arXiv subjects

Junxue Zhang

Publications and source records attributed to Junxue Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Some conjectures on $r$-graphs and equivalences

An $r$-regular graph is an $r$-graph, if every odd set of vertices is connected to its complement by at least $r$ edges. Seymour [On multicolourings of cubic graphs, and conjectures of Fulkerson and Tutte.~\emph{Proc.~London Math.~Soc.}~(3), 38(3): 423-460, 1979] conjectured (1) that every planar $r$-graph is $r$-edge colorable and (2) that every $r$-graph has $2r$ perfect matchings such that every edge is contained in precisely two of them. We study several variants of these conjectures. A $(t,r)$-PM is a multiset of $t \cdot r$ perfect matchings of an $r$-graph $G$ such that every edge is in precisely $t$ of them. We show that the following statements are equivalent for every $t, r \geq 1$: 1. Every planar $r$-graph has a $(t,r)$-PM. 2. Every $K_5$-minor-free $r$-graph has a $(t,r)$-PM. 3. Every $K_{3,3}$-minor-free $r$-graph has a $(t,r)$-PM. 4. Every $r$-graph whose underlying simple graph has crossing number at most $1$ has a $(t,r)$-PM.

math.CO↗

arXiv2026

CALVO: Improve Serving Efficiency for LLM Inferences with Intense Network Demands

Distributed prefix caching has become a core technique for efficient LLM serving. However, for long-context requests with high cache hit ratios, retrieving reusable KVCache blocks from remote servers has emerged as a new performance bottleneck. Such network-intensive LLM inference is expected to become increasingly common as agentic AI workloads continue to grow. However, existing LLM inference engines remain largely compute-centric: they treat KVCache loading as a subordinate phase to GPU execution and often fail to account for its delay explicitly during scheduling. We present CALVO, an LLM serving engine that treats KVCache loading as a first-class concern. CALVO decouples KVCache loading and GPU computation into independently managed, asynchronously progressing stages, enabling better utilization of network, PCIe, and computation resources. In addition, CALVO incorporates KVCache loading delay as an explicit component of per-request service cost, leading to more accurate scheduling decisions. Experiments on a real testbed with diverse long-context workloads show that CALVO substantially improves the efficiency of network-intensive LLM inference, achieving up to 61.67% higher SLO attainment than the baseline.

cs.DC↗

arXiv2026

Unlocking Full Efficiency of Token Filtering in Large Language Model Training

Token filtering has been proposed to enhance the utility of large language models (LLMs) by eliminating inconsequential tokens during training. While usingfewer tokens is expected to reduce computational workloads, existing methods have not yet achieved a real-world efficiency boost. This is primarily due to two factors: (1) existing work has inadequate sparsity for speedup, and (2) token filtering operates within a sparsity range that is non-standard in existing machine learning (ML) libraries and thus cannot be efficiently supported. This paper presents Centrifuge, a system that leverages algorithm and system co-design to unleash the full efficiency of token filtering in LLM training. At the algorithm level, Centrifuge filters activations of inconsequential tokens in the attention backward kernel to amplify the sparsity in backward computation. At the system level, Centrifuge proposes an automatic workflow that transforms sparse GEMM into dimension-reduced dense GEMM for optimized efficiency using standard ML libraries. Evaluations on models with various scales--from 1.1B to 40B--demonstrate that Centrifuge reduces backpropagation time by up to 49.9\% and end-to-end training time by up to 34.7\% when filtering 50\% of tokens. Utility assessments indicate that Centrifuge preserves the utility benefits of token filtering and significantly enhances model performance by up to 26.6\% compared to standard training. Centrifuge is designed for seamless integration into existing LLM training frameworks, enabling systems already utilizing token filtering to accelerate training with just one line of code.

