arXiv subjects

Gao Zhang

Publications and source records attributed to Gao Zhang.

9 recordsLinked to original sources

arXiv2026

Remarks on $d$-independent topological groups

A non-trivial topological group is called \emph{$d$-independent} if for every subgroup of cardinality less than the continuum there exists a countable dense subgroup intersecting it trivially. This notion was introduced by Márquez and Tkachenko and has been intensively studied in the metrizable setting. In particular, they proved that a second-countable locally compact abelian group is $d$-independent if and only if it is algebraically an $M$-group, and asked whether the same conclusion holds for all separable locally compact groups. In this paper we give an affirmative answer to this question. We show that every separable locally compact abelian $M$-group is $d$-independent, thereby removing the metrizability assumption from the result of Márquez and Tkachenko. In addition, we investigate several further aspects of $d$-independence. We study its behaviour under taking powers of topological groups and extend the notion of $d$-independence to the non-abelian setting. Moreover, we prove that every separable connected compact group is $d$-independent, thereby answering another question posed by Márquez and Tkachenko.

math.GR↗

arXiv2025

AI Hiring with LLMs: A Context-Aware and Explainable Multi-Agent Framework for Resume Screening

Resume screening is a critical yet time-intensive process in talent acquisition, requiring recruiters to analyze vast volume of job applications while remaining objective, accurate, and fair. With the advancements in Large Language Models (LLMs), their reasoning capabilities and extensive knowledge bases demonstrate new opportunities to streamline and automate recruitment workflows. In this work, we propose a multi-agent framework for resume screening using LLMs to systematically process and evaluate resumes. The framework consists of four core agents, including a resume extractor, an evaluator, a summarizer, and a score formatter. To enhance the contextual relevance of candidate assessments, we integrate Retrieval-Augmented Generation (RAG) within the resume evaluator, allowing incorporation of external knowledge sources, such as industry-specific expertise, professional certifications, university rankings, and company-specific hiring criteria. This dynamic adaptation enables personalized recruitment, bridging the gap between AI automation and talent acquisition. We assess the effectiveness of our approach by comparing AI-generated scores with ratings provided by HR professionals on a dataset of anonymized online resumes. The findings highlight the potential of multi-agent RAG-LLM systems in automating resume screening, enabling more efficient and scalable hiring workflows.

cs.CL↗

arXiv2024

Constructing Psuedo-$τ$-fine Precompact Groups

Let $τ$ be an uncountable cardinal. The notion of a \emph{$τ$-fine} topological group was introduced in 2021. More recently, H. Zhang et al. generalized this concept by defining pseudo-$τ$-fine topological groups to study certain factorization properties of continuous functions on topological groups. It is known that $τ$-fineness cannot coexist with precompactness in topological groups with uncountable character. In this paper, we investigate this problem further. We prove that, in topological groups with uncountable pseudocharacter, precompactness can coexist with pseudo-$τ$-fineness for some bounded $τ$ but pseudocompactness can never.

math.GN↗

arXiv2023

On the Intrinsic Structures of Spiking Neural Networks

Recent years have emerged a surge of interest in SNNs owing to their remarkable potential to handle time-dependent and event-driven data. The performance of SNNs hinges not only on selecting an apposite architecture and fine-tuning connection weights, similar to conventional ANNs, but also on the meticulous configuration of intrinsic structures within spiking computations. However, there has been a dearth of comprehensive studies examining the impact of intrinsic structures. Consequently, developers often find it challenging to apply a standardized configuration of SNNs across diverse datasets or tasks. This work delves deep into the intrinsic structures of SNNs. Initially, we unveil two pivotal components of intrinsic structures: the integration operation and firing-reset mechanism, by elucidating their influence on the expressivity of SNNs. Furthermore, we draw two key conclusions: the membrane time hyper-parameter is intimately linked to the eigenvalues of the integration operation, dictating the functional topology of spiking dynamics, and various hyper-parameters of the firing-reset mechanism govern the overall firing capacity of an SNN, mitigating the injection ratio or sampling density of input data. These findings elucidate why the efficacy of SNNs hinges heavily on the configuration of intrinsic structures and lead to a recommendation that enhancing the adaptability of these structures contributes to improving the overall performance and applicability of SNNs. Inspired by this recognition, we propose two feasible approaches to enhance SNN learning. These involve leveraging self-connection architectures and employing stochastic spiking neurons to augment the adaptability of the integration operation and firing-reset mechanism, respectively. We verify the effectiveness of the proposed methods from perspectives of theory and practice.

cs.NE↗

arXiv2022

On the Approximation and Complexity of Deep Neural Networks to Invariant Functions

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and complexity, i.e., showing which architecture and size are sufficient to handle the concerned tasks. This work takes one step on this direction by theoretically studying the approximation and complexity of deep neural networks to invariant functions. We first prove that the invariant functions can be universally approximated by deep neural networks. Then we show that a broad range of invariant functions can be asymptotically approximated by various types of neural network models that includes the complex-valued neural networks, convolutional neural networks, and Bayesian neural networks using a polynomial number of parameters or optimization iterations. We also provide a feasible application that connects the parameter estimation and forecasting of high-resolution signals with our theoretical conclusions. The empirical results obtained on simulation experiments demonstrate the effectiveness of our method.

cs.LG↗

arXiv2021

Sober topological spaces valued in a quantale

The notion of sobriety is extended to the realm of topological spaces valued in a commutative and unital quantale, via an adjunction between a category of quantale modules and the category of quantale-valued topological spaces. Relations between such sober spaces and quantale-valued domains based on flat ideals are investigated.

math.GN↗

arXiv2020

The saturated prefilter monad

This paper considers some extensions of the notion of filter to the quantale-valued context, including saturated prefilter, $\top$-filter and bounded saturated prefilter. The question is whether these constructions give rise to monads on the category of sets. It is shown that the answer depends on the structure of the quantale. Specifically, if the quantale is the unit interval equipped with a continuous t-norm, then these constructions give rise to monads if and only if the implication operator corresponding to that t-norm is continuous at each point off the diagonal.

math.CT↗

arXiv2018

A comparative study of ideals in fuzzy orders

This paper presents a comparative study of three kinds of ideals in fuzzy order theory: forward Cauchy ideals (generated by forward Cauchy nets), flat ideals and irreducible ideals, including their role in connecting fuzzy order with fuzzy topology.

math.GM↗

arXiv2018

Flat ideals in the unit interval with the canonical fuzzy order

A characterization of flat ideals in the unit interval with the canonical fuzzy order is obtained with the help of the ordinal sum decomposition of continuous t-norms. This characterization will be useful in the study of topological and domain theoretic properties of fuzzy orders.

math.GM↗