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Winfree Oscillatory Neural Network
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Proposes WONN, a neural architecture built on generalized Winfree oscillator dynamics on a torus, which scales to ImageNet-1K and reaches 80.1% on Maze-hard with 0.396M parameters via energy voting.
Problem
Whether synchronization-based oscillator dynamics can scale beyond object discovery to standard vision benchmarks (CIFAR, ImageNet) and to combinatorial reasoning (Maze-hard, Sudoku) in a parameter-efficient way.
Approach
Replaces Kuramoto pairwise-phase coupling with generalized Winfree dynamics (separable sensitivity and influence functions) on the torus (S^1)^d, with grouped hierarchical interactions, attention-based global coupling, and a dual phase-frequency state; the interaction can be fixed trigonometric or learnable MLPs, and trigonometric variants admit an interaction energy used for test-time voting.
Key results
- On Maze-hard, WONN reaches 76.2% with 0.396M parameters and 80.1% with energy voting over 32 trajectories, versus HRM 74.5% at 27M.
- On CIFAR-10 WONN (Ch=256 to 256, MLP) reaches 95.24% with 12.02M parameters, above ResNet-50 at 94.22% with 23.52M.
- On ImageNet-1K WONN reaches 76.78% with 12.28M parameters, close to ResNet-50's 76.89% with 25.56M.
Surprising findings
- WONN reaches perfect 100.0% on Sudoku with 1.58M parameters, matching R-Transformer.
- Trigonometric and MLP interaction functions perform similarly, suggesting gains come from the oscillatory structure rather than parameterization.
Limitations
- Recurrent dynamics add computation cost relative to feed-forward ResNets and ViTs.
- Scaling to larger models and language modeling is left unexplored.
- Energy voting requires sampling 32 trajectories at inference.
Experimental setup
Datasets: CIFAR-10 CIFAR-100 ImageNet-100 ImageNet-1K Maze-hard Sudoku
Benchmarks: CIFAR-10 CIFAR-100 ImageNet-100 ImageNet-1K Maze-hard Sudoku
Metrics: accuracy parameter count
Baselines: ResNet-18 ResNet-50 ViT AKOrN HRM TRM DeepSeek-R1 Claude 3.7 o3-mini
Builds on: AKOrN Winfree model Kuramoto model HRM
Closest papers by meaning
- Artificial Kuramoto Oscillatory Neurons (ICLR 2025 · similarity 0.85)
- From Cortical Synchronous Rhythm to Brain Inspired Learning Mechanism: An Oscillatory Spiking Neural Network with Time-Delayed Coordination (NeurIPS 2026 · similarity 0.85)
- Unconditional stability of a recurrent neural circuit implementing divisive normalization (NeurIPS 2024 · similarity 0.85)
- Recurrent neural network dynamical systems for biological vision (NeurIPS 2024 · similarity 0.85)
- Mechanistic Interpretability of RNNs emulating Hidden Markov Models (NeurIPS 2025 · similarity 0.84)
- C-Voting: Confidence-Based Test-Time Voting without Explicit Energy Functions (ICLR 2026 · similarity 0.84)
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