arXiv subjects

Leilei Zhang

Publications and source records attributed to Leilei Zhang.

26 records · Page 2Linked to original sources

arXiv2022

Enabling Fast and Flexible Distributed Deep Learning with Programmable Switches

Deep learning has been used in a wide range of areas and made a huge breakthrough. With the ever-increasing model size and train-ing data volume, distributed deep learning emerges which utilizes a cluster to train a model in parallel. Unfortunately, the performance is often far from linear speedup due to the communication overhead between cluster nodes. To address this challenge, this paper designs and implements Libra, a network aggregator, that utilizes in-network computation to optimize the communication for distributed DL training in two aspects: 1) reduce active connections and 2) aggregate exchanged network packets. We implemented our Libra on Intel Tofino switches, customized a lightweight host stack and integrated it into an open-source training framework PS-lite. The experimental result shows that our Libra can achieve 1.5~4 times speedup.

cs.NI↗

arXiv2022

The maximum number of $K_{r_1,\ldots,r_s}$ in graphs with a given circumference or matching number

Let $K_{r_1,\ldots,r_s}$ denote the complete multipartite graph with class sizes $r_1,\ldots,r_s$ and let $K_s$ denote the complete graph of order $s$. In 2018, Luo determined the maximum number of $K_s$ in 2-connected graphs with a given circumference. Recently, Lu, Yuan and Zhang determined the maximum number of $K_{r_1,r_2}$ in 2-connected graphs with a given circumference, and Wang determined the maximum number of $K_s$ or $K_{r_1,1,\ldots,1}$ in graphs with given matching number. Motivated by these works, we determine the maximum number of $K_{r_1,\ldots,r_s}$ in $2$-connected graphs with given circumference and large minimum degree. The maximum number of $K_{r_1,\ldots,r_s}$ in graphs with given matching number and large minimum degree is also given. Consequently, we determine the maximum number of $K_{r_1,\ldots,r_s}$ in graphs with a given circumference or matching number. We also solve the corresponding problems for graphs with a given detour order.

math.CO↗

arXiv2021

The maximum size of a graph with prescribed order, circumference and minimum degree

Erdős determined the maximum size of a nonhamiltonian graph of order $n$ and minimum degree at least $k$ in 1962. Recently, Ning and Peng generalized. Erdős' work and gave the maximum size $h(n,c,k)$ of graphs with prescribed order $n$, circumference $c$ and minimum degree at least $k.$ But for some triples $n,c,k,$ the maximum size is not attained by a graph of minimum degree $k.$ For example, $h(15,14,3)=77$ is attained by a unique graph of minimum degree $7,$ not $3.$ In this paper we obtain more precise information by determining the maximum size of a graph with prescribed order, circumference and minimum degree. Consequently we solve the corresponding problem for longest paths. All these results on the size of graphs have clique versions.

math.CO↗

arXiv2021

Proof of a conjecture on hamiltonian-connected graphs

We prove that every 3-connected claw-free graph with domination number at most 3 is hamiltonian-connected. The result is sharp and it is inspired by a conjecture posed by Zheng, Broersma, Wang and Zhang in 2020.

math.CO↗

arXiv2021

Improved cooperation by balancing exploration and exploitation in intertemporal social dilemma tasks

When an individual's behavior has rational characteristics, this may lead to irrational collective actions for the group. A wide range of organisms from animals to humans often evolve the social attribute of cooperation to meet this challenge. Therefore, cooperation among individuals is of great significance for allowing social organisms to adapt to changes in the natural environment. Based on multi-agent reinforcement learning, we propose a new learning strategy for achieving coordination by incorporating a learning rate that can balance exploration and exploitation. We demonstrate that agents that use the simple strategy improve a relatively collective return in a decision task called the intertemporal social dilemma, where the conflict between the individual and the group is particularly sharp. We also explore the effects of the diversity of learning rates on the population of reinforcement learning agents and show that agents trained in heterogeneous populations develop particularly coordinated policies relative to those trained in homogeneous populations.

cs.MA↗

arXiv2021

The maximum size of a nonhamiltonian graph with given order and connectivity

Motivated by work of Erdős, Ota determined the maximum size $g(n,k)$ of a $k$-connected nonhamiltonian graph of order $n$ in 1995. But for some pairs $n,k,$ the maximum size is not attained by a graph of connectivity $k.$ For example, $g(15,3)=77$ is attained by a unique graph of connectivity $7,$ not $3.$ In this paper we obtain more precise information by determining the maximum size of a nonhamiltonian graph of order $n$ and connectivity $k,$ and determining the extremal graphs. Consequently we solve the corresponding problem for nontraceable graphs.

math.CO↗

arXiv2021

Prediction of anomalous LA-TA splitting in electrides

Electrides are an emerging class of materials with excess electrons localized in interstices and acting as anionic interstitial quasi-atoms (ISQs). The spatial ion-electron separation means that electrides can be treated physically as ionic crystals, and this unusual behavior leads to extraordinary physical and chemical phenomena. Here, a completely different effect in electrides is predicted. By recognizing the long-range Coulomb interactions between matrix atoms and ISQs that are unique in electrides, a nonanalytic correction to the forces exerted on matrix atoms is proposed. This correction gives rise to an LA-TA splitting in the acoustic branch of lattice phonons near the zone center, similar to the well-known LO-TO splitting in the phonon spectra of ionic compounds. The factors that govern this splitting are investigated, with isotropic fcc-Li and anisotropic hP4-Na as the typical examples. It is found that not all electrides can induce a detectable splitting, and criteria are given for this type of splitting. The present prediction unveils the rich phenomena in electrides and could lead to unprecedented applications.

cond-mat.mtrl-sci↗

arXiv2021

Prediction of Stable Ground-State Binary Sodium-Potassium Interalkalis under High Pressures

The complex structures and electronic properties of alkali metals and their alloys provide a natural laboratory for studying the interelectronic interactions of metals under compression. A recent theoretical study (J. Phys. Chem. Lett. 2019, 10, 3006) predicted an interesting pressure-induced decomposition-recombination behavior of the Na2K compound over a pressure range of 10 - 500 GPa. However, a subsequent experiment (Phys. Rev. B 2020, 101, 224108) reported the formation of NaK rather than Na2K at pressures above 5.9 GPa. To address this discordance, we study the chemical stability of different stoichiometries of NaxK (x = 1/4, 1/3, 1/2, 2/3, 3/4, 4/3, 3/2 and 1 - 4) by effective structure searching method combined with first-principles calculations. Na2K is calculated to be unstable at 5 - 35 GPa due to the decomposition reaction Na2K-> NaK + Na, coinciding well with the experiment. NaK undergoes a combination-decomposition-recombination process accompanied by an opposite charge-transfer behavior between Na and K with pressure. Besides NaK, two hitherto unknown compounds NaK3 and Na3K2 are uncovered. NaK3 is a typical metallic alloy, while Na3K2 is an electride with strong interstitial electron localization.

cond-mat.mtrl-sci↗