Research
Research
Research
Research
873+ open-access research outputs.
Large language model (LLM) agents increasingly operate as sequential software systems, but their reliability is often summarized by scalar benchmark metrics. Metrics such as pass$@k$, pass$^k$, and th…
Gate elimination is the primary technique for proving explicit lower bounds against general Boolean circuits, including Li and Yang's state-of-the-art $3.1n - o(n)$ bound for affine dispersers (STOC 2…
We study SINGLE-SOURCE SHORTEST PATH (SSSP) on unweighted intersection graphs whose node set corresponds to a set of $n$ constant-complexity objects in the plane. We prove SSSP can be solved in $O(U(n…
We study a variant of a polygon partition problem, introduced by Chung, Iwama, Liao, and Ahn [ISAAC'25]. Given orthogonal unit vectors $\mathbf{u},\mathbf{v}\in \mathbb{R}^2$ and a polygon $P$ with $n…
The subspace design property for additive codes is a higher-dimensional generalization of the minimum distance property. As shown recently by Brakensiek, Chen, Dhar and Zhang, it implies that the code…
We consider a fast approximation algorithm for the linear matroid intersection problem. In this problem, we are given two $r \times n$ matrices $M_1$ and $M_2$, and the objective is to find a largest …
Entropic independence is a structural property of measures that underlies modern proofs of functional inequalities, notably (modified) log-Sobolev inequalities, via ``annealing'' or local-to-global sc…
We prove two results on the mixing times of Markov chains for two-spin systems. First, we show that the Glauber dynamics mixes in polynomial time for the Gibbs distributions of antiferromagnetic two-s…
Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work on learning and testi…
Effective detection of unknown network security threats in multi-class imbalanced environments is critical for maintaining cyberspace security. Current methods focus on learning class representations …
We show that every directed graph $G$ with $n$ vertices and $m$ edges admits a directed acyclic graph (DAG) with $m^{1+o(1)}$ edges, called a DAG projection, that can either $(1+1/\text{polylog} (n))$…
We study the Subset Balancing problem: given $x \in \mathbb{Z}^n$ and a coefficient set $C \subseteq \mathbb{Z}$, find a nonzero vector $c \in C^n$ such that $c\cdot x = 0$. The standard meet-in-the-m…
Alice and Bob are given $n$-bit integer pairs $(x,y)$ and $(a,b)$, respectively, and they must decide if $y=ax+b$. We prove that the randomised communication complexity of this Point--Line Incidence p…
Minimum dominating set is a basic local covering problem and a core task in distributed computing. Despite extensive study, in the classic LOCAL model there exist significant gaps between known algori…
While first-order stationary points (FOSPs) are the traditional targets of non-convex optimization, they often correspond to undesirable strict saddle points. To circumvent this, attention has shifted…
We present a new algorithm for finding an $\epsilon$-approximate fixed point of an $\ell_\infty$-contracting function $f : [0, 1]^d \rightarrow [0, 1]^d$. Our algorithm is based on the query-efficient…
We present novel randomized approximation schemes for the Edit Distance (ED) problem and the Longest Common Subsequence (LCS) problem that, for any constant $\epsilon>0$, compute a $(1+\epsilon)$-appr…
Neighborhood graphs and clustering algorithms are fundamental structures in both computational geometry and data analysis. Visualizing them can help build insight into their behavior and properties. T…
Current AI alignment paradigms rely on behavioral correction: external supervisors (e.g., RLHF) observe outputs, judge against preferences, and adjust parameters. This paper argues that behavioral cor…
We study the complexity of approximating the partition function of dense Ising models in the critical regime. Recent work of Chen, Chen, Yin, and Zhang (FOCS 2025) established fast mixing at criticali…
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