10 papers
Learning Situation-Conditioned Thinking Policies for Long-Term LLM Agents
Hong Su
Long-running autonomous agents must reuse accumulated reasoning experience without allowing explicit historical memory and LLM context to grow indefinitely. However, existing memor…
Theoretical guarantees for stochastic gradient Langevin dynamics
Daniel Paulin, Peter A. Whalley
We prove asymptotic bias bounds for stochastic gradient Langevin dynamics in Wasserstein distance of order two. We assume that the negative log-density is strongly convex with a Li…
Training-Free Generative Sampling via Moment-Matched Score Smoothing
Zhenyu Yao, Daniel Paulin
Diffusion models generate samples by denoising along the score of a perturbed target distribution. In practice, one trains a neural diffusion model, which is computationally expens…
Theoretical guarantees for stochastic gradient sampling methods via Gaussian convolution inequalities
Daniel Paulin, Peter A. Whalley
We derive first-order (in the stepsize) bounds on the bias in Wasserstein distances of the invariant measure of stochastic gradient kinetic Langevin dynamics with minimal assumptio…
Infinite-dimensional generative diffusions via Doob's h-transform
Thorben Pieper-Sethmacher, Daniel Paulin
This paper introduces a rigorous framework for defining generative diffusion models in infinite dimensions via Doob's h-transform. Rather than relying on time reversal of a noising…
A Semiparametric Discrete Hawkes Model with a Collapsed Gaussian-Process Prior
Trinnhallen Brisley, Gordon Ross, Daniel Paulin
Hawkes processes are used in settings where past events increase the likelihood of future events occurring, resulting in a natural clustering structure. Traditional Hawkes process…
Divide, Interact, Sample: The Two-System Paradigm
James Chok, Myung Won Lee, Daniel Paulin +1
Mean-field, ensemble-chain, and adaptive samplers have historically been viewed as distinct approaches to Monte Carlo sampling. In this paper, we present a unifying {two-system} fr…
Sampling from Bayesian Neural Network Posteriors with Symmetric Minibatch Splitting Langevin Dynamics
Daniel Paulin, Peter A. Whalley, Neil K. Chada +1
We propose a scalable kinetic Langevin dynamics algorithm for sampling parameter spaces of big data and AI applications. Our scheme combines a symmetric forward/backward sweep over…
Correction to "Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations"
Daniel Paulin, Peter A. Whalley
A method for analyzing non-asymptotic guarantees of numerical discretizations of ergodic SDEs in Wasserstein-2 distance is presented by Sanz-Serna and Zygalakis in ``Wasserstein di…
Unbiased Kinetic Langevin Monte Carlo with Inexact Gradients
Neil K. Chada, Benedict Leimkuhler, Daniel Paulin +1
We present an unbiased method for Bayesian posterior means based on kinetic Langevin dynamics that combines advanced splitting methods with enhanced gradient approximations. Our ap…