arXiv subjects

Zehua He

Publications and source records attributed to Zehua He.

2 recordsLinked to original sources

arXiv2026

Distance and resistance on random series-parallel graphs: logarithmic speeds and near-critical asymptotics

We study the graph distance $D_n(p)$ and effective resistance $R_n(p)$ between the boundary vertices of a depth-$n$ random series--parallel graph, obtained by recursively joining two independent copies in series with probability $p$ and in parallel with probability $1-p$. We prove the existence of deterministic logarithmic speeds: for every $p\in[0,1]$, $n^{-1}\log D_n(p)$ and $n^{-1}\log R_n(p)$ converge to deterministic limits $v_D(p)$ and $v_R(p)$, respectively, almost surely and in $L^1$. The limiting speeds agree with the corresponding first-moment logarithmic rates for every $p\in[0,1]$ in the distance case and for $p\in[1/2,1]$ in the resistance case. We further determine the near-critical behavior of the resistance speed: $v_R(\frac12+δ)\sim 2ζ(3)^{1/3}λ_*δ^{2/3}$ as $δ\downarrow0$, where $λ_*>0$ is characterized by an explicit nonlinear boundary-value problem. This exponent $2/3$ contrasts with the exponent $1/2$ for distance obtained by Chen, Derrida, Duquesne, and Shi (2026). The main idea of this work was proposed by ChatGPT 5.6 Sol, and the authors take full responsibility for the mathematical content. The three main theorems and their supporting proof dependencies have been formalized in Lean 4, relative to two explicitly documented external mathematical inputs.

math.PR↗

arXiv2025

FedPURIN: Programmed Update and Reduced INformation for Sparse Personalized Federated Learning

Personalized Federated Learning (PFL) has emerged as a critical research frontier addressing data heterogeneity issue across distributed clients. Novel model architectures and collaboration mechanisms are engineered to accommodate statistical disparities while producing client-specific models. Parameter decoupling represents a promising paradigm for maintaining model performance in PFL frameworks. However, the communication efficiency of many existing methods remains suboptimal, sustaining substantial communication burdens that impede practical deployment. To bridge this gap, we propose Federated Learning with Programmed Update and Reduced INformation (FedPURIN), a novel framework that strategically identifies critical parameters for transmission through an integer programming formulation. This mathematically grounded strategy is seamlessly integrated into a sparse aggregation scheme, achieving a significant communication reduction while preserving the efficacy. Comprehensive evaluations on standard image classification benchmarks under varied non-IID conditions demonstrate competitive performance relative to state-of-the-art methods, coupled with quantifiable communication reduction through sparse aggregation. The framework establishes a new paradigm for communication-efficient PFL, particularly advantageous for edge intelligence systems operating with heterogeneous data sources.

cs.LG↗