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Feng Qi

Publications and source records attributed to Feng Qi.

At least 19 recordsLinked to original sources
arXiv2026

Expressing a difference between two Hurwitz zeta functions in terms of the Gauss hypergeometric functions

In the paper, the author expresses the difference $2^m[ζ(-m,λz)-ζ(-m,λz+μ)]$ for $m\in\mathbb{N}_0$ and $\Re(z)>0$ with $λ,μ>0$ in terms of the functions $Γ(j+1){\,}_2F_1(-j,-z;1;2)$ for $0\le j\le m$ and $z\in\mathbb{C}$ in the form of matrix equations, where $Γ(z)$, $ζ(z,α)$, and ${}_2F_1(a,b;c;z)$ stand for the classical Euler gamma function, the Hurwitz zeta function, and the Gauss hypergeometric function, respectively. The case of non-integer $t$ in $2^t[ζ(-t,λz)-ζ(-t,λz+μ)]$ is left open. The coefficients are characterized by matrix formulas and by an explicit recursion; closed-form expressions for them are not obtained. This problem originates from the Landau level quantization in solid state materials.

math.CA↗
arXiv2026

Combinatorial identities derived from explicit formulas of Gauss hypergeometric functions

In the present paper, with the help of the Faà di Bruno formula and several identities of partial Bell polynomials, the author establishes explicit formulas of the Gauss hypergeometric functions \begin{gather*} {\,}_2F_1\biggl(\frac{1-n}{2},\frac{2-n}{2};\frac{3}{2}-m;z^2\biggr), \quad {\,}_2F_1\biggl(-\frac{n}{2},\frac{1-n}{2};\frac{1}{2}-m;z^2\biggr),\\ {\,}_2F_1\biggl(a,a+\frac{1}{2};\frac{3}{2}-m;z^2\biggr), \quad {\,}_2F_1\biggl(a,a+\frac{1}{2};\frac{1}{2}-m;z^2\biggr) \end{gather*} for $m,n\in\mathbb{N}$ and $a\in\mathbb{C}$, and then derives two combinatorial identities \begin{equation*} \sum_{k=0}^{m}\frac{2^k}{k!} \binom{2m-2k}{m-k} \sum_{\ell=0}^{k} \frac{(-1)^\ell}{2^\ell} \frac{(2k-2\ell-1)!!}{(n-\ell)!} \binom{2k-\ell-1}{\ell-1} =\frac{1}{n!}\binom{2m-n}{m} \end{equation*} and \begin{equation*} \sum_{k=1}^{m}\frac{1}{(k!)^2}\binom{2m-2k}{m-k} \sum_{\ell=1}^{k} \binom{k}{\ell}\ell(2k-\ell-1)! (2a)_\ell =\binom{2m+2a}{m}-\binom{2m}{m}, \end{equation*} where $m\in\mathbb{N}_0$, $n\in\mathbb{Z}$, and $a\in\mathbb{C}$. These newly-established identities extend and generalize the beautiful combinatorial identity \begin{equation*} \sum_{k=0}^{n} \frac{2^{k}}{k!}\binom{2n-2k}{n-k} \sum_{j=0}^{k}\frac{(-1)^{j}}{2^j} \frac{(2k-2j-1)!!}{(n-j)!} \binom{2k-j-1}{j-1} =\frac{1}{n!}, \quad n\in\mathbb{N}_0, \end{equation*} which was obtained in Theorem 4 of the paper "F. Qi, C.-Y. He, and D. Lim, Explicit formulas of two Gauss hypergeometric functions and several combinatorial identities, Discrete Appl. Math. Vol. 393 (2026), 215--229. DOI: https://doi.org/10.1016/j.dam.2026.06.023."

math.CO↗
arXiv2026

Infinite and finite series involving central binomial coefficients and closed forms of generalized hypergeometric functions

