Kuramoto & oscillator Ising machines. Coupled-oscillator synchronization is textbook nonlinear dynamics; oscillator Ising machines (Wang & Roychowdhury) solve optimisation by phase. Solid and demonstrated.
Oscillatory neural nets. Real hardware — four spin-torque nano-oscillators recognised spoken vowels (Romera & Grollier, Nature 2018); VO₂ & CMOS ONNs exist — but small and finicky to scale.
Large phase-computing nets. Scaling oscillator networks into general learning machines, with stable precision, is open.
A swarm of oscillators, each with its own natural rhythm, scattered around the phase circle. With no coupling they drift independently and the crowd is a smear. Turn the coupling K up and each one feels a pull toward the others — dθᵢ/dt = ωᵢ + (K/N) Σⱼ sin(θⱼ − θᵢ) — until, past a threshold, the smear snaps into a single moving cluster. The length of the order vector is how synchronized they are: 0 for chaos, 1 for one mind.
Encode a bit as a phase: lock to the reference (in-phase, +1) or sit a half-cycle off it (anti-phase, −1). Feed two such inputs to an output oscillator through weighted couplings; it feels the net pull and locks in-phase when the weighted vote is positive, anti-phase when negative. Read its phase against the reference and you've read a thresholded weighted sum — a perceptron whose output is whether it ended up beating with you or against you.
Wire oscillators with signed couplings and let them settle — they relax to the phase pattern that satisfies the most couplings, which is exactly minimising an Ising energy. A triangle that all wants to disagree can't win everywhere: it lands two-against-one, the best a frustrated graph allows. The neuron learns AND/OR; XOR is one cut, so it needs more oscillators (depth). The gift is that relaxation is the computation — no clocked steps, just a network humming its way to the answer.
Honest place in the family: oscillator networks shine at optimisation and pattern completion — letting a system relax rather than step. They overlap the noise body (both minimise an energy) but the variable is different: deterministic phase, not thermal chance. It's the audit's last distinct avenue, and now it's filled.