arXiv:2608.15214 2026 Regularization 1 ideas extracted · analyzed Sep 1, 2026
The paper provides a constructive decomposition of the average effect of periodic forcing in a nonlinear cascade into local Jensen gaps propagated by downstream incremental gains. This is transferable to stacked recurrent or state-space neural networks, where oscillatory inputs and hidden-state fluctuations can create systematic mean shifts unrelated to the input mean. The most practical adaptation is a curvature-aware regularizer that measures or predicts the counterfactual constant-input output and penalizes unwanted gain of entrainment, while retaining the decomposition as a layerwise diagnostic. A second use is to deliberately shape these Jensen-gap contributions when periodic modulation is beneficial rather than harmful.
Add a mean-preserving periodic-input consistency penalty to a stacked leaky recurrent or state-space network. The penalty suppresses output shifts caused purely by hidden-state fluctuations and nonlinear curvature, improving invariance to temporal modulation while preserving the average input signal.