7 papers
The Depth Ceiling: On the Limits of Large Language Models in Discovering Latent Planning
Yi Xu, Philipp Jettkant, Laura Ruis
The viability of chain-of-thought (CoT) monitoring hinges on models being unable to reason effectively in their latent representations. Yet little is known about the limits of such…
Particle Systems and McKean--Vlasov Dynamics with Singular Interaction through Local Times
Graeme Baker, Ben Hambly, Philipp Jettkant
We study a system of reflected Brownian motions on the positive half-line in which each particle has a drift toward the origin determined by the local times at the origin of all th…
The Atlas Model and SDEs with Boundary Interaction
Philipp Jettkant
We study the mean-field limit of the Atlas model and its connection to SDEs with dependence on the distribution of hitting and local times. The Atlas model describes a system of Br…
Control of McKean--Vlasov SDEs with Contagion Through Killing at a State-Dependent Intensity
Ben Hambly, Philipp Jettkant
We consider a novel McKean--Vlasov control problem with contagion through killing of particles and common noise. Each particle is killed at an exponential rate according to an inte…
Control of Conditional Processes and Fleming--Viot Dynamics
Philipp Jettkant
We discuss equivalent formulations of the control of conditional processes introduced by Lions. In this problem, a controlled diffusion process is killed once it hits the boundary…
Optimal Control of the Nonlinear Stochastic Fokker--Planck Equation
Ben Hambly, Philipp Jettkant
We consider a control problem for the nonlinear stochastic Fokker--Planck equation. This equation describes the evolution of the distribution of nonlocally interacting particles af…