DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion

Qitian Wu, Chenxiao Yang, Wentao Zhao, Yixuan He, David Wipf, Junchi Yan

Keywords: structured representation learning, diffusion model, optimization-induced model, node prediction

Abstract: Real-world data generation often involves complex inter-dependencies among instances, violating the IID-data hypothesis of standard learning paradigms and posing a challenge for uncovering the geometric structures for learning desired instance representations. To this end, we introduce an energy constrained diffusion model which encodes a batch of instances from a dataset into evolutionary states that progressively incorporate other instances' information by their interactions. The diffusion process is constrained by descent criteria w.r.t. a principled energy function that characterizes the global consistency of instance representations over latent structures. We provide rigorous theory that implies closed-form optimal estimates for the pairwise diffusion strength among arbitrary instance pairs, which gives rise to a new class of neural encoders, dubbed as DIFFormer (diffusion-based Transformers), with two instantiations: a simple version with linear complexity for prohibitive instance numbers, and an advanced version for learning complex structures. Experiments highlight the wide applicability of our model as a general-purpose encoder backbone with superior performance in various tasks, such as node classification on large graphs, semi-supervised image/text classification, and spatial-temporal dynamics prediction. The codes are available at https://github.com/qitianwu/DIFFormer.

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TL;DR: We introduce an energy constrained diffusion model for semi-supervised representation learning, based on which a new class of nerual encoders is derived for efficiently and effectively learning inter-instance latent graphs