cs.LG↗

arXiv2026

The perturbation threshold of degenerate graphs

We show that for any $d\ge 2$ and $Δ>0$ there exists $η>0$ such that the following holds: Let $G$ be an $n$-vertex graph with at least $Ω(n^2)$ edges and let $H$ be an $n$-vertex $d$-degenerate graph with maximum degree at most $Δ$. Then with high probability, $G \cup G(n, n^{-1/d - η})$ contains a copy of $H$. We also prove that the same conclusion extends to $d$-regular graphs with $d\ge 4$ satisfying a certain edge expansion property, with the threshold improved to $n^{-2/d - η}$. Such a property is satisfied by almost all $d$-regular graphs and for even $d$, by the $(d/2)$-th power of a Hamilton cycle.

math.CO↗

arXiv2026

The minimum spectral radius of $tP_4$-saturated graphs

A graph $G$ is called {\em$F$-saturated} if $G$ does not contain $F$ as a subgraph but adding any missing edge to $G$ creates a copy of $F$. In this paper, we consider the spectral saturation problem for the linear forest $tP_4$, proving that every $n$-vertex $tP_4$-saturated graph $G$ with $t\geq 2$ and $n\ge 4t$ satisfies $ρ(G)\ge \frac{1+\sqrt{17}}{2}$, and characterizing all $tP_4$-saturated graphs for which equality holds. Moreover, we obtain that, for $t=2$ with odd $n\ge 13 $, and for $t\ge 3$ with $n\ge 6t+4$, the set of $n$-vertex $tP_4$-saturated graphs minimizing the spectral radius is disjoint from that minimizing the number of edges.

math.CO↗

arXiv2025

Perturbation of dense graphs

In the past two decades, various properties of randomly perturbed/augmented (hyper)graphs have been intensively studied, since the model was introduced by Bohman, Frieze and Martin in 2003. The model usually considers a deterministic graph $G$ with minimum degree condition, perturbed/augmented by a binomial random graph $G(n,p)$ on the same vertex set. In this paper, we show that for many problems of finding spanning subgraphs, one can indeed relax the minimum degree condition to a density condition. This includes the embedding problem for $F$-factors when $F$ is not a forest, graphs with bounded maximum degree, $r$-th power of $k$-uniform tight Hamilton cycles for $r,k\ge 2$, and $k$-uniform Hamilton $\ell$-cycles for $\ell\in[2,k-1]$. These results strengthen the results of Balogh, Treglown, and Wagner, of Böttcher, Montgomery, Parczyk, and Person, and of Chang, Han and Thoma.

math.CO↗

arXiv2025

Design and Operation of Shared Machine Learning Clusters on Campus

Amid the rapid advancements in large machine learning (ML) models, universities worldwide are investing substantial funds and efforts into GPU clusters. However, managing a shared GPU cluster poses a pyramid of challenges, from hardware configuration to resource allocation among users. This paper introduces SING, a full-stack solution designed to streamline the management of shared GPU clusters in academic institutions. Motivated by the pressing need for efficient resource sharing and the challenges posed by limited staffing, we present a comprehensive view of SING's architecture and design choices, which achieves operational efficiency (i.e., low maintenance cost and high resource utilization). We also share experience and insights from the real-world operations of SING, including analysis of its usage patterns and management of incidents and failures. This paper is part of our ongoing effort to improve the management of shared ML clusters. We open-source relevant resources to facilitate the development and operation of similar clusters for ML.

cs.DC↗

arXiv2025

Swift: Rethinking RDMA Control Plane for Elastic Computing

Elastic computing enables dynamic scaling to meet workload demands, and Remote Direct Memory Access (RDMA) enhances this by providing high-throughput, low-latency network communication. However, integrating RDMA into elastic computing remains a challenge, particularly in control plane operations for RDMA connection setup. This paper revisits the assumptions of prior work on high-performance RDMA for elastic computing, and reveals that extreme microsecond-level control plane optimizations are often unnecessary. By challenging the conventional beliefs on the slowness of user-space RDMA control plane and the difficulty of user-space RDMA resource sharing, we uncover new design opportunities. Our key insight is that user-space RDMA connection setup can be significantly improved with caching, while RDMA resources can be efficiently shared among processes using fork. In light of this, we propose Swift, a simple yet effective solution that co-designs RDMA with a serverless framework to optimize performance for elastic computing. At its very core, Swift handles cold and warm serverless requests by swiftly initializing the RDMA control plane with cache-optimized libibverbs, and manages fork requests by leveraging the RDMA's fork capability. Implemented with OpenWhisk, Swift delivers 30.56-46.50% higher average throughput and 18.55-37.21% lower latency, at a cost of 6.5% control plane overhead, compared to prior solutions.

