Gradient Descent Through Quantum Wave Dynamics: WDDS-v3 and WDDS-v3.1 for Physics-Native Reinforcement Learning

This work presents WDDS-v3 and WDDS-v3.1, physics-native reinforcement-learning architectures in which policy-relevant representations are generated through differentiable Schrödinger-type wave dynamics. The framework uses a learnable potential field and FFT-based wave evolution, allowing gradients to propagate through wave-field computation while preserving the wave-dynamical substrate as the core processing mechanism. WDDS-v3.1 adds stabilization mechanisms for continuous control, including action smoothing, reward normalization, checkpoint restoration, behavioral-cloning replay from high-return trajectories, and exploration-noise decay. Across discrete control, signal navigation, and continuous-control benchmarks, WDDS demonstrates strong learning gains, high best-case discovery, and improved continuous-control stability. On HalfCheetah-v4, WDDS-v3.1 achieves a mean return of -11.46 over 3 seeds and 100 episodes, compared with -48.76 for WDDS-v3-Phase3 and -60.40 for the random baseline. On SignalNav-v0, WDDS-v3 reaches a best episode score of 259.7, indicating strong best-case wave-field policy discovery. These results support WDDS as a promising wave-based adaptive computation framework for physics-inspired reinforcement learning.