TIDE: Asymmetric Neural Circuits for Stabilized Temporal Inhibitory-Excitatory Dynamics

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.

Existing sequence models, including RNNs, LSTMs, continuous-time networks, and Transformers, share a common structural principle: layer-wise dynamics, where all neurons in the same layer co-evolve through a shared parameterized operator, leaving individual neurons no freedom to evolve independently. Yet in many complex dynamical systems, rich global behavior emerges precisely from locally evolving units interacting through structured connectivity. Inspired by this principle, we introduce Topological Neural Dynamics (TND), a sequence modeling framework that shifts computation from layer-wise to neuron-wise dynamics. TND represents a neural system as a directed neuron graph, an interaction operator, and a local dynamics function, where each neuron evolves independently and collective computation emerges from interactions through the explicit graph topology. We instantiate TND as a discrete-time graph-coupled dynamical system and evaluate it as a case study on a behavior cloning task in single-player Pong. Compared with Vanilla RNN, Sparse RNN, LSTM, Closed-form continuous-time neural network (CfC), and Transformer baselines, TND achieves the best catch rate and a mean of 17.47 consecutive catches per round, more than three times that of the strongest baseline. These results suggest that shifting from layer-wise to neuron-wise dynamics provides an effective inductive bias for sequence modeling.

Biological neural circuits obey Dale's principle: each neuron's synapses are uniformly excitatory or inhibitory. Artificial networks that respect this constraint must coordinate separate excitatory and inhibitory populations, fundamentally changing how credit is assigned during learning. Several biologically plausible learning rules avoid backpropagation's weight transport requirement, but it has been difficult to achieve strong performance under Dale's principle beyond MNIST. Error Diffusion (ED) was originally proposed in a dual-stream excitatory/inhibitory architecture, where learning is driven by routing global error signals to all layers without transporting transposed forward weights or relying on random feedback matrices. Whether such a rule can scale under Dale's principle across both supervised classification and reinforcement learning remains unknown. Here, we introduce modulo error routing to extend Error Diffusion beyond binary classification, and show that a dual-stream excitatory/inhibitory architecture trained with this method achieves 96.7% on MNIST and establishes a 61.7% baseline on CIFAR-10, demonstrating that representation learning is possible even when strictly enforcing Dale's principle. For the classification setting, we introduce three domain-specific innovations: layer-specific sigmoid widths, batch-centered class error signals, and asymmetric initialization, and ablation analysis reveals that their relative importance reverses between MNIST and CIFAR-10, exposing task-dependent credit-assignment bottlenecks invisible to single-benchmark evaluation. In reinforcement learning, we integrate ED with Proximal Policy Optimization (PPO) and evaluate it on continuous-control tasks in Google Brax and on Craftax, an open-ended exploration task. We show that ED-PPO achieves competitive performance relative to Direct Feedback Alignment, a backpropagation-free baseline.