cs.NI↗

arXiv2025

FLASH-FHE: A Heterogeneous Architecture for Fully Homomorphic Encryption Acceleration

While many hardware accelerators have recently been proposed to address the inefficiency problem of fully homomorphic encryption (FHE) schemes, none of them is able to deliver optimal performance when facing real-world FHE workloads consisting of a mixture of shallow and deep computations, due primarily to their homogeneous design principle. This paper presents FLASH-FHE, the first FHE accelerator with a heterogeneous architecture for mixed workloads. At its heart, FLASH-FHE designs two types of computation clusters, ie, bootstrappable and swift, to optimize for deep and shallow workloads respectively in terms of cryptographic parameters and hardware pipelines. We organize one bootstrappable and two swift clusters into one cluster affiliation, and present a scheduling scheme that provides sufficient acceleration for deep FHE workloads by utilizing all the affiliations, while improving parallelism for shallow FHE workloads by assigning one shallow workload per affiliation and dynamically decomposing the bootstrappable cluster into multiple swift pipelines to accelerate the assigned workload. We further show that these two types of clusters can share valuable on-chip memory, improving performance without significant resource consumption. We implement FLASH-FHE with RTL and synthesize it using both 7nm and 14/12nm technology nodes, and our experiment results demonstrate that FLASH-FHE achieves an average performance improvement of $1.4\times$ and $11.2\times$ compared to state-of-the-art FHE accelerators CraterLake and F1 for deep workloads, while delivering up to $8.0\times$ speedup for shallow workloads due to its heterogeneous architecture.

cs.AR↗

arXiv2024

PackVFL: Efficient HE Packing for Vertical Federated Learning

As an essential tool of secure distributed machine learning, vertical federated learning (VFL) based on homomorphic encryption (HE) suffers from severe efficiency problems due to data inflation and time-consuming operations. To this core, we propose PackVFL, an efficient VFL framework based on packed HE (PackedHE), to accelerate the existing HE-based VFL algorithms. PackVFL packs multiple cleartexts into one ciphertext and supports single-instruction-multiple-data (SIMD)-style parallelism. We focus on designing a high-performant matrix multiplication (MatMult) method since it takes up most of the ciphertext computation time in HE-based VFL. Besides, devising the MatMult method is also challenging for PackedHE because a slight difference in the packing way could predominantly affect its computation and communication costs. Without domain-specific design, directly applying SOTA MatMult methods is hard to achieve optimal. Therefore, we make a three-fold design: 1) we systematically explore the current design space of MatMult and quantify the complexity of existing approaches to provide guidance; 2) we propose a hybrid MatMult method according to the unique characteristics of VFL; 3) we adaptively apply our hybrid method in representative VFL algorithms, leveraging distinctive algorithmic properties to further improve efficiency. As the batch size, feature dimension and model size of VFL scale up to large sizes, PackVFL consistently delivers enhanced performance. Empirically, PackVFL propels existing VFL algorithms to new heights, achieving up to a 51.52X end-to-end speedup. This represents a substantial 34.51X greater speedup compared to the direct application of SOTA MatMult methods.

cs.CR↗

arXiv2024

A Survey for Federated Learning Evaluations: Goals and Measures

Evaluation is a systematic approach to assessing how well a system achieves its intended purpose. Federated learning (FL) is a novel paradigm for privacy-preserving machine learning that allows multiple parties to collaboratively train models without sharing sensitive data. However, evaluating FL is challenging due to its interdisciplinary nature and diverse goals, such as utility, efficiency, and security. In this survey, we first review the major evaluation goals adopted in the existing studies and then explore the evaluation metrics used for each goal. We also introduce FedEval, an open-source platform that provides a standardized and comprehensive evaluation framework for FL algorithms in terms of their utility, efficiency, and security. Finally, we discuss several challenges and future research directions for FL evaluation.

