FANoS-v2: Feedback-Controlled Momentum with Thermostat Damping for Lightweight Neural Optimization

FANOS is a PyTorch optimizer that augments RMS-preconditioned momentum with a scalar feedback controller over update energy. The public reference implementation stores momentum in parameter-update units, applies a non-negative thermostat damping coefficient, supports diagonal, factored, and raw-gradient preconditioning, and exposes diagnostics intended for stability audits. This study gives a complete mathematical specification of the released optimizer, including the exact parameter-unit update, the study-equation physical update mode, bounded log-ratio thermostat control, adaptive preconditioner softening, warmup guardrails, and the experimental Fast profile. We report the v0.2 evidence: five-seed reduced-sample MNIST, Fashion-MNIST, and CIFAR-10 experiments show mean top-1 gains of 0.889, 2.197, and 2.666 percentage points over AdamW for Fast, but with 49.8%, 61.6%, and 56.8% higher wall-clock time. Preliminary scientific, PINN, and EEG smoke tests are mixed and are treated as hypothesis-generating only. The evidence supports FANOS as an alpha-stage research optimizer with a reproducible lightweight-vision signal and an explicit runtime bottleneck.