Embedding martingale diffusions as binary posteriors in sequential inference

What the math gives to ML

The paper characterizes a broad, programmable family of bounded stochastic states whose conditional mean is preserved while their variance grows until they reach a binary absorbing decision. This gives neural networks a principled confidence or routing variable: uncertainty can evolve through state-dependent noise without unconstrained logit drift, and computation can terminate when the state becomes decisive. The most direct transfer is an adaptive-depth or MoE controller whose scalar state follows a learned autonomous win-martingale, with volatility controlling how quickly examples commit to an expert or exit. The useful mathematical asset is the combination of boundedness, martingale calibration, state-dependent exploration, and eventual binary absorption.