cs.LG↗

arXiv2024

SoK: Fully Homomorphic Encryption Accelerators

Fully Homomorphic Encryption~(FHE) is a key technology enabling privacy-preserving computing. However, the fundamental challenge of FHE is its inefficiency, due primarily to the underlying polynomial computations with high computation complexity and extremely time-consuming ciphertext maintenance operations. To tackle this challenge, various FHE accelerators have recently been proposed by both research and industrial communities. This paper takes the first initiative to conduct a systematic study on the 14 FHE accelerators -- cuHE/cuFHE, nuFHE, HEAT, HEAX, HEXL, HEXL-FPGA, 100$\times$, F1, CraterLake, BTS, ARK, Poseidon, FAB and TensorFHE. We first make our observations on the evolution trajectory of these existing FHE accelerators to establish a qualitative connection between them. Then, we perform testbed evaluations of representative open-source FHE accelerators to provide a quantitative comparison on them. Finally, with the insights learned from both qualitative and quantitative studies, we discuss potential directions to inform the future design and implementation for FHE accelerators.

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arXiv2023

The saturation number of $C_6$

A graph $G$ is called $C_k$-saturated if $G$ is $C_k$-free but $G+e$ not for any $e\in E(\overline{G})$. The saturation number of $C_k$, denoted $sat(n,C_k)$, is the minimum number of edges in a $C_k$-saturated graph on $n$ vertices. Finding the exact values of $sat(n,C_k)$ has been one of the most intriguing open problems in extremal graph theory. In this paper, we study the saturation number of $C_6$. We prove that ${4n}/{3}-2 \le sat(n,C_6) \le {(4n+1)}/{3}$ for $n\ge9$, which significantly improves the existing lower and upper bounds for $sat(n,C_6)$.

math.CO↗

arXiv2023

Linear saturation numbers of Berge-$C_3$ and Berge-$C_4$

The linear saturation number $sat^{lin}_k(n,\mathcal{F})$ (linear extremal number $ex^{lin}_k(n,\mathcal{F})$) of $\mathcal{F}$ is the minimum (maximum) number of hyperedges of an $n$-vertex linear $k$-uniform hypergraph containing no member of $\mathcal{F}$ as a subgraph, but the addition of any new hyperedge such that the result hypergraph is still a linear $k$-uniform hypergraph creates a copy of some hypergraph in $\mathcal{F}$. Determining $ex_3^{lin}(n$, Berge-$C_3$) is equivalent to the famous (6,3)-problem, which has been settled in 1976. Since then, determining the linear extremal numbers of Berge cycles was extensively studied. As the counterpart of this problem in saturation problems, the problem of determining the linear saturation numbers of Berge cycles is considered. In this paper, we prove that $sat^{lin}_k$($n$, Berge-$C_t)\ge \big\lfloor\frac{n-1}{k-1}\big\rfloor$ for any integers $k\ge3$, $t\ge 3$, and the equality holds if $t=3$. In addition, we provide an upper bound for $sat^{lin}_3(n,$ Berge-$C_4)$ and for any disconnected Berge-$C_4$-saturated linear 3-uniform hypergraph, we give a lower bound for the number of hyperedges of it.

math.CO↗

arXiv2023

Extremal numbers of disjoint triangles in $r$-partite graphs

For two graphs $G$ and $F$, the extremal number of $F$ in $G$, denoted by {ex}$(G,F)$, is the maximum number of edges in a spanning subgraph of $G$ not containing $F$ as a subgraph. Determining {ex}$(K_n,F)$ for a given graph $F$ is a classical extremal problem in graph theory. In 1962, Erdős determined {ex}$(K_n,kK_3)$, which generalized Mantel's Theorem. On the other hand, in 1974, {Bollobás}, Erdős, and Straus determined {ex}$(K_{n_1,n_2,\dots,n_r},K_t)$, which extended Turán's Theorem to complete multipartite graphs. { In this paper,} we determine {ex}$(K_{n_1,n_2,\dots,n_r},kK_3)$ for $r\ge 4$ and $10k-4\le n_1+4k\le n_2\le n_3\le \cdots \le n_r$.