Let $\mathbb{Z}^-=\{-1,-2,\dotsc\}$ and $\mathbb{N}=\{1,2,\dotsc\}$. In 2023, Qi and Lim gave two claims for summing the infinite series $\sum_{k=1}^{\infty}\binom{2k}{k}\frac{1}{α+k}\bigl(\frac{\pm1}{4}\bigr)^k$ for $α\in\mathbb{C}\setminus\mathbb{Z}^-$. In this paper, we confirm these claims by expressing the infinite series $\sum_{k=1}^{\infty}\binom{2k}{k}\frac{1}{α+k}\bigl(\frac{z}{4}\bigr)^k$ and the finite series $\sum_{k=1}^{n}\binom{2k}{k}\frac{1}{α+k}\bigl(\frac{z}{4}\bigr)^k$ in terms of the Gauss hypergeometric function ${}_2F_1\bigl[\tfrac12,α;1+α;z\bigr]$ and a generalized hypergeometric function ${}_3F_2$, for $|z|\le1$ and $n\in\mathbb{N}$. Using the Euler integral representation, we derive closed forms, in terms of finite sums of sines and cosines of $\arcsin\sqrt{z}\,$, for ${}_2F_1\bigl[\tfrac12,\tfrac12+n;\tfrac32+n;z\bigr]$, ${}_2F_1\bigl[\tfrac12,1+n;2+n;z\bigr]$, two related ${}_3F_2$ functions, and the incomplete beta functions $B_z\bigl(\frac12+n,\frac12\bigr)$ and $B_z\bigl(1+n,\frac12\bigr)$. By the Pfaff transformation, we obtain closed forms of several further Gauss hypergeometric functions with parameters shifted by $n$. We also give a closed form of $\bigl[(1-z)\frac{\operatorname{d}}{\operatorname{d}z}(1-z)\bigr]^n\frac{\arcsin\sqrt{z}\,}{\sqrt{z(1-z)}\,}$ and a combinatorial identity.

math.GM↗
arXiv2026

Bernstein and Stieltjes properties of some functions involving logarithmic functions

We show that $\frac1{g(x)}$, with $g(x)=\frac{x-1}{x\ln x}$, is a complete Bernstein function and give its Lévy measure explicitly. For $h(x)=\frac{(x^2-1)\ln(x+1)}{x^2\ln x}$, we prove that $h$ is not a Stieltjes function, so $\frac1h$ is not a complete Bernstein function, but $\frac1h$ is a Bernstein function. The latter rests on the positivity of a function built from the convolution of the exponential integrals $E_1$ and $E_2$. We also give a related completely monotonic function that is not a Stieltjes function.

math.GM↗
arXiv2026

A power series expansion of the Wilf function

In this work, the author employs the Faà di Bruno formula, identities for the partial Bell polynomials, two combinatorial identities, and the (logarithmically) complete monotonicity of generating functions for several integer sequences, together with the Wronski theorem, to investigate a collection of analytic and combinatorial structures. The study establishes Taylor series expansions for various functions involving the inverse (hyperbolic) tangent function and derives the Maclaurin expansion of the Wilf function, a composite of the inverse tangent, square root, and exponential functions. The coefficients in this expansion are expressed in terms of Stirling numbers of the second kind, and their generating functions, limits, positivity, monotonicity, and logarithmic convexity are analyzed. The paper further presents closed-form formulas for special values of the Gauss hypergeometric function and for certain partial Bell polynomials, along with several infinite series representations of the circular constant and related sequences. An asymptotic rational approximation to the circular constant is recovered, and connections among several integer sequences are established via determinants.

math.CO↗
arXiv2026

Theory of Normalized Remainders in Taylor Series Expansions

Since 2023, through the detailed examination of numerous concrete examples, the author and his collaborators have identified a recurring pattern. Building upon this observation, they introduced the concept of the normalized remainder. They deliberately chose this term and subsequently explored its historical background and mathematical significance. In 2026, Abu-Ghuwaleh propelled the subject forward at a deeper structural level. By exploring the broader dynamical and theoretical framework surrounding the normalized remainder family, he significantly developed and formalized the concept, firmly embedding it within the field. Consequently, the notion of the normalized remainder now carries richer and more profound mathematical significance. In this chapter, the author presents a synthesis of the research process and the principal findings related to the normalized remainder.

