Эксперимент: Frequency-Response Regularization for Neural Dynamics (#1345)

{ "worked": true, "confidence": 8, "verdict": "Built a self-contained discrete-time RNN frequency-response regularizer and reproducible experiment. The toy check clearly reproduced the claimed nonnormal phenomenon: two matrices with identical stable eigenvalues and spectral radius 0.72 had a 17.8x difference in resolvent peak, while the nonnormal matrix showed 10.18x transient gain. In the RNN experiment, frequency regularization reduced the final resolvent peak by 54.4% versus baseline, but slightly worsened task loss by 0.0135, so it controlled sensitivity without demonstrating an accuracy win.", "metrics": { "baseline": "final task loss 0.5048; resolvent peak 3.6520; spectral radius 1.7548", "idea": "final task loss 0.5182; resolvent peak 1.6644; spectral radius 1.7254; peak reduction 54.4%" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 frequency_response_experiment.py", "files": [ "frequency_response_experiment.py", "results.json" ], "limitations": "The training comparison used one fixed seed, a tiny 8-unit tanh RNN, and a short sequence-to-sum task. The regularizer used exact linearization at zero state rather than minibatch local Jacobians, no spectral-radius-regularized control was run, and the trained recurrent matrices remained above unit spectral radius, so this is evidence for peak control rather than a complete stability result." }