Robust Langevin Sampling under State-Dependent Heavy-Tailed Noise with Applications to LLM Fine-Tuning

arXiv:2610.12865v1 Announce Type: new Abstract: Existing convergence guarantees for non-log-concave sampling with stochastic gradient Langevin Monte Carlo (SG-LMC) typically assume globally Lipschitz gradients and uniformly bounded noise variance. Both assumptions can fail even in elementary sampling problems, and relaxing them better reflects practical applications such as Bayesian fine-tuning of large language models (LLMs). We relax both assumptions through generalized smoothness and our proposed state-dependent heavy-tailed oracle with finite $p$-th moments, $1