arXiv subjects

Qiyu Sun

Publications and source records attributed to Qiyu Sun.

At least 19 recordsLinked to original sources

arXiv2026

Multi-Agent Systems: From Classical Paradigms to Large Foundation Model-Enabled Futures

With the rapid advancement of artificial intelligence, multi-agent systems (MASs) are evolving from classical paradigms toward architectures built upon large foundation models (LFMs). This survey provides a systematic review and comparative analysis of classical MASs (CMASs) and LFM-based MASs (LMASs). First, within a closed-loop coordination framework, CMASs are reviewed across four fundamental dimensions: perception, communication, decision-making, and control. Beyond this framework, LMASs integrate LFMs to lift collaboration from low-level state exchanges to semantic-level reasoning, enabling more flexible coordination and improved adaptability across diverse scenarios. Then, a comparative analysis is conducted to contrast CMASs and LMASs across architecture, operating mechanism, adaptability, and application. Finally, future perspectives on MASs are presented, summarizing open challenges and potential research opportunities.

cs.AI↗

arXiv2026

Shift-invariant spaces on finite undirected graphs

Shift-invariant spaces (SISs) on the real line provide a natural framework for representing, analyzing and processing signals with inherent shift-invariant structure. In this paper, we extend this framework to the finite undirected graph setting by introducing the concept of graph shift-invariant spaces (GSISs). We examine several properties of GSISs, including their characterization via range functions and fiber functions in the Fourier domain, their connections to shift-invariant filters and polynomial filters, the frame and Riesz basis structures of finitely generated GSISs, and their intricate relationships with bandlimited spaces, finitely generated GSISs, and graph reproducing kernel Hilbert spaces with shift-invariant reproducing kernels (SIGRKHSs). Our analysis reveals several distinctions between SISs on the line and GSISs, such as the shift-invariance of the frame operator, the existence of shift-invariant dual frames, the emergence of fractional shift-invariance, and the interrelationships among GSISs, finitely generated GSISs, SIGRKHSs and bandlimited spaces. In this paper, we also introduce a spectral decomposition of the identity associated with graph shifts and propose a novel definition of the graph Fourier transform (GFT) of spectral type, together with explicit formulations for the GFTs on complete graphs and circulant graphs. In addition, we establish a clear connection between polynomial filters and shift-invariant filters, and we derive a graph uncertainty principle governing the essential supports of a nonzero graph signal and its GFT.

math.FA↗

arXiv2026

inversedMixup: Data Augmentation via Inverting Mixed Embeddings

Mixup generates augmented samples by linearly interpolating inputs and labels with a controllable ratio. However, since it operates at the latent embedding level, the resulting samples are not human-interpretable. In contrast, LLM-based augmentation methods produce sentences via prompts at the token level, yielding readable outputs but offering limited control over the generation process. Inspired by recent advances in LLM inversion, which reconstructs natural language from embeddings and helps bridge the gap between latent embedding space and discrete token space, we propose inversedMixup, a unified framework that combines the controllability of Mixup with the interpretability of LLM-based generation. Specifically, inversedMixup aligns the output embedding space of a task-specific model with the input embedding space of an LLM, so that mixed embeddings can be reconstructed, under a controllable mixing ratio, into human-interpretable sentences. This interpretability provides the first empirical evidence of the manifold intrusion phenomenon in text Mixup. Building on this, we extend inversedMixup into a three-stage data augmentation method, and introduce a simple yet effective strategy to mitigate manifold intrusion during augmentation. Extensive experiments demonstrate the effectiveness and generalizability of our approach in both few-shot and fully supervised scenarios.

cs.CL↗

arXiv2025

Beyond Carleman Linearization of Nonlinear Dynamical System: Insights from a Case Study

Nonlinear dynamical systems are widely encountered in various scientific and engineering fields. Despite significant advances in theoretical understanding, developing complete and integrated frameworks for analyzing and designing these systems remains challenging, which underscores the importance of efficient linearization methods. In this paper, we introduce a general linearization framework with emphasis on Carleman linearization and Carleman-Fourier linearization. A detailed case study on finite-section approximation to the lifted infinite-dimensional dynamical system is provided for the dynamical system with its governing function being a trigonometric polynomial of degree one.

math.DS↗

arXiv2025

Exponential convergence of a distributed divide-and-conquer algorithm for constrained convex optimization on networks

We propose a divide-and-conquer (DAC) algorithm for constrained convex optimization over networks, where the global objective is the sum of local objectives attached to individual agents. The algorithm is fully distributed: each iteration solves local subproblems around selected fusion centers and coordinates only with neighboring fusion centers. Under standard assumptions of smoothness, strong convexity, and locality on the objective function, together with polynomial growth conditions on the underlying graph, we establish exponential convergence of the DAC iterations and derive explicit bounds for both exact and inexact local solvers. Numerical experiments on three representative losses ($L_2$ distance, quadratic, and entropy) confirm the theory and demonstrate scalability and effectiveness.

math.OC↗

arXiv2025

Kalman Filtering of Stationary Graph Signals

In this paper, we propose a novel definition of stationary graph signals, formulated with respect to a symmetric graph shift, such as the graph Laplacian. We show that stationary graph signals can be generated by transmitting white noise through polynomial graph channels, and that their stationarity is preserved under polynomial channel transmission. In this paper, we also investigate Kalman filtering to dynamical systems characterized by polynomial state and observation matrices. We demonstrate that Kalman filtering maintains the stationarity of graph signals, while effectively incorporating both system dynamics and noise structure. In comparison to the static inverse filtering method and naive zero-signal strategy, the Kalman filtering procedure yields more accurate and adaptive signal estimates, highlighting its robustness and versatility in graph signal processing.

