Zhixiong Chen

Zhixiong Chen, Wenqiang Yi, Arumugam Nallanathan et al.

The data heterogeneity across devices and the limited communication resources, e.g., bandwidth and energy, are two of the main bottlenecks for wireless federated learning (FL). To tackle these challenges, we first devise a novel FL framework with partial model aggregation (PMA). This approach aggregates the lower layers of neural networks, responsible for feature extraction, at the parameter server while keeping the upper layers, responsible for complex pattern recognition, at devices for personalization. The proposed PMA-FL is able to address the data heterogeneity and reduce the transmitted information in wireless channels. Then, we derive a convergence bound of the framework under a non-convex loss function setting to reveal the role of unbalanced data size in the learning performance. On this basis, we maximize the scheduled data size to minimize the global loss function through jointly optimize the device scheduling, bandwidth allocation, computation and communication time division policies with the assistance of Lyapunov optimization. Our analysis reveals that the optimal time division is achieved when the communication and computation parts of PMA-FL have the same power. We also develop a bisection method to solve the optimal bandwidth allocation policy and use the set expansion algorithm to address the device scheduling policy. Compared with the benchmark schemes, the proposed PMA-FL improves 3.13\% and 11.8\% accuracy on two typical datasets with heterogeneous data distribution settings, i.e., MINIST and CIFAR-10, respectively. In addition, the proposed joint dynamic device scheduling and resource management approach achieve slightly higher accuracy than the considered benchmarks, but they provide a satisfactory energy and time reduction: 29\% energy or 20\% time reduction on the MNIST; and 25\% energy or 12.5\% time reduction on the CIFAR-10.

Yequan Zhao, Xinling Yu, Zhixiong Chen et al.

Backward propagation (BP) is widely used to compute the gradients in neural network training. However, it is hard to implement BP on edge devices due to the lack of hardware and software resources to support automatic differentiation. This has tremendously increased the design complexity and time-to-market of on-device training accelerators. This paper presents a completely BP-free framework that only requires forward propagation to train realistic neural networks. Our technical contributions are three-fold. Firstly, we present a tensor-compressed variance reduction approach to greatly improve the scalability of zeroth-order (ZO) optimization, making it feasible to handle a network size that is beyond the capability of previous ZO approaches. Secondly, we present a hybrid gradient evaluation approach to improve the efficiency of ZO training. Finally, we extend our BP-free training framework to physics-informed neural networks (PINNs) by proposing a sparse-grid approach to estimate the derivatives in the loss function without using BP. Our BP-free training only loses little accuracy on the MNIST dataset compared with standard first-order training. We also demonstrate successful results in training a PINN for solving a 20-dim Hamiltonian-Jacobi-Bellman PDE. This memory-efficient and BP-free approach may serve as a foundation for the near-future on-device training on many resource-constraint platforms (e.g., FPGA, ASIC, micro-controllers, and photonic chips).

Tianyu Wang, Nianjun Zhou, Zhixiong Chen

Large language models (LLMs) and prompt engineering hold significant potential for advancing computer programming education through personalized instruction. This paper explores this potential by investigating three critical research questions: the systematic categorization of prompt engineering strategies tailored to diverse educational needs, the empowerment of LLMs to solve complex problems beyond their inherent capabilities, and the establishment of a robust framework for evaluating and implementing these strategies. Our methodology involves categorizing programming questions based on educational requirements, applying various prompt engineering strategies, and assessing the effectiveness of LLM-generated responses. Experiments with GPT-4, GPT-4o, Llama3-8b, and Mixtral-8x7b models on datasets such as LeetCode and USACO reveal that GPT-4o consistently outperforms others, particularly with the "multi-step" prompt strategy. The results show that tailored prompt strategies significantly enhance LLM performance, with specific strategies recommended for foundational learning, competition preparation, and advanced problem-solving. This study underscores the crucial role of prompt engineering in maximizing the educational benefits of LLMs. By systematically categorizing and testing these strategies, we provide a comprehensive framework for both educators and students to optimize LLM-based learning experiences. Future research should focus on refining these strategies and addressing current LLM limitations to further enhance educational outcomes in computer programming instruction.

