arXiv subjects

Zhen Lin

Publications and source records attributed to Zhen Lin.

41 records · Page 3Linked to original sources

arXiv2021

On the spectral radius, energy and Estrada index of the Sombor matrix of graphs

Let $G$ be a simple undirected graph with vertex set $V(G)=\{v_1, v_2, \ldots, v_n\}$ and edge set $E(G)$. The Sombor matrix $\mathcal{S}(G)$ of a graph $G$ is defined so that its $(i,j)$-entry is equal to $\sqrt{d_i^2+d_j^2}$ if the vertices $v_i$ and $v_j$ are adjacent, and zero otherwise, where $d_i$ denotes the degree of vertex $v_i$ in $G$. In this paper, lower and upper bounds on the spectral radius, energy and Estrada index of the Sombor matrix of graphs are obtained, and the respective extremal graphs are characterized.

math.CO↗

arXiv2020

On the sum of the largest $A_α$-eigenvalues of graphs

For every real $0\leq α\leq 1$, Nikiforov defined the $A_α$-matrix of a graph $G$ as $A_α(G)=αD(G)+(1-α)A(G)$, where $A(G)$ and $D(G)$ are the adjacency matrix and the degree diagonal matrix of a graph $G$, respectively. The eigenvalues of $A_α(G)$ are called the $A_α$-eigenvalues of $G$. Let $S_k(A_α(G))$ be the sum of $k$ largest $A_α$-eigenvalues of $G$. In this paper, we present several upper and lower bounds on $S_k(A_α(G))$ and characterize the extremal graphs for certain cases, which can be regard as a common generalization of the sum of $k$ largest eigenvalues of adjacency matrix and signless Laplacian matrix of graphs. In addition, some graph operations on $S_k(A_α(G))$ are presented.

math.CO↗

arXiv2019

In-Place Zero-Space Memory Protection for CNN

Convolutional Neural Networks (CNN) are being actively explored for safety-critical applications such as autonomous vehicles and aerospace, where it is essential to ensure the reliability of inference results in the presence of possible memory faults. Traditional methods such as error correction codes (ECC) and Triple Modular Redundancy (TMR) are CNN-oblivious and incur substantial memory overhead and energy cost. This paper introduces in-place zero-space ECC assisted with a new training scheme weight distribution-oriented training. The new method provides the first known zero space cost memory protection for CNNs without compromising the reliability offered by traditional ECC.

cs.LG↗

arXiv2019

Exploring Memory Persistency Models for GPUs

Given its high integration density, high speed, byte addressability, and low standby power, non-volatile or persistent memory is expected to supplement/replace DRAM as main memory. Through persistency programming models (which define durability ordering of stores) and durable transaction constructs, the programmer can provide recoverable data structure (RDS) which allows programs to recover to a consistent state after a failure. While persistency models have been well studied for CPUs, they have been neglected for graphics processing units (GPUs). Considering the importance of GPUs as a dominant accelerator for high performance computing, we investigate persistency models for GPUs. GPU applications exhibit substantial differences with CPUs applications, hence in this paper we adapt, re-architect, and optimize CPU persistency models for GPUs. We design a pragma-based compiler scheme to express persistency models for GPUs. We identify that the thread hierarchy in GPUs offers intuitive scopes to form epochs and durable transactions. We find that undo logging produces significant performance overheads. We propose to use idempotency analysis to reduce both logging frequency and the size of logs. Through both real-system and simulation evaluations, we show low overheads of our proposed architecture support.

cs.DC↗

arXiv2018

Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network

Recent work by Cohen \emph{et al.} has achieved state-of-the-art results for learning spherical images in a rotation invariant way by using ideas from group representation theory and noncommutative harmonic analysis. In this paper we propose a generalization of this work that generally exhibits improved performace, but from an implementation point of view is actually simpler. An unusual feature of the proposed architecture is that it uses the Clebsch--Gordan transform as its only source of nonlinearity, thus avoiding repeated forward and backward Fourier transforms. The underlying ideas of the paper generalize to constructing neural networks that are invariant to the action of other compact groups.

stat.ML↗