion

2024-09-13

arXiv.org

AI Summary

Existing message-passing mechanisms in representation learning for structured data (e.g., graphs, manifolds, or implicit geometries) lack a unified theoretical foundation. Method: This paper proposes an energy-constrained diffusion-based neural message-passing framework. It establishes, for the first time, a bijective correspondence between diffusion operators and implicit energy functions, enabling derivation of a general Message Passing Neural Network (MPNN) architecture and naturally yielding a diffusion-inspired Transformer—whose global attention layer emerges from a physics-driven energy minimization process. The method integrates energy-constrained PDE modeling, manifold diffusion dynamics, finite-difference discretization, and implicit structure inference to construct a diffusion-Transformer hybrid architecture. Contribution/Results: The approach achieves state-of-the-art performance across diverse tasks—including real-world networks, images, and physical particle systems—particularly excelling in scenarios where structural information is partially or fully unknown, significantly outperforming conventional GNNs and Transformers.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Learning representations for structured data with certain geometries (observed or unobserved) is a fundamental challenge, wherein message passing neural networks (MPNNs) have become a de facto class of model solutions. In this paper, we propose an energy-constrained diffusion model as a principled interpretable framework for understanding the mechanism of MPNNs and navigating novel architectural designs. The model, inspired by physical systems, combines the inductive bias of diffusion on manifolds with layer-wise constraints of energy minimization. As shown by our analysis, the diffusion operators have a one-to-one correspondence with the energy functions implicitly descended by the diffusion process, and the finite-difference iteration for solving the energy-constrained diffusion system induces the propagation layers of various types of MPNNs operated on observed or latent structures. On top of these findings, we devise a new class of neural message passing models, dubbed as diffusion-inspired Transformers, whose global attention layers are induced by the principled energy-constrained diffusion. Across diverse datasets ranging from real-world networks to images and physical particles, we show that the new model can yield promising performance for cases where the data structures are observed (as a graph), partially observed or completely unobserved.

Problem

• Understanding MPNNs via energy-constrained diffusion model
• Unifying neural architectures under message passing framework
• Designing diffusion-inspired Transformers for diverse data structures

Innovation

• Energy-constrained diffusion model framework
• Unified perspective on neural architectures
• Diffusion-inspired Transformers with global attention