Tianyu Wang, Nianjun Zhou, Zhixiong Chen

Many non-traditional students in cybersecurity programs often lack access to advice from peers, family members and professors, which can hinder their educational experiences. Additionally, these students may not fully benefit from various LLM-powered AI assistants due to issues like content relevance, locality of advice, minimum expertise, and timing. This paper addresses these challenges by introducing an application designed to provide comprehensive support by answering questions related to knowledge, skills, and career preparation advice tailored to the needs of these students. We developed a learning tool platform, CyberMentor, to address the diverse needs and pain points of students majoring in cybersecurity. Powered by agentic workflow and Generative Large Language Models (LLMs), the platform leverages Retrieval-Augmented Generation (RAG) for accurate and contextually relevant information retrieval to achieve accessibility and personalization. We demonstrated its value in addressing knowledge requirements for cybersecurity education and for career marketability, in tackling skill requirements for analytical and programming assignments, and in delivering real time on demand learning support. Using three use scenarios, we showcased CyberMentor in facilitating knowledge acquisition and career preparation and providing seamless skill-based guidance and support. We also employed the LangChain prompt-based evaluation methodology to evaluate the platform's impact, confirming its strong performance in helpfulness, correctness, and completeness. These results underscore the system's ability to support students in developing practical cybersecurity skills while improving equity and sustainability within higher education. Furthermore, CyberMentor's open-source design allows for adaptation across other disciplines, fostering educational innovation and broadening its potential impact.

Rajeeb Thapa Chhetri, Zhixiong Chen, Saurab Thapa

A fundamental limitation of supervised deep learning in high-dimensional tabular domains is "Generalization Collapse": models learn precise decision boundaries for known distributions but fail catastrophically when facing Out-of-Distribution (OOD) data. We hypothesize that this failure stems from the lack of topological constraints in the latent space, resulting in diffuse manifolds where novel anomalies remain statistically indistinguishable from benign data. To address this, we propose Latent Sculpting, a hierarchical two-stage representation learning framework. Stage 1 utilizes a hybrid 1D-CNN and Transformer Encoder trained with a novel Dual-Centroid Compactness Loss (DCCL) to actively "sculpt" benign traffic into a low-entropy, hyperspherical cluster. Unlike standard contrastive losses that rely on triplet mining, DCCL optimizes global cluster centroids to enforce absolute manifold density. Stage 2 conditions a Masked Autoregressive Flow (MAF) on this pre-structured manifold to learn an exact density estimate. We evaluate this methodology on the rigorous CIC-IDS-2017 benchmark, treating it as a proxy for complex, non-stationary data streams. Empirical results demonstrate that explicit manifold sculpting is a prerequisite for robust zero-shot generalization. While supervised baselines suffered catastrophic performance collapse on unseen distribution shifts (F1 approx 0.30) and the strongest unsupervised baseline achieved only 0.76, our framework achieved an F1-Score of 0.87 on strictly zero-shot anomalies. Notably, we report an 88.89% detection rate on "Infiltration" scenarios--a complex distributional shift where state-of-the-art supervised models achieved 0.00% accuracy. These findings suggest that decoupling structure learning from density estimation provides a scalable path toward generalized anomaly detection.

Zhixiong Chen, Bingjie Zhu, Jiangzhou Wang et al.

Large language models (LLMs) have advanced rapidly, emerging as versatile tools across fields thanks to their exceptional language understanding, generation, and reasoning capabilities. However, performing LLM inference at the network edge remains challenging due to their large memory and compute demands. This survey outlines the challenges specific to LLM edge inference and provides a comprehensive overview of recent progress, covering system architectures, model optimization and deployment, and resource management and scheduling. By synthesizing state-of-the-art techniques and mapping future directions, this survey aims to unlock the potential of LLMs in resource-constrained edge environments.

