Winfree Oscillatory Neural Network

2026-05-20

AI Summary

Existing machine learning approaches based on synchronization dynamics struggle to scale to large-scale vision tasks and complex logical reasoning. This work proposes the Winfree Oscillatory Neural Network (WONN), which evolves representations through structured oscillatory interactions on the torus $(S^1)^d$, integrating phase-based inductive biases with hierarchical dynamical mechanisms. WONN is the first method to effectively extend synchronization-based learning to ImageNet-1K while achieving remarkable parameter efficiency. It delivers strong performance across diverse benchmarks—including CIFAR, ImageNet, Maze-hard, and Sudoku—attaining 80.1% accuracy on Maze-hard with only 1% of the parameters used by previous state-of-the-art models.

Abstract

Oscillations and synchronization are widely believed to play a fundamental role in representation and computation. However, existing machine learning approaches based on synchronization dynamics have largely been confined to specialized settings such as object discovery, with limited evidence of scalability to standard vision benchmarks or logic reasoning tasks. We propose the Winfree Oscillatory Neural Network (WONN), a dynamical neural architecture based on generalized Winfree dynamics. WONN evolves representations on the torus $(S^1)^d$ through structured oscillatory interactions, combining phase-based inductive biases with flexible and hierarchical interaction mechanisms instantiated as either fixed trigonometric mappings or learnable neural networks. We evaluate WONN on image recognition and complex reasoning tasks, including CIFAR, ImageNet, Maze-hard, and Sudoku. Across these domains, WONN achieves competitive or superior performance with strong parameter efficiency. In particular, WONN is, to our knowledge, the first synchronization-based oscillatory architecture to scale competitively to ImageNet-1K. Furthermore, on Maze-hard, WONN achieves 80.1% accuracy using only 1% of the parameters of prior state-of-the-art models. These results suggest that structured oscillatory dynamics provide a scalable and parameter-efficient alternative to conventional neural architectures.

Problem

• synchronization
• scalability
• oscillatory dynamics
• vision benchmarks
• logic reasoning

Innovation

• Winfree dynamics
• oscillatory neural network
• phase-based representation
• synchronization
• parameter efficiency