math.GM↗
arXiv2026

Extensions of several famous combinatorial identities via hypergeometric functions

The objective of this paper is to develop an extension of Kummer's second theorem and to establish generalized forms of four classical combinatorial identities---Knuth's old sum (also known as Reed--Dawson's combinatorial identity), Riordan's combinatorial identity, Gould's combinatorial identity, and Touchard's combinatorial identity---using a hypergeometric-series approach. Several new identities also arise as special cases of our main results.

math.GM↗
arXiv2026

Tokenizing Numerical and Embedding Features for LLM RecSys

Large language models (LLMs) are increasingly used as backbone architectures for recommender systems because of their strong sequence modeling and representation learning capabilities. However, most LLM-based recommenders operate primarily on discrete textual tokens, whereas practical recommendation pipelines also rely on continuous numerical features and dense embedding features produced by upstream feature engineering or pretrained encoders. This mismatch limits the ability of LLM-based models to exploit fine-grained non-textual signals. We propose a soft-token fusion framework that maps numerical and embedding features into the LLM embedding space, allowing heterogeneous recommendation signals to be consumed through the standard token interface. We instantiate the framework in a shared-parameter LLM-based two-tower retrieval model and introduce an interaction-based fusion module that refines embedding and numerical soft tokens before they are inserted into the final LLM input. Experiments on three Amazon recommendation benchmarks show that soft-token fusion improves retrieval performance over LLM-based baselines, and that interaction-based fusion is more effective than direct concatenation of heterogeneous soft tokens.

cs.IR↗
arXiv2026

The Case Against Generation for Retrieval: Discriminative Language Models as Effective Retrievers

Large Language Models (LLMs) have emerged as powerful assets for recommender systems. However, deploying them as generative recommenders or zero-shot rankers at web-scale remains bottlenecked by prohibitive computational overhead and grounding challenges. In this paper, we revitalize the classic, highly efficient two-tower retrieval architecture by adapting LLMs as semantic representation backbones rather than generative engines. We introduce an LLM-native two-tower framework engineered for high-throughput, large-scale retrieval. Our architecture introduces several key innovations: a shared LLM encoder for joint user-item modeling, End-Of-Sentence (EOS) token pooling for compact sequence embedding, cross-dataset transfer learning, knowledge distillation from powerful cross-encoder teachers, and latent reasoning within the user tower. Extensive evaluation across three public benchmarks demonstrates that cross-encoder architecture outperforms current state-of-the-art (SoTA) models, while the efficient two-tower student achieves SoTA-comparable retrieval performance. Furthermore, experiments on internal large-scale production systems yield substantial topline retrieval improvements along with high resilience to model staleness and superior data scaling. Our findings demonstrate that when augmented with modern representation learning, the traditional two-tower paradigm remains an exceptionally competitive and practical solution for industrial retrieval systems.

cs.IR↗
arXiv2026

Monotonicity and inequalities for ratios of Bernoulli polynomials and numbers

In the work, the authors establish the monotonicity of the ratios $$ \frac{B_{2\ell-1}(s)}{B_{2\ell+1}(s)}, \quad \frac{B_{2\ell}(s)}{B_{2\ell+1}(s)}, \quad \frac{B_{2m}(s)}{B_{2\ell}(s)}, \quad \frac{B_{2\ell}(s)}{B_{2\ell-1}(s)}, $$ where $B_\ell(s)$ denotes the Bernoulli polynomials. Using these newly established monotonicity properties, the authors derive several new inequalities and also recover a number of known inequalities involving the Bernoulli polynomials $B_\ell(s)$, the Bernoulli numbers $B_{2\ell}$, and their ratios such as $\frac{B_{2\ell+2}}{B_{2\ell}}$.

