Selected recent publications

* means equal contribution. A complete list is on my CV and Google Scholar.

Dimension-Independent Convergence of Underdamped Langevin Monte Carlo in KL Divergence

Shiyuan Zhang*, Qiwei Di*, Xuheng Li*, Quanquan Gu. ICML 2026. arXiv

  • First dimension-independent KL convergence bounds for discretized underdamped Langevin dynamics.
  • The rates depend on $\mathrm{tr}(\mathbf{H})$ (an upper bound on the Hessian of $V$), not on the ambient dimension $d$.
  • In the strongly convex setting, ULMC improves over overdamped Langevin whenever $\mathrm{tr}(\mathbf{H})\ll d$.
  • In the convex setting, we also obtain the first dimension-free KL rates for standard ULMC and the randomized midpoint discretization.

On the Limits of Test-Time Compute: Sequential Reward Filtering for Better Inference

Yue Yu, Qiwei Di, Quanquan Gu, Dongruo Zhou. ICML 2026. arXiv

  • Analyze test-time compute under a mixture-of-reference-policies model, and prove that standard best-of-$n$ is inherently suboptimal.
  • Propose reward-filtered sequential inference: only high-reward generations are written back into the context.
  • This concentrates later samples on better policies and drops poor candidates.
  • The method has strictly stronger guarantees than best-of-$n$, and it improves over common TTC baselines on reasoning benchmarks.

Best-of-Majority: Minimax-Optimal Strategy for Pass@$k$ Inference Scaling

Qiwei Di*, Kaixuan Ji*, Xuheng Li*, Heyang Zhao, Quanquan Gu. ICLR 2026. arXiv

  • Study Pass@$k$ inference, where the model may submit $k$ answers.
  • Prove that majority voting and best-of-$N$ do not scale correctly in both $k$ and the sampling budget $N$.
  • Best-of-Majority keeps high-frequency answers among $N$ samples, then selects the top-$k$ by reward.
  • When $N=\tilde{\Omega}(C^*)$, the regret is $O\bigl(\epsilon_{\mathrm{opt}}+\sqrt{\epsilon_{\mathrm{RM}}^2 C^*/k}\bigr)$, matching a lower bound for any Pass@$k$ rule.
  • Unlike majority voting and best-of-$N$, the bound does not degrade as $N$ grows. BoM also outperforms both on math reasoning tasks.