Spectral Early-Warning Signals of Adaptive Fragility in Reinforcement Learning.

Modern reinforcement learning agents are typically evaluated through reward-centric metrics. However, stable reward performance may conceal latent structural degradation in the agent’s future behavioral flexibility. We investigate whether graph-spectral observables derived from rolling transition dynamics provide early-warning signals of adaptive fragility. We construct rolling transition graphs over discretized trajectory spaces and analyze the dominant eigenvalue of the resulting adjacency operator as a coarse proxy for future trajectory accessibility. We hypothesize that prolonged optimization may induce a grad- ual contraction of accessible future behavioral structure despite stable task performance — a phenomenon we term silent adaptive collapse. To test this hypothesis, we propose a falsifiable experimental protocol using PPO agents trained on CartPole under long-horizon optimization. We measure spectral trajectory dynamics during training and evaluate whether pre-perturbation spectral contraction predicts out-of-distribution robustness collapse after environmental shifts. Preliminary observations from a 100 000-step validation run confirm that spectral viability evolves non-monotonically, decorrelates from reward after task saturation, and contracts in the post-convergence phase — consistent with the proposed mechanism. We further introduce complementary observables (eigenvalue gap, effective rank, size- normalized spectral density) that partially resolve the ambiguity between genuine behavioral diversity and unstructured stochastic wandering. The framework is intentionally modest in scope. We do not propose a general theory of intelligence or cognition. We investigate whether graph-spectral trajectory observables can serve as practical robustness diagnostics for adaptive systems.