arXiv subjects
Publications and source records attributed to Feng Qi.
In the paper, the author develops a general convexity lemma and applies it to demonstrate the monotonic decrease of a function involving polygamma functions, arising from the sectional curvature of the Fisher--Rao manifold of beta distributions.
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.
Let $\mathbb{Z}^-=\setminus\{-1,-2,\dotsc\}$. In 2023, Qi and Lim gave two claims for summing the infinite series $$ \sum_{k=1}^{\infty} \binom{2k}{k} \frac{1}{\alpha+k} \biggl(\frac{\pm1}{4}\biggr)^k, \quad \alpha\in\mathbb{C}\setminus\mathbb{Z}^-. $$ In present paper, the authors establish several sum functions of the infinite and finite series $$ \sum_{k=1}^{\infty}\binom{2k}{k}\frac{1}{\alpha+k}\biggl(\frac{z}{4}\biggr)^k \quad\text{and}\quad \sum_{k=1}^{n}\binom{2k}{k}\frac{1}{\alpha+k}\biggl(\frac{z}{4}\biggr)^k $$ for $\alpha\in\mathbb{C}\setminus\mathbb{Z}^-$ and $n\in\mathbb{N}=\{1,2,\dotsc\}$ in terms of the Gauss hypergeometric functions ${}_2F_1$ and the generalized hypergeometric functions ${}_3F_2$ for $\alpha\in\mathbb{C}\setminus\mathbb{Z}^-$ and $n\in\mathbb{N}$. In light of the Euler integral representation of the Gauss hypergeometric function ${}_2F_1$, the author present several closed forms of two Gauss hypergeometric functions ${}_2F_1$, two generalized hypergeometric functions ${}_3F_2$, and the classical incomplete beta functions $B_z\bigl(\frac12, \frac{1}{2}+n\bigr)$ and $B_z\bigl(\frac12, 1+n\bigr)$. With the help of the Euler hypergeometric transform, the authors derive closed forms of five Gauss hypergeometric functions. In addition, the authors also obtain a closed form of the differential operator $\bigl[(1-z)\frac{\operatorname{d}}{\operatorname{d}z}(1-z)\bigr]^n \frac{\arcsin\sqrt{z}}{\sqrt{z(1-z)}}$ for $n\in\mathbb{N}_0=\{0\}\cup\mathbb{N}$.
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.
In present paper, with the help of the Fa\`a di Bruno formula and 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}, \end{equation*} where $m\in\mathbb{N}_0$, $n\in\mathbb{Z}$, and $a\in\mathbb{C}$. These newly-established identities generalize the nice and 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 recent 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".
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.
In the paper, in light of the generating function of the complete Bell polynomials and other techniques, the author presents concise and elegant proofs of three formulas for the complete Bell polynomials.
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.
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%.
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.
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.
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.
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.
The efficiency of GPU kernels is central to the progress of modern AI, yet optimizing them remains a difficult and labor-intensive task due to complex interactions between memory hierarchies, thread scheduling, and hardware-specific characteristics. While recent advances in large language models (LLMs) provide new opportunities for automated code generation, existing approaches largely treat LLMs as single-shot generators or naive refinement tools, limiting their effectiveness in navigating the irregular kernel optimization landscape. We introduce an LLM agentic framework for GPU kernel optimization that systematically explores the design space through multi-agent collaboration, grounded instruction, dynamic context management, and strategic search. This framework mimics the workflow of expert engineers, enabling LLMs to reason about hardware trade-offs, incorporate profiling feedback, and refine kernels iteratively. We evaluate our approach on KernelBench, a benchmark for LLM-based kernel optimization, and demonstrate substantial improvements over baseline agents: our system produces correct solutions where baselines often fail, and achieves kernels with up to 16x faster runtime performance. These results highlight the potential of agentic LLM frameworks to advance fully automated, scalable GPU kernel optimization.
In the note, the authors give a unified proof of Identities~67, 84, and~85 in the monograph "M. Z. Spivey, The Art of Proving Binomial Identities, Discrete Mathematics and its Applications, CRC Press, Boca Raton, FL, 2019; available online at https://doi.org/10.1201/9781351215824" and connect these three identities with a computing formula for the Stirling numbers of the second kind. Moreover, in terms of the notion of Qi's normalized remainders of the exponential and logarithmic functions, the authors reformulate the definitions of the Stirling numbers of the first and second kind and their generalizations by Howard in 1967 and 1980, Carlitz in 1980, and Broder in 1984.
We propose Quick Feedforward (QF) Learning, a novel knowledge consolidation framework for transformer-based models that enables efficient transfer of instruction derived knowledge into model weights through feedforward activations without any gradient back propagation. Unlike traditional finetuning, QF updates are computed in closed form, require minimal parameter modification, and preserve prior knowledge. Importantly, QF allows models to train and infer within the same runtime environment, making the process more resource efficient and closely aligned with how the human brain operates. Code and models are open sourced on GitHub. I hope QF Learning inspires a more efficient and brain-like paradigm for AI systems.
In this paper, by virtue of a determinantal formula for derivatives of the ratio between two differentiable functions, in view of the Fa\`a di Bruno formula, and with the help of several identities and closed-form formulas for the partial Bell polynomials $\operatorname{B}_{n,k}$, the author establishes thirteen Maclaurin series expansions of the functions \begin{align*} &\ln\frac{\operatorname{e}^x+1}{2}, && \ln\frac{\operatorname{e}^x-1}{x}, && \ln\cosh x, \\ &\ln\frac{\sinh x}{x}, && \biggl[\frac{\ln(1+x)}{x}\biggr]^r, && \biggl(\frac{\operatorname{e}^x-1}{x}\biggr)^r \end{align*} for $r=\pm\frac{1}{2}$ and $r\in\mathbb{R}$ in terms of the Dirichlet eta function $\eta(1-2k)$, the Riemann zeta function $\zeta(1-2k)$, and the Stirling numbers of the first and second kinds $s(n,k)$ and $S(n,k)$. presents four determinantal expressions and three recursive relations for the Bernoulli numbers $B_{2n}$. finds out three closed-form formulas for the Bernoulli numbers $B_{2n}$ and the generalized Bernoulli numbers $B_n^{(r)}$ in terms of the Stirling numbers of the second kind $S(n,k)$, and deduce two combinatorial identities for the Stirling numbers of the second kind $S(n,k)$. acquires two combinatorial identities, which can be regarded as diagonal recursive relations, involving the Stirling numbers of the first and second kinds $s(n,k)$ and $S(n,k)$. recovers an integral representation and a closed-form formula, and establish an alternative explicit and closed-form formula, for the Bernoulli numbers of the second kind $b_n$ in terms of the Stirling numbers of the first kind $s(n,k)$. obtains three identities connecting the Stirling numbers of the first and second kinds $s(n,k)$ and $S(n,k)$.
In the paper, the author expresses the difference $2^m\bigl[\zeta\bigl(-m,\frac{1+x}{2}\bigr)-\zeta\bigl(-m,\frac{2+x}{2}\bigr)\bigr]$ in terms of a linear combination of the function $\Gamma(m+1){\,}_2F_1(-m,-x;1;2)$ for $m\in\mathbb{N}_0$ and $x\in(-1,\infty)$ in the form of matrix equations, where $\Gamma(z)$, $\zeta(z,\alpha)$, and ${}_2F_1(a,b;c;z)$ stand for the classical Euler gamma function, the Hurwitz zeta function, and the Gauss hypergeometric function, respectively. This problem originates from the Landau level quantization in solid state materials.