Semi-Markovian switching in a fluctuating harmonic trap: An age-structured formulation

What the math gives to ML

The paper provides a constructive representation of non-Markovian switching by augmenting the state with the age of the currently active regime. Its key transferable asset is an explicit hazard function, which converts arbitrary residence-time distributions into local transition rules while retaining memory of how long a regime has persisted. This suggests replacing memoryless MoE routing or latent-state transitions with an age-conditioned semi-Markov router, allowing neural modules to persist for learned durations rather than reconsidering the route independently at every token. The first practical target is a recurrent, SSM, or MoE layer where duration-aware routing can reduce temporal route jitter and improve coherent computation.