Attractor-Basin Failure under Transient Perturbations and the Limits of Spectral Trajectory Summaries

Abstract

We study how large transient inputs cause post-perturbation memory failure in small recurrent neural networks (RNNs), and whether spectral summaries of early hidden-state trajectories provide information beyond simpler time-domain descriptions. Mechanistically, each of three tanh memory RNNs contained two stable zero-input fixed points corresponding to the remembered bits and an intervening unstable fixed point. In the causal replication, every induced behavioral failure across all three seeds converged to the wrong semantic basin. Moving failed states toward the correct basin rescued 77.4%-96.2% of episodes; full target-fixed-point reset rescued 100%, while matched-magnitude away and random controls rescued at most 0.17%. Conversely, replacing a correct clean state with the opposite fixed point caused 100% failure, target-fixed-point replacement preserved 100% accuracy, and same-distance random interventions caused only 1.2%-8.4% failure. The spectral result was weaker. Spectral centroid and entropy improved held-out ROC AUC beyond four basic time-domain summaries, and temporal shuffling removed the initial gain. However, the increment disappeared against a 19-feature time-domain baseline and the complete ordered hidden trajectory, varied across seeds in recovery-only tests, and did not generalize consistently to a running-sum task or the completed FordB experiment. Spectral features therefore functioned as compact trajectory summaries rather than uniquely informative coordinates of the computation. Together, these complementary interventions strongly support attractor-basin switching as the mechanism underlying disturbance-induced memory failure in this synthetic, extreme-stress RNN setting. They do not establish a general runtime monitor, a uniquely spectral mechanism, or transfer of the result to broader recurrent systems. Transparency & AI Assistance Notice: This work was conducted with iterative analytical and coding assistance from Large Language Models (LLMs), including ChatGPT, Gemini, Claude, and Grok. Full conversation logs and reproduction code are documented in the paper.