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

• URL: http://arxiv.org/abs/2301.09474v4
• Date: Sun, 28 May 2023 09:19:49 GMT
• Title: DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion
• Authors: Qitian Wu, Chenxiao Yang, Wentao Zhao, Yixuan He, David Wipf, Junchi Yan
• Abstract summary: We introduce an energy constrained diffusion model which encodes a batch of instances from a dataset into evolutionary states. We provide rigorous theory that implies closed-form optimal estimates for the pairwise diffusion strength among arbitrary instance pairs. Experiments highlight the wide applicability of our model as a general-purpose encoder backbone with superior performance in various tasks.
• Score: 66.21290235237808
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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