Zobrazeno 1 - 10
of 43
pro vyhledávání: '"Huang, Brice"'
Autor:
Huang, Brice
We show that the capacity of the Ising perceptron is with high probability upper bounded by the constant $\alpha_\star \approx 0.833$ conjectured by Krauth and M\'ezard, under the condition that an explicit two-variable function $\mathscr{S}_\star(\l
Externí odkaz:
http://arxiv.org/abs/2404.18902
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 measure up to vanishing total variation error, for any model whose mi
Externí odkaz:
http://arxiv.org/abs/2404.15651
Autor:
Huang, Brice, Sellke, Mark
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-field model. Our method follows the TAP approach developed recently in e.g
Externí odkaz:
http://arxiv.org/abs/2311.15495
Autor:
Huang, Brice, Sellke, Mark
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 establish its equivalence with a quenched \emph{strong topological trivializat
Externí odkaz:
http://arxiv.org/abs/2308.09677
Autor:
Huang, Brice, Sellke, Mark
This paper develops approximate message passing algorithms to optimize multi-species spherical spin glasses. We first show how to efficiently achieve the algorithmic threshold energy identified in our companion work, thus confirming that the Lipschit
Externí odkaz:
http://arxiv.org/abs/2308.09672
Autor:
Huang, Brice, Sellke, Mark
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 Lipschitz with respect to the disorder through a variational principle th
Externí odkaz:
http://arxiv.org/abs/2303.12172
Autor:
Huang, Brice
We study the limits of efficient algorithms in random optimization problems. In these problems, we are given a random objective function and our goal is to find an input achieving a large output. These problems often exhibit information-computation g
Externí odkaz:
https://hdl.handle.net/1721.1/143164
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 least a $\frac{3-\sqrt{5}}{2} \approx 0.38$ fraction of the sets in $F$.
Externí odkaz:
http://arxiv.org/abs/2211.11731
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 is smaller than a specified threshold. We study when it is possible to
Externí odkaz:
http://arxiv.org/abs/2206.14896
We consider the classic question of state tomography: given copies of an unknown quantum state $\rho\in\mathbb{C}^{d\times d}$, output $\widehat{\rho}$ which is close to $\rho$ in some sense, e.g. trace distance or fidelity. When one is allowed to ma
Externí odkaz:
http://arxiv.org/abs/2206.05265