Asymptotics of input-constrained binary symmetric channel capacity

高信噪比渐进行为的熵约束高斯信道容量

High signal-to-noise ratio asymptotics of entropy-constrained Gaussian channel capacity

本文研究了高信噪比下熵约束高斯信道容量的行为，证明了容量达到分布为离散高斯分布，并刻画了熵与容量差距的指数衰减特性。

关于基于矩问题的熵约束高斯信道容量

On entropy-constrained Gaussian channel capacity via the moment problem

本文研究输入端带有熵约束的功率受限加性高斯信道容量，通过证明矩匹配问题的一般结果，刻画了低信噪比与小熵条件下的容量，并指出具有正小熵的离散变量最多能匹配连续变量的三个初始矩。

Space-time large deviations in capacity-constrained relay networks

We consider a single-cell network of random transmitters and fixed relays in a bounded domain of Euclidean space. The transmitters arrive over time and select one relay according to a spatially inhomogeneous preference kernel. Once a transmitter is connected to a relay, the connection remains and the relay is occupied. If an occupied relay is selected by another transmitters with later arrival time, this transmitter becomes frustrated. We derive a large deviation principle for the space-time evolution of frustrated transmitters in the high-density regime.

Storage capacity in symmetric binary perceptrons

We study the problem of determining the capacity of the binary perceptron for two variants of the problem where the corresponding constraint is symmetric. We call these variants the rectangle-binary-perceptron (RPB) and the $u-$function-binary-perceptron (UBP). We show that, unlike for the usual step-function-binary-perceptron, the critical capacity in these symmetric cases is given by the annealed computation in a large region of parameter space (for all rectangular constraints and for narrow enough $u-$function constraints, $K<K^*$). We prove this fact (under two natural assumptions) using t…

基于完全提升随机对偶理论的二元感知器容量研究

Binary perceptrons capacity via fully lifted random duality theory

本文利用完全提升随机对偶理论（fl RDT）建立通用框架，研究具有一般阈值的二元感知器统计容量，所得结果精确匹配副本对称破缺预测，并复现了零阈值情形下$α\approx0.8330786$的经典容量值。

关于二元感知机容量的注记

A note on the capacity of the binary perceptron

针对二元感知机容量$α_c$的长期研究问题，本文整理给出了$α_c$<0.847上界的完整证明，采用条件一阶矩方法结合球形感知机已知结果，补全了此前Krauth和Mezard概述的论证。