Brice Huang

activity

20182026

most citedCyclic Descents for General Skew Tableaux

13 citations · 42 across the 23 of their papers we have counts for

collaborators

25 papers

math.PR2026

Sampling from the Sherrington-Kirkpatrick Model up to Criticality

Hang Du, Brice Huang, Sidhanth Mohanty +1

We prove that the simulated annealing algorithm efficiently samples from the Sherrington-Kirkpatrick model at inverse temperature $β < 1$ to an arbitrary inverse polynomial accuracy…

math.PR2026

Algorithmic threshold for high-dimensional projection pursuit I: general theory

Brice Huang, Mark Sellke, Nike Sun

We study a null model of high-dimensional projection pursuit: we are given $M$ points sampled i.i.d. from a standard gaussian in $N$ dimensions, where $M, N \to \infty$ with $M/N\toα\…

math.PR2026

Overlap distribution of the critical Sherrington-Kirkpatrick model

Hang Du, Brice Huang

We study the distribution of the two-replica overlap $R_{1, 2}$ in the Ising and spherical Sherrington-Kirkpatrick models at the critical inverse temperature $β = 1$ . Our main result…

math.PR2026

Fluctuations of the Sherrington-Kirkpatrick free energy at critical temperature

Hang Du, Brice Huang

We consider the Sherrington-Kirkpatrick spin glass model at the critical inverse temperature $β = 1$ with zero external field. We prove that the free energy $F_{N} = F_{N, β = 1}$ of thi…

cs.CC2026

Stable algorithms cannot reliably find isolated perceptron solutions

Shuyang Gong, Brice Huang, Shuangping Li +1

We study the binary perceptron, a random constraint satisfaction problem that asks to find a Boolean vector in the intersection of independently chosen random halfspaces. A strikin…

cs.DS2025

On zeros and algorithms for disordered systems: mean-field spin glasses

Ferenc Bencs, Brice Huang, Daniel Z. Lee +2

Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statisti…

cond-mat.dis-nn2025

Strong Low Degree Hardness for Stable Local Optima in Spin Glasses

Brice Huang, Mark Sellke

It is a folklore belief in the theory of spin glasses and disordered systems that out-of-equilibrium dynamics fail to find stable local optima exhibiting e.g. local strict convexit…

math.PR2024

Weak Poincaré Inequalities, Simulated Annealing, and Sampling from Spherical Spin Glasses

Brice Huang, Sidhanth Mohanty, Amit Rajaraman +1

There has been a recent surge of powerful tools to show rapid mixing of Markov chains, via functional inequalities such as Poincaré inequalities. In many situations, Markov chains…

math.PR2024★ 1 cited

Sampling from Spherical Spin Glasses in Total Variation via Algorithmic Stochastic Localization

Brice Huang, Andrea Montanari, Huy Tuan Pham

We consider the problem of algorithmically sampling from the Gibbs measure of a mixed $p$ -spin spherical spin glass. We give a polynomial-time algorithm that samples from the Gibbs…

math.PR2024

Capacity threshold for the Ising perceptron

Brice Huang

We show that the capacity of the Ising perceptron is with high probability upper bounded by the constant $α_{⋆} \approx 0.833$ conjectured by Krauth and Mézard, under the conditi…

math.PR2023

A Constructive Proof of the Spherical Parisi Formula

Brice Huang, Mark Sellke

The Parisi formula for the free energy is among the crown jewels in the theory of spin glasses. We present a simpler proof of the lower bound in the case of the spherical mean-fiel…

math.PR2023

Strong Topological Trivialization of Multi-Species Spherical Spin Glasses

Brice Huang, Mark Sellke

We study the landscapes of multi-species spherical spin glasses. Our results determine the phase boundary for annealed trivialization of the number of critical points, and establis…

math.PR2023

Optimization Algorithms for Multi-Species Spherical Spin Glasses

Brice Huang, Mark Sellke

This paper develops approximate message passing algorithms to optimize multi-species spherical spin glasses. We first show how to efficiently achieve the algorithmic threshold ener…

math.PR2023★ 1 cited

Algorithmic Threshold for Multi-Species Spherical Spin Glasses

Brice Huang, Mark Sellke

We study efficient optimization of the Hamiltonians of multi-species spherical spin glasses. Our results characterize the maximum value attained by algorithms that are suitably Lip…

math.CO2022★ 1 cited

Improved Lower Bound for Frankl's Union-Closed Sets Conjecture

Ryan Alweiss, Brice Huang, Mark Sellke

We verify an explicit inequality conjectured recently by Gilmer, thus proving that for any nonempty union-closed family $F \subseteq 2^{[n]}$ , some $i \in [n]$ is contained in at le…

math.ST2022★ 1 cited

Threshold for Detecting High Dimensional Geometry in Anisotropic Random Geometric Graphs

Matthew Brennan, Guy Bresler, Brice Huang

In the anisotropic random geometric graph model, vertices correspond to points drawn from a high-dimensional Gaussian distribution and two vertices are connected if their distance…

quant-ph2022★ 6 cited

When Does Adaptivity Help for Quantum State Learning?

