We present a neural architecture where the only learnable transform is the transfer function of a damped harmonic oscillator: H (w) = 1/ (w0² - w² + 2igw). Each oscillator has two learnable parameters — natural frequency w0 and damping g — which are physically meaningful and directly interpretable. The architecture decomposes signals via an oscillator bank (FFT, transfer function multiplication, IFFT), processes oscillator states through attention, and resynthesizes via weighted additive synthesis. We validate with three experiments: (1) a tautology test where the network learns to replicate a state variable filter at 22. 6 dB SNR, discovering a distributed multi-oscillator solution; (2) causal speech generation where a 411K parameter model produces a continuation of a voice clip at 26. 4 dB SNR — continuous-valued autoregressive audio generation without a tokenizer or codec; and (3) a causal oscillator language model that achieves 1. 34 BPB on FineWeb at 14. 8M parameters — within 0. 12 of the transformer baseline — by encoding each token as a physical impulse whose damped resonance creates temporal context through physics rather than learned position embeddings. The architecture is provably an energy-based model, with damping guaranteeing deterministic convergence. Code is available at https: //github. com/rolandnsharp/resonance.
Roland Hall Sharp (Mon,) studied this question.