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Why Adversarial Interaction Creates Non-Homogeneous Patterns: A Pseudo-Reaction-Diffusion Model for Turing Instability

arXiv 2010.00521 ↗First posted 1 Oct 2020cs.LG cs.CV stat.MLcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Long after Turing's seminal Reaction-Diffusion (RD) model, the elegance of his fundamental equations alleviated much of the skepticism surrounding pattern formation. Though Turing model is a simplification and an idealization, it is one of the best-known theoretical models to explain patterns as a reminiscent of those observed in nature. Over the years, concerted efforts have been made to align theoretical models to explain patterns in real systems. The apparent difficulty in identifying the specific dynamics of the RD system makes the problem particularly challenging. Interestingly, we observe Turing-like patterns in a system of neurons with adversarial interaction. In this study, we establish the involvement of Turing instability to create such patterns. By theoretical and empirical studies, we present a pseudo-reaction-diffusion model to explain the mechanism that may underlie these phenomena. While supervised learning attains homogeneous equilibrium, this paper suggests that the introduction of an adversary helps break this homogeneity to create non-homogeneous patterns at equilibrium. Further, we prove that randomly initialized gradient descent with over-parameterization can converge exponentially fast to an ε-stationary point even under adversarial interaction. In addition, different from sole supervision, we show that the solutions obtained under adversarial interaction are not limited to a tiny subspace around initialization.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 20 of its 46 references that are in the map. First posted on arXiv 1 Oct 2020.

Builds on

20 of 46 references.

References · 20

  1. 2017Improved Training of Wasserstein GANscited by 2,235
  2. 2014Conditional Generative Adversarial Netscited by 2,162
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  11. 2018Cycle-Dehaze: Enhanced CycleGAN for Single Image Dehazingcited by 79
  12. 2016Semantic Segmentation using Adversarial Networkscited by 73
8 more
  1. 2019RL-GAN-Net: A Reinforcement Learning Agent Controlled GAN Network for Real-Time Point Cloud Shape Completioncited by 58
  2. 2019Generalization in Deep Networks: The Role of Distance from Initializationcited by 51
  3. 2016Generative Image Modeling using Style and Structure Adversarial Networkscited by 50
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