Exact First-Passage Time Response Theory from Steady-State Response

What the math gives to ML

The paper provides a nonstandard response-theory mechanism: the transient sensitivity of a mean first-passage time can be converted exactly into a steady-state response of an auxiliary continuous-time Markov process. This is transferable to neural networks whose hidden-state evolution is modeled as a stochastic transition system, especially recurrent networks, state-space models, diffusion samplers, and neural controllers with threshold events. The most practical adaptation is a first-passage response regularizer: construct a reset auxiliary process for a desired target event, estimate its stationary occupancy under perturbations, and use the resulting response to predict and control changes in decision or sampling latency without repeatedly simulating long hitting-time trajectories.