Yequan Zhao, Xian Xiao, Xinling Yu et al.

Solving partial differential equations (PDEs) numerically often requires huge computing time, energy cost, and hardware resources in practical applications. This has limited their applications in many scenarios (e.g., autonomous systems, supersonic flows) that have a limited energy budget and require near real-time response. Leveraging optical computing, this paper develops an on-chip training framework for physics-informed neural networks (PINNs), aiming to solve high-dimensional PDEs with fJ/MAC photonic power consumption and ultra-low latency. Despite the ultra-high speed of optical neural networks, training a PINN on an optical chip is hard due to (1) the large size of photonic devices, and (2) the lack of scalable optical memory devices to store the intermediate results of back-propagation (BP). To enable realistic optical PINN training, this paper presents a scalable method to avoid the BP process. We also employ a tensor-compressed approach to improve the convergence and scalability of our optical PINN training. This training framework is designed with tensorized optical neural networks (TONN) for scalable inference acceleration and MZI phase-domain tuning for \textit{in-situ} optimization. Our simulation results of a 20-dim HJB PDE show that our photonic accelerator can reduce the number of MZIs by a factor of $1.17\times 10^3$, with only $1.36$ J and $1.15$ s to solve this equation. This is the first real-size optical PINN training framework that can be applied to solve high-dimensional PDEs.

Yequan Zhao, Xinling Yu, Xian Xiao et al.

Physics-informed neural networks (PINNs) have shown promise in solving partial differential equations (PDEs), with growing interest in their energy-efficient, real-time training on edge devices. Photonic computing offers a potential solution to achieve this goal because of its ultra-high operation speed. However, the lack of photonic memory and the large device sizes prevent training real-size PINNs on photonic chips. This paper proposes a completely back-propagation-free (BP-free) and highly salable framework for training real-size PINNs on silicon photonic platforms. Our approach involves three key innovations: (1) a sparse-grid Stein derivative estimator to avoid the BP in the loss evaluation of a PINN, (2) a dimension-reduced zeroth-order optimization via tensor-train decomposition to achieve better scalability and convergence in BP-free training, and (3) a scalable on-chip photonic PINN training accelerator design using photonic tensor cores. We validate our numerical methods on both low- and high-dimensional PDE benchmarks. Through circuit simulation based on real device parameters, we further demonstrate the significant performance benefit (e.g., real-time training, huge chip area reduction) of our photonic accelerator.

Huaning Liu, Zhixiong Chen, Chenhuang Wu

Fermat-Euler quotients arose from the study of the first case of Fermat's Last Theorem, and have numerous applications in number theory. Recently they were studied from the cryptographic aspects by constructing many pseudorandom binary sequences, whose linear complexities and trace representations were calculated. In this work, we further study their correlation measures by using the approach based on Dirichlet characters, Ramanujan sums and Gauss sums. Our results show that the $4$-order correlation measures of these sequences are very large. Therefore they may not be suggested for cryptography.

Vladimir Edemskiy, Zhixiong Chen

R. Hofer and A. Winterhof proved that the 2-adic complexity of the two-prime (binary) generator of period $pq$ with two odd primes $p\neq q$ is close to its period and it can attain the maximum in many cases. When the two-prime generator is applied to producing quaternary sequences, we need to determine the 4-adic complexity. We present the formulae of possible values of the 4-adic complexity, which is larger than $pq-\log_4(pq^2)-1$ if $p<q$. So it is good enough to resist the attack of the rational approximation algorithm.

Zhixiong Chen, Andrew Klapper

For each non-constant Boolean function $q$, Klapper introduced the notion of $q$-transforms of Boolean functions. The {\em $q$-transform} of a Boolean function $f$ is related to the Hamming distances from $f$ to the functions obtainable from $q$ by nonsingular linear change of basis. In this work we discuss the existence of $q$-nearly bent functions, a new family of Boolean functions characterized by the $q$-transform. Let $q$ be a non-affine Boolean function. We prove that any balanced Boolean functions (linear or non-linear) are $q$-nearly bent if $q$ has weight one, which gives a positive answer to an open question (whether there exist non-affine $q$-nearly bent functions) proposed by Klapper. We also prove a necessary condition for checking when a function isn't $q$-nearly bent.