Sitan Chen, Brice Huang, Jerry Li +2

We consider the classic question of state tomography: given copies of an unknown quantum state $ρ \in C^{d \times d}$ , output $ρ$ which is close to $ρ$ in some sense,…

quant-ph2022★ 1 cited

Tight Bounds for Quantum State Certification with Incoherent Measurements

Sitan Chen, Brice Huang, Jerry Li +1

We consider the problem of quantum state certification, where we are given the description of a mixed state $σ \in C^{d \times d}$ , $n$ copies of a mixed state $ρ\in \mathb…

math.PR2021★ 2 cited

Tight Lipschitz Hardness for Optimizing Mean Field Spin Glasses

Brice Huang, Mark Sellke

We study the problem of algorithmically optimizing the Hamiltonian $H_{N}$ of a spherical or Ising mixed $p$ -spin glass. The maximum asymptotic value $OPT$ of $H_{N} / N$ is cha…

cs.CC2021

The Algorithmic Phase Transition of Random $k$ -SAT for Low Degree Polynomials

Guy Bresler, Brice Huang

Let $Φ$ be a uniformly random $k$ -SAT formula with $n$ variables and $m$ clauses. We study the algorithmic task of finding a satisfying assignment of $Φ$ . It is known that satisfyi…

math.PR2021★ 7 cited

De Finetti-Style Results for Wishart Matrices: Combinatorial Structure and Phase Transitions

Matthew Brennan, Guy Bresler, Brice Huang

A recent line of work has studied the relationship between the Wishart matrix $X^{⊤} X$ , where $X \in R^{d \times n}$ has i.i.d. standard Gaussian entries, and the correspo…

math.CO2018★ 6 cited

An Upper Bound on the Number of $(132, 213)$ -Avoiding Cyclic Permutations

Brice Huang

We show a $n^{2} \cdot 2^{n /2}$ upper bound on the number of $(132, 213)$ avoiding cyclic permutations. This is the first nontrivial upper bound on the number of such permutations. We…

math.CO2018★ 13 cited

Cyclic Descents for General Skew Tableaux

Brice Huang

A cyclic descent function on standard Young tableaux of size $n$ is a function that restricts to the usual descent function when $n$ is omitted, such that the number of standard Yo…

math.CO2018★ 1 cited

On the Local Geometry of Graphs in Terms of Their Spectra

Brice Huang, Mustazee Rahman

In this paper we consider the relation between the spectrum and the number of short cycles in large graphs. Suppose $G_{1}, G_{2}, G_{3}, \dots$ is a sequence of finite and connected gr…

Sampling from the Sherrington-Kirkpatrick Model up to Criticality

Algorithmic threshold for high-dimensional projection pursuit I: general theory

Overlap distribution of the critical Sherrington-Kirkpatrick model

Fluctuations of the Sherrington-Kirkpatrick free energy at critical temperature

Stable algorithms cannot reliably find isolated perceptron solutions

On zeros and algorithms for disordered systems: mean-field spin glasses

Strong Low Degree Hardness for Stable Local Optima in Spin Glasses

Weak Poincaré Inequalities, Simulated Annealing, and Sampling from Spherical Spin Glasses

Sampling from Spherical Spin Glasses in Total Variation via Algorithmic Stochastic Localization

Capacity threshold for the Ising perceptron

A Constructive Proof of the Spherical Parisi Formula

Strong Topological Trivialization of Multi-Species Spherical Spin Glasses

Optimization Algorithms for Multi-Species Spherical Spin Glasses

Algorithmic Threshold for Multi-Species Spherical Spin Glasses

Improved Lower Bound for Frankl's Union-Closed Sets Conjecture

Threshold for Detecting High Dimensional Geometry in Anisotropic Random Geometric Graphs

When Does Adaptivity Help for Quantum State Learning?

Tight Bounds for Quantum State Certification with Incoherent Measurements

Tight Lipschitz Hardness for Optimizing Mean Field Spin Glasses

The Algorithmic Phase Transition of Random k-SAT for Low Degree Polynomials

De Finetti-Style Results for Wishart Matrices: Combinatorial Structure and Phase Transitions

An Upper Bound on the Number of (132,213)-Avoiding Cyclic Permutations

Cyclic Descents for General Skew Tableaux

On the Local Geometry of Graphs in Terms of Their Spectra

The Algorithmic Phase Transition of Random $k$ -SAT for Low Degree Polynomials

An Upper Bound on the Number of $(132, 213)$ -Avoiding Cyclic Permutations