Winfree Oscillatory Neural Network

TL;DR

The paper introduces the Winfree Oscillatory Neural Network (WONN), a scalable, parameter-efficient architecture based on oscillatory dynamics, demonstrating competitive performance on vision and reasoning tasks including ImageNet and Sudoku.

Contribution

WONN is the first to scale synchronization-based oscillatory neural networks to large benchmarks like ImageNet-1K, combining phase-based biases with learnable interactions for improved efficiency.

Findings

WONN achieves competitive performance on CIFAR and ImageNet.

On Maze-hard, WONN attains 80.1% accuracy with only 1% of prior model parameters.

WONN scales effectively to complex reasoning tasks using structured oscillatory dynamics.

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.