Zhixiong Chen, Qiuyan Wang

Let $q=p^r$ be a power of an odd prime $p$. We study binary sequences $σ=(σ_0,σ_1,\ldots)$ with entries in $\{0,1\}$ defined by using the quadratic character $χ$ of the finite field $\mathbb{F}_q$: $$ σ_n=\left\{ \begin{array}{ll} 0,& \mathrm{if}\quad n= 0,\\ (1-χ(ξ_n))/2,&\mathrm{if}\quad 1\leq n< q, \end{array} \right. $$ for the ordered elements $ξ_0,ξ_1,\ldots,ξ_{q-1}\in \mathbb{F}_q$. The $σ$ is Legendre sequence if $r=1$. Our first contribution is to prove a lower bound on the linear complexity of $σ$ for $r\geq 2$. The bound improves some results of Meidl and Winterhof. Our second contribution is to study the $k$-error linear complexity of $σ$ for $r=2$. It seems that we cannot settle the case when $r>2$ and leave it open.

Zhixiong Chen, Vladimir Edemskiy, Pinhui Ke et al.

We investigate the $k$-error linear complexity of pseudorandom binary sequences of period $p^{\mathfrak{r}}$ derived from the Euler quotients modulo $p^{\mathfrak{r}-1}$, a power of an odd prime $p$ for $\mathfrak{r}\geq 2$. When $\mathfrak{r}=2$, this is just the case of polynomial quotients (including Fermat quotients) modulo $p$, which has been studied in an earlier work of Chen, Niu and Wu. In this work, we establish a recursive relation on the $k$-error linear complexity of the sequences for the case of $\mathfrak{r}\geq 3$. We also state the exact values of the $k$-error linear complexity for the case of $\mathfrak{r}=3$. From the results, we can find that the $k$-error linear complexity of the sequences (of period $p^{\mathfrak{r}}$) does not decrease dramatically for $k<p^{\mathfrak{r}-2}(p-1)^2/2$.

Chenhuang Wu, Chunxiang Xu, Zhixiong Chen et al.

We consider the $k$-error linear complexity of a new binary sequence of period $p^2$, proposed in the recent paper "New generalized cyclotomic binary sequences of period $p^2$", by Z. Xiao et al., who calculated the linear complexity of the sequences (Designs, Codes and Cryptography, 2017, https://doi.org/10.1007/s10623-017-0408-7). More exactly, we determine the values of $k$-error linear complexity over $\mathbb{F}_2$ for almost $k>0$ in terms of the theory of Fermat quotients. Results indicate that such sequences have good stability.

Zhixiong Chen, Ting Gu, Andrew Klapper

For each non-constant $q$ in the set of $n$-variable Boolean functions, the {\em $q$-transform} of a Boolean function $f$ is related to the Hamming distances from $f$ to the functions obtainable from $q$ by nonsingular linear change of basis. Klapper conjectured that no Boolean function exists with its $q$-transform coefficients equal to $\pm 2^{n/2}$ (such function is called $q$-bent). In our early work, we only gave partial results to confirm this conjecture for small $n$. Here we prove thoroughly that the conjecture is true by investigating the nonexistence of the partial difference sets in Abelian groups with special parameters. We also introduce a new family of functions called almost $q$-bent functions, which are close to $q$-bentness.

Zhixiong Chen

We continue to investigate binary sequence $(f_u)$ over $\{0,1\}$ defined by $(-1)^{f_u}=\left(\frac{(u^w-u^{wp})/p}{p}\right)$ for integers $u\ge 0$, where $\left(\frac{\cdot}{p}\right)$ is the Legendre symbol and we restrict $\left(\frac{0}{p}\right)=1$. In an earlier work, the linear complexity of $(f_u)$ was determined for $w=p-1$ under the assumption of $2^{p-1}\not\equiv 1 \pmod {p^2}$. In this work, we give possible values on the linear complexity of $(f_u)$ for all $1\le w<p-1$ under the same conditions. We also state that the case of larger $w(\geq p)$ can be reduced to that of $0\leq w\leq p-1$.