math.GM↗
arXiv2026

Monotonicity and absolute convexity of two functions involving Riemann zeta function

Let $ρ>0$ be a constant, let $j\ge0$ be an integer, and let $Γ(z)$ denote the Euler gamma function. With the aid of the integral representation for the Riemann zeta function $ζ(z)$, by virtue of a monotonicity rule, and by means of some properties of the function $\frac{1}{\operatorname{e}^t-1}$ and its derivatives, the authors discuss the increasing monotonicity of the function $t\mapsto\binom{t+ρ+j}ρ\frac{ζ(t+ρ)}{ζ(t)}$, where $\binom{z}{w}$ denotes the extended binomial coefficient, study the absolute convexity and logarithmic convexity of the function $t\mapstoΓ(t+j)ζ(t)$, and derive the increasing monotonicity and inequalities of some sequences involving the ratios $\bigl|\frac{B_{2n+2}} {B_{2n}}\bigr|$ of the Bernoulli numbers $B_{2n}$.

math.NT↗
arXiv2026

MADCrowner: Margin Aware Dental Crown Design with Template Deformation and Refinement

Dental crown restoration is one of the most common treatment modalities for tooth defect, where personalized dental crown design is critical. While computer-aided design (CAD) systems have notably enhanced the efficiency of dental crown design, extensive manual adjustments are still required in the clinic workflow. Recent studies have explored the application of learning-based methods for the automated generation of restorative dental crowns. Nevertheless, these approaches were challenged by inadequate spatial resolution, noisy outputs, and overextension of surface reconstruction. To address these limitations, we propose \totalframework, a margin-aware mesh generation framework comprising CrownDeformR and CrownSegger. Inspired by the clinic manual workflow of dental crown design, we designed CrownDeformR to deform an initial template to the target crown based on anatomical context, which is extracted by a multi-scale intraoral scan encoder. Additionally, we introduced \marginseg, a novel margin segmentation network, to extract the cervical margin of the target tooth. The performance of CrownDeformR improved with the cervical margin as an extra constraint. And it was also utilized as the boundary condition for the tailored postprocessing method, which removed the overextended area of the reconstructed surface. We constructed a large-scale intraoral scan dataset and performed extensive experiments. The proposed method significantly outperformed existing approaches in both geometric accuracy and clinical feasibility.

cs.CV↗
arXiv2026

IGAA: Intent-Driven General Agentic AI for Edge Services Scheduling using Generative Meta Learning

Agentic AI (AAI), which extends Large Language Models with enhanced reasoning capabilities, has emerged as a promising paradigm for autonomous edge service scheduling. However, user mobility creates highly dynamic service demands in edge networks, and existing service scheduling agents often lack generalization capabilities for new scenarios. Therefore, this paper proposes a novel Intent-Driven General Agentic AI (IGAA) framework. Leveraging a meta-learning paradigm, IGAA enables AAI to continuously learn from prior service scheduling experiences to achieve generalized scheduling capabilities. Particularly, IGAA incorporates three core mechanisms. First, we design a Network-Service-Intent matrix mapping method to allow agents to simulate novel scenarios and generate training datasets. Second, we present an easy-to-hard generalization learning scheme with two customized algorithms, namely Resource Causal Effect-aware Transfer Learning (RCETL) and Action Potential Optimality-aware Transfer Learning (APOTL). These algorithms help IGAA adapt to new scenarios. Furthermore, to prevent catastrophic forgetting during continual IGAA learning, we propose a Generative Intent Replay (GIR) mechanism that synthesizes historical service data to consolidate prior capabilities. Finally, to mitigate the effect of LLM hallucinations on scenario simulation, we incorporate a scenario evaluation and correction model to guide agents in generating rational scenarios and datasets. Extensive experiments demonstrate IGAA's strong generalization and scalability. Specifically, IGAA enables rapid adaptation by transferring learned policies to analogous new ones, such as applying latency-sensitive patterns from real-time computing to optimize novel Internet of Vehicles (IoV) services. Compared to scenario-specific methods, IGAA maintains the intent-satisfaction rate gap within 3.81%.

