1 citations · 1 across the 7 of their papers we have counts for
8 papers
On the Cardinality of the Smith Set Under Impartial Culture with Many Alternatives
Zachary Berchenko, Kaizhao Liu
For some integer , consider voters, each of which has a preference ranking over alternatives. The Smith set is the smallest nonempty set of alternatives…
Propagation of Chaos in Contextual Flow Maps
Shi Chen, Zhengjiang Lin, Kaizhao Liu +1
We develop a quantitative statistical theory of transformers in the large-context regime by adopting the abstraction of contextual flow maps (CFMs): dynamical systems that evolve a…
Theoretical Tensions in RLHF: Reconciling Empirical Success with Inconsistencies in Social Choice Theory
Jiancong Xiao, Zhekun Shi, Kaizhao Liu +2
Despite its empirical success, Reinforcement Learning from Human Feedback (RLHF) has been shown to violate almost all the fundamental axioms in social choice theory -- such as majo…
Fundamental Limits of Game-Theoretic LLM Alignment: Smith Consistency and Preference Matching
Zhekun Shi, Kaizhao Liu, Qi Long +2
Nash Learning from Human Feedback is a game-theoretic framework for aligning large language models (LLMs) with human preferences by modeling learning as a two-player zero-sum game.…
Statistical Impossibility and Possibility of Aligning LLMs with Human Preferences: From Condorcet Paradox to Nash Equilibrium
Kaizhao Liu, Qi Long, Zhekun Shi +2
Aligning large language models (LLMs) with diverse human preferences is critical for ensuring fairness and informed outcomes when deploying these models for decision-making. In thi…
Error Bounds for Open Quantum Systems with Harmonic Bosonic Bath
Kaizhao Liu, Jianfeng Lu
We investigate the dependence of physical observable of open quantum systems with Bosonic bath on the bath correlation function. We provide an error estimate of the difference of p…
Orthogonal Bootstrap: Efficient Simulation of Input Uncertainty
Kaizhao Liu, Jose Blanchet, Lexing Ying +1
Bootstrap is a popular methodology for simulating input uncertainty. However, it can be computationally expensive when the number of samples is large. We propose a new approach cal…
The Local Landscape of Phase Retrieval Under Limited Samples
Kaizhao Liu, Zihao Wang, Lei Wu
In this paper, we present a fine-grained analysis of the local landscape of phase retrieval under the regime of limited samples. Specifically, we aim to ascertain the minimal sampl…