Oscillatory Neural Network with High-Order Sub-Harmonic Injection Locking

Oscillatory neural networks (ONNs), utilizing oscillator phases as a computational metric, are a promising platform for neuromorphic computing. While sub-harmonic injection locking has been used in ONNs to achieve locking at first- or second-harmonic, device-level demonstrations of high-order sub-harmonic injection locking (N^th-HIL) in ONNs with N ≥ 3, have not yet been reported. In this work, we experimentally demonstrate N^th-HIL ranging from N = 1 to 9, by employing a submicrometer-scale bistable resistor (biristor) as the oscillator. When an external signal at N times the biristor's natural frequency is injected, the output phase becomes quantized into N discrete states. We leverage this multistate phase quantization in ONNs to solve graph coloring problems and determine the corresponding chromatic numbers. These results establish a pathway for extending the computational capability of phase-based neuromorphic hardware.