cs.NI↗
arXiv2026

Generative Intent Prediction Agentic AI empowered Edge Service Function Chain Orchestration

With the development of artificial intelligence (AI), Agentic AI (AAI) based on large language models (LLMs) is gradually being applied to network management. However, in edge network environments, high user mobility and implicit service intents pose significant challenges to the passive and reactive management of traditional AAI. To address the limitations of existing approaches in handling dynamic demands and predicting users' implicit intents, in this paper we propose an edge service function chain (SFC) orchestration framework empowered by a Generative Intent Prediction Agent (GIPA). Our GIPA aims to shift the paradigm from passive execution to proactive prediction and orchestration. First, we construct a multidimensional intent space that includes functional preferences, QoS sensitivity, and resource requirements, enabling the mapping from unstructured natural language to quantifiable physical resource demands. Second, to cope with the complexity and randomness of intent sequences, we design an intent prediction model based on a Generative Diffusion Model (GDM), which reconstructs users' implicit intents from multidimensional context through a reverse denoising process. Finally, the predicted implicit intents are embedded as global prompts into the SFC orchestration model to guide the network in proactively and ahead-of-time optimizing SFC deployment strategies. Experiment results show that GIPA outperforms existing baseline methods in highly concurrent and highly dynamic scenarios.

cs.NI↗
arXiv2025

Toward Integrated Air-Ground Computing and Communications: A Synergy of Computing Power Networks and Low-Altitude Economy Network

With the rapid rise of the Low-Altitude Economy (LAE), the demand for intelligent processing and real-time response in services such as aerial traffic, emergency communications, and environmental monitoring continues to grow. Meanwhile, the Computing Power Network (CPN) aims to integrate global computing resources and perform on-demand scheduling to efficiently handle services from diverse sources. However, it is limited by static deployment and limited adaptability. In this paper, we analyze the complementary relationship between LAE and CPN and propose a novel air-ground collaborative intelligent service provision with an agentification paradigm. Through synergy between LAE and CPNs, computing and communication services are jointly scheduled and collaboratively optimized to enhance the execution efficiency of low-altitude services and improve the flexibility of CPNs. It also integrates LAE's strengths in aerial sensing, mobile coverage, and dynamic communication links, forming a cloud-edge-air collaborative framework. Hence, we review the characteristics and limitations of both LAE and CPN and explore how they can cooperate to overcome these limitations. Then we demonstrate the flexibility of the integrated CPN and LAE framework through a case study. Finally, we summarize the key challenges in constructing an integrated air-ground computing and communication system and discuss future research directions toward emerging technologies.

cs.NI↗
arXiv2025

ArchPilot: A Proxy-Guided Multi-Agent Approach for Machine Learning Engineering

Recent LLM-based agents have demonstrated strong capabilities in automated ML engineering. However, they heavily rely on repeated full training runs to evaluate candidate solutions, resulting in significant computational overhead, limited scalability to large search spaces, and slow iteration cycles. To address these challenges, we introduce ArchPilot, a multi-agent system that integrates architecture generation, proxy-based evaluation, and adaptive search into a unified framework. ArchPilot consists of three specialized agents: an orchestration agent that coordinates the search process using a Monte Carlo Tree Search (MCTS)-inspired novel algorithm with a restart mechanism and manages memory of previous candidates; a generation agent that iteratively generates, improves, and debugs candidate architectures; and an evaluation agent that executes proxy training runs, generates and optimizes proxy functions, and aggregates the proxy scores into a fidelity-aware performance metric. This multi-agent collaboration allows ArchPilot to prioritize high-potential candidates with minimal reliance on expensive full training runs, facilitating efficient ML engineering under limited budgets. Experiments on MLE-Bench demonstrate that ArchPilot outperforms SOTA baselines such as AIDE and ML-Master, validating the effectiveness of our multi-agent system.

cs.AI↗