Schindler's Duffing ring beats FFT for shape discrimination at low SNR
A driven ring's broken symmetry yields a single-number observable that outperforms classical spectral analysis.
Kaspar Anton Schindler's arXiv paper studies bundling and binding operations on a cycle graph of N nodes under a single master equation. The linear regime sorts temporal input across U(1)-organized eigenmodes, matching a windowed-FFT baseline at high SNR and modestly outperforming it for transient signals at low SNR. The Duffing regime activates cubic mode-mixing with a symmetry-constrained selection rule on integer wavenumbers, generating shape-dependent harmonic content. A single-number observable φ₀ summarizes the bound representation’s response to input shape, with exact π-periodicity in the shape parameter; time-reversal symmetry that would render φ₀ degenerate is broken by dissipation. Numerical experiments confirm φ₀ retains its information content under additive band-limited noise, with seed-averaged means staying clearly above the symmetric-attractor value down to 0 dB input SNR. The framework is developed on synthetic signals only.
- The Duffing ring (cycle graph + cubic nonlinearity) breaks time-reversal symmetry via dissipation, enabling shape discrimination with a single scalar φ₀.
- φ₀ outperforms windowed-FFT for transient signals at low SNR (down to 0 dB) while matching it at high SNR.
- The work uses a physical substrate metaphor—bundling and binding—to connect nonlinear dynamics with distributed computation.
Why It Matters
A single-number measure from a simple physical system could inspire low-power, noise-robust analog signal processing hardware.