Intrinsic-Noise Consolidation: A Doob-Barrier-Conditioned Diffusion Turns Analog Device Noise into a Continual-Learning Resource

What the math gives to ML

The paper converts intrinsic parameter noise into a state-dependent continual-learning force by conditioning each noisy weight trajectory to remain inside a memory-critical interval. The transferable mechanism is a Doob h-transform: its drift correction scales with noise variance, points toward the stored anchor, and becomes very large near the interval boundaries. This differs qualitatively from quadratic EWC or OU anchoring and predicts a falsifiable inverted-U relationship between noise amplitude and memory retention. The most direct neural-network application is a rehearsal-free optimizer rule applied to parameters after each task boundary.