cs.DM↗

arXiv2023

A Survey on Vertical Federated Learning: From a Layered Perspective

Vertical federated learning (VFL) is a promising category of federated learning for the scenario where data is vertically partitioned and distributed among parties. VFL enriches the description of samples using features from different parties to improve model capacity. Compared with horizontal federated learning, in most cases, VFL is applied in the commercial cooperation scenario of companies. Therefore, VFL contains tremendous business values. In the past few years, VFL has attracted more and more attention in both academia and industry. In this paper, we systematically investigate the current work of VFL from a layered perspective. From the hardware layer to the vertical federated system layer, researchers contribute to various aspects of VFL. Moreover, the application of VFL has covered a wide range of areas, e.g., finance, healthcare, etc. At each layer, we categorize the existing work and explore the challenges for the convenience of further research and development of VFL. Especially, we design a novel MOSP tree taxonomy to analyze the core component of VFL, i.e., secure vertical federated machine learning algorithm. Our taxonomy considers four dimensions, i.e., machine learning model (M), protection object (O), security model (S), and privacy-preserving protocol (P), and provides a comprehensive investigation.

cs.LG↗

arXiv2022

FedEval: A Holistic Evaluation Framework for Federated Learning

Federated Learning (FL) has been widely accepted as the solution for privacy-preserving machine learning without collecting raw data. While new technologies proposed in the past few years do evolve the FL area, unfortunately, the evaluation results presented in these works fall short in integrity and are hardly comparable because of the inconsistent evaluation metrics and experimental settings. In this paper, we propose a holistic evaluation framework for FL called FedEval, and present a benchmarking study on seven state-of-the-art FL algorithms. Specifically, we first introduce the core evaluation taxonomy model, called FedEval-Core, which covers four essential evaluation aspects for FL: Privacy, Robustness, Effectiveness, and Efficiency, with various well-defined metrics and experimental settings. Based on the FedEval-Core, we further develop an FL evaluation platform with standardized evaluation settings and easy-to-use interfaces. We then provide an in-depth benchmarking study between the seven well-known FL algorithms, including FedSGD, FedAvg, FedProx, FedOpt, FedSTC, SecAgg, and HEAgg. We comprehensively analyze the advantages and disadvantages of these algorithms and further identify the suitable practical scenarios for different algorithms, which is rarely done by prior work. Lastly, we excavate a set of take-away insights and future research directions, which are very helpful for researchers in the FL area.

cs.LG↗

arXiv2022

The saturation number of $K_{3,3}$

A graph $G$ is called $F$-saturated if $G$ does not contain $F$ as a subgraph (not necessarily induced) but the addition of any missing edge to $G$ creates a copy of $F$. The saturation number of $F$, denoted by $sat(n,F)$, is the minimum number of edges in an $n$-vertex $F$-saturated graph. Determining the saturation number of complete partite graphs is one of the most important problems in the study of saturation number. The value of $sat(n,K_{2,2})$ was shown to be $\lfloor\frac{3n-5}{2}\rfloor$ by Ollmann, and a shorter proof was later given by Tuza. For $K_{2,3}$, there has been a series of study aiming to determine $sat(n,K_{2,3})$ over the years. This was finally achieved by Chen who confirmed a conjecture of Bohman, Fonoberova, and Pikhurko that $sat(n, K_{2,3})= 2n-3$ for all $n\geq 5$. In this paper, we prove a conjecture of Pikhurko and Schmitt that $sat(n, K_{3,3})=3n-9$ when $n \geq 9$.

math.CO↗