Zhixiong Chen, Vladimir Edemskiy

We determine the exact values of the linear complexity of 2p-periodic quaternary sequences over Z_4 (the residue class ring modulo 4) defined from the generalized cyclotomic classes modulo 2p in terms of the theory of of Galois rings of characteristic 4, where p is an odd prime. Compared to the case of quaternary sequences over the finite field of order 4, it is more dificult and complicated to consider the roots of polynomials in Z_4[X] due to the zero divisors in Z_4 and hence brings some interesting twists. We answer an open problem proposed by Kim, Hong and Song.

Zhixiong Chen

We define a family of quaternary sequences over the residue class ring modulo $4$ of length $pq$, a product of two distinct odd primes, using the generalized cyclotomic classes modulo $pq$ and calculate the discrete Fourier transform (DFT) of the sequences. The DFT helps us to determine the exact values of linear complexity and the trace representation of the sequences.

Zhihua Niu, Zhixiong Chen, Xiaoni Du

The Euler quotient modulo an odd-prime power $p^r~(r>1)$ can be uniquely decomposed as a $p$-adic number of the form $$ \frac{u^{(p-1)p^{r-1}} -1}{p^r}\equiv a_0(u)+a_1(u)p+\ldots+a_{r-1}(u)p^{r-1} \pmod {p^r},~ \gcd(u,p)=1, $$ where $0\le a_j(u)<p$ for $0\le j\le r-1$ and we set all $a_j(u)=0$ if $\gcd(u,p)>1$. We firstly study certain arithmetic properties of the level sequences $(a_j(u))_{u\ge 0}$ over $\mathbb{F}_p$ via introducing a new quotient. Then we determine the exact values of linear complexity of $(a_j(u))_{u\ge 0}$ and values of $k$-error linear complexity for binary sequences defined by $(a_j(u))_{u\ge 0}$.

Zhixiong Chen, Xiaoni Du, Radwa Marzouk

We give the trace representation of a family of binary sequences derived from Euler quotients by determining the corresponding defining polynomials. Trace representation can help us producing the sequences efficiently and analyzing their cryptographic properties, such as linear complexity.

Zhixiong Chen, Zhihua Niu, Chenhuang Wu

We investigate the $k$-error linear complexity of $p^2$-periodic binary sequences defined from the polynomial quotients (including the well-studied Fermat quotients), which is defined by $$ q_{p,w}(u)\equiv \frac{u^w-u^{wp}}{p} \bmod p ~ \mathrm{with} 0 \le q_{p,w}(u) \le p-1, ~u\ge 0, $$ where $p$ is an odd prime and $1\le w<p$. Indeed, first for all integers $k$, we determine exact values of the $k$-error linear complexity over the finite field $\F_2$ for these binary sequences under the assumption of f2 being a primitive root modulo $p^2$, and then we determine their $k$-error linear complexity over the finite field $\F_p$ for either $0\le k<p$ when $w=1$ or $0\le k<p-1$ when $2\le w<p$. Theoretical results obtained indicate that such sequences possess `good' error linear complexity.

Zhixiong Chen

We describe the trace representations of two families of binary sequences derived from Fermat quotients modulo an odd prime $p$ (one is the binary threshold sequences, the other is the Legendre-Fermat quotient sequences) via determining the defining pairs of all binary characteristic sequences of cosets, which coincide with the sets of pre-images modulo $p^2$ of each fixed value of Fermat quotients. From the defining pairs, we can obtain an earlier result of linear complexity for the binary threshold sequences and a new result of linear complexity for the Legendre-Fermat quotient sequences under the assumption of $2^{p-1}\not\equiv 1 \bmod {p^2}$.