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"Modern AI systems are increasingly built by placing trained models inside larger computational loops. Inference-time algorithms are a basic instance of this idea: they use one or more trained models at test time to incorporate new information, exploit pretrained models as priors, and trade computational effort for accuracy, sample quality, or control. Examples include generator-verifier search for reasoning, diffusion models for solving inverse problems, and reward-guided generation. Theoretically, this revisits a classical question from optimization and theoretical computer science: what can be done with access to an oracle? Here, however, the oracles are new and non-standard: they model the capabilities of large pretrained models, making them powerful, but also imperfect because they are learned. This combination leads to new questions about algorithm design and error propagation.

This talk studies two central aspects of this paradigm: computational efficiency and error propagation. The first vignette considers generator-verifier systems, and shows how stochastic backtracking can trade additional computation for accuracy, giving a principled version of test-time scaling even with imperfect learned oracles. The second vignette studies diffusion steering: when can we efficiently bias a pretrained diffusion model toward higher-reward samples while staying close to the original model? We show that tractability depends strongly on both the reward structure and the alignment objective, and that simple primitives—such as sampling from linear tilts—can be surprisingly useful for handling richer reward classes."

Let μ(dx) ∝ e^(−U(x)) dx on ℝ^d, where U is m-strongly convex and L-smooth, and denote by κ = L/m the condition number. We consider windowed thinning, an exact simulation method for the bouncy particle sampler and the coordinate Zigzag process. The method divides a trajectory into deterministic windows and uses a gradient evaluation at the beginning of each window to construct a tractable local envelope for the event rate. Combining this construction with quantitative mixing estimates and finite-time bounds on the expected numbers of bounces and flips yields query complexity guarantees from a Gaussian cold start.

For total-variation error ε, the expected query counts are O(κ^(1/2) · d · (d log κ + log(1/ε))) gradient queries for the bouncy particle sampler and O(κ · d^(1/4) · (d log κ + log(1/ε))) full-gradient equivalents for Zigzag, where d coordinate-partial queries count as one equivalent.

Rare events such as conformational changes in biomolecules, phase transitions, and chemical reactions are central to the behavior of many physical systems, yet they are extremely difficult to study computationally because unbiased simulations seldom produce them. Transition Path Theory (TPT) provides a rigorous statistical framework for analyzing such events: it characterizes the ensemble of reactive trajectories between two designated metastable states (reactant and product), and its central object--the committor function, which gives the probability that the system will next reach the product rather than the reactant--encodes all essential kinetic and thermodynamic information. We introduce a framework that casts committor estimation as a stochastic optimal control (SOC) problem. In this formulation the committor defines a feedback control--proportional to the gradient of its logarithm--that actively steers trajectories toward the reactive region, thereby enabling efficient sampling of reactive paths. To solve the resulting hitting-time control problem we develop two complementary objectives: a direct backpropagation loss and a principled off-policy Value Matching loss, for which we establish first-order optimality guarantees. We further address metastability, which can trap controlled trajectories in intermediate basins, by introducing an alternative sampling process that preserves the reactive current while lowering effective energy barriers. On benchmark systems, the framework yields markedly more accurate committor estimates, reaction rates, and equilibrium constants than existing methods. The talk will mostly cover the manuscript https://arxiv.org/abs/2604.13213.