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