Use the trajectory martingale decomposition to separate predictable training updates from genuinely unpredictable residual updates, then scale the residual according to its estimated response to future loss. The method targets stochastic or event-driven optimization with history-dependent samples and predicts that response-weighted residual energy, rather than total gradient variance, controls update noise and instability.
Paper: The Memory Hidden in Response Fluctuations: Trajectory-Level Fluctuation-Response Theory and Inequalities for Non-Markovian Jump DynamicsarXiv:2608.20328
Replace the raw DFA outer-product update with a damped left-right preconditioned update that whitens both presynaptic activity directions and local-error directions. The activity factor removes nuisance-dominated input anisotropy, while the error factor equalizes postsynaptic credit coordinates; separate damping prevents noisy error covariances from destabilizing training.