Fixed, Learned, or Both? A Machine-Learning Study of Self-Calibrating Gated Couplings of Transform Dictionaries and Learned Unitary Bases for Compact Signal Classification

Code and paper for a study comparing three front-ends into one shared self-organizing classification head: S1, a pooled dictionary of fixed transforms (Fourier, wavelets, scattering); S2, a single orthogonal transform learned from scratch as a unitary matrix U = exp(C - C^H); and S3/S3+, a gated coupling of the two whose L1-pruned protective gate self-calibrates to the data, collapsing to the cheap dictionary where it suffices and engaging the learned transform only where it helps. Includes break-even analysis, warm-start reachability fix, robustness and SINR sweeps, parameter/convergence cost vs spiking (LIF) and deep-MLP baselines, validation on four real datasets (handwritten digits, ECG, GunPoint, Coffee), a directional (shearlet-like) extension, and a transform-discovery suite that reads the learned matrix U to recover clean, reusable, data-specific transforms. All figures are regenerated by short deterministic scripts; results are reported over 5 seeds with error bars.