A new probabilistic approach for mean field games of optimal stopping

What the math gives to ML

The paper introduces randomized stopping through an adapted, non-increasing càdlàg process L taking values in [0,1], and represents equilibria with reflected forward-backward McKean–Vlasov dynamics. The transferable asset is a disciplined survival process: stopping mass can be distributed across time, while interactions depend on the occupation measure of agents that have not stopped. This suggests an adaptive-computation module for Transformers or MoE systems in which tokens have monotone survival probabilities, termination incurs a compute cost, and routing statistics are computed over the surviving population. The reflected optimality conditions can be approximated by an obstacle/complementarity loss rather than allowing unconstrained, oscillatory halting probabilities.