eess.SP↗

arXiv2025

Blind Deconvolution of Nonstationary Graph Signals over Shift-Invariant Channels

In this paper, we investigate blind deconvolution of nonstationary graph signals from noisy observations, transmitted through an unknown shift-invariant channel. The deconvolution process assumes that the observer has access to the covariance structure of the original graph signals. To evaluate the effectiveness of our channel estimation and blind deconvolution method, we conduct numerical experiments using a temperature dataset in the Brest region of France.

cs.IT↗

arXiv2025

Easy Dataset: A Unified and Extensible Framework for Synthesizing LLM Fine-Tuning Data from Unstructured Documents

Large language models (LLMs) have shown impressive performance on general-purpose tasks, yet adapting them to specific domains remains challenging due to the scarcity of high-quality domain data. Existing data synthesis tools often struggle to extract reliable fine-tuning data from heterogeneous documents effectively. To address this limitation, we propose Easy Dataset, a unified framework for synthesizing fine-tuning data from unstructured documents via an intuitive graphical user interface (GUI). Specifically, Easy Dataset allows users to easily configure text extraction models and chunking strategies to transform raw documents into coherent text chunks. It then leverages a persona-driven prompting approach to generate diverse question-answer pairs using public-available LLMs. Throughout the pipeline, a human-in-the-loop visual interface facilitates the review and refinement of intermediate outputs to ensure data quality. Experiments on a financial question-answering task show that fine-tuning LLMs on the synthesized dataset significantly improves domain-specific performance while preserving general knowledge. The source code and installable package are available at https://github.com/ConardLi/easy-dataset and have garnered over 9,000 GitHub stars.

cs.CL↗

arXiv2025

Iterative Polynomial Approximation Algorithms for Inverse Graph Filters

Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose iterative polynomial approximation algorithms to implement the inverse filter with a polynomial graph filter of commutative graph shifts in a distributed manner. The proposed algorithms exhibit exponential convergence properties, and they can be implemented on distributed networks in which agents are equipped with a data processing subsystem for limited data storage and computation power, and with a one-hop communication subsystem for direct data exchange only with their adjacent agents. Our simulations show that the proposed polynomial approximation algorithms may converge faster than the Chebyshev polynomial approximation algorithm and the conventional gradient descent algorithm do.

eess.SP↗

arXiv2025

Carleman-Fourier linearization of nonlinear real dynamical systems with quasi-periodic fields

This paper presents Carleman-Fourier linearization for analyzing nonlinear real dynamical systems with periodic vector fields. Using Fourier basis functions, this novel framework transforms such dynamical systems into equivalent infinite-dimensional linear dynamical systems. In this paper, we establish the exponential convergence of the primary block in the finite-section approximation of this linearized system to the state vector of the original nonlinear system. To showcase the efficacy of our approach, we apply it to the Kuramoto model, a prominent model for coupled oscillators. The results demonstrate promising accuracy in approximating the original system's behavior.

math.DS↗

arXiv2025

Causal Learning for Heterogeneous Subgroups Based on Nonlinear Causal Kernel Clustering

Due to the challenge posed by multi-source and heterogeneous data collected from diverse environments, causal relationships among features can exhibit variations influenced by different time spans, regions, or strategies. This diversity makes a single causal model inadequate for accurately representing complex causal relationships in all observational data, a crucial consideration in causal learning. To address this challenge, the nonlinear Causal Kernel Clustering method is introduced for heterogeneous subgroup causal learning, highlighting variations in causal relationships across diverse subgroups. The main component for clustering heterogeneous subgroups lies in the construction of the $u$-centered sample mapping function with the property of unbiased estimation, which assesses the differences in potential nonlinear causal relationships in various samples and supported by causal identifiability theory. Experimental results indicate that the method performs well in identifying heterogeneous subgroups and enhancing causal learning, leading to a reduction in prediction error.

cs.LG↗

arXiv2024

Shift-invariant spaces, bandlimited spaces and reproducing kernel spaces with shift-invariant kernels on undirected finite graphs

In this paper, we introduce the concept of graph shift-invariant space (GSIS) on an undirected finite graph, which is the linear space of graph signals being invariant under graph shifts, and we study its bandlimiting, kernel reproducing and sampling properties. Graph bandlimited spaces have been widely applied where large datasets on networks need to be handled efficiently. In this paper, we show that every GSIS is a bandlimited space, and every bandlimited space is a principal GSIS. Functions in a reproducing kernel Hilbert space with shift-invariant kernel could be learnt with significantly low computational cost. In this paper, we demonstrate that every GSIS is a reproducing kernel Hilbert space with a shift-invariant kernel. Based on the nested Krylov structure of GSISs in the spatial domain, we propose a novel sampling and reconstruction algorithm with finite steps, with its performance tested for well-localized signals on circulant graphs and flight delay dataset of the 50 busiest airports in the USA.

eess.SP↗

arXiv2024

Carleman-Fourier Linearization of Complex Dynamical Systems: Convergence and Explicit Error Bounds

This paper presents a Carleman-Fourier linearization method for nonlinear dynamical systems with periodic vector fields involving multiple fundamental frequencies. By employing Fourier basis functions, the nonlinear dynamical system is transformed into a linear model on an infinite-dimensional space. The proposed approach yields accurate approximations over extended regions around equilibria and for longer time horizons, compared to traditional Carleman linearization with monomials. Additionally, we develop a finite-section approximation for the resulting infinite-dimensional system and provide explicit error bounds that demonstrate exponential convergence to the original system's solution as the truncation length increases. For specific classes of dynamical systems, exponential convergence is achieved across the entire time horizon. The practical significance of these results lies in guiding the selection of suitable truncation lengths for applications such as model predictive control, safety verification through reachability analysis, and efficient quantum computing algorithms. The theoretical findings are validated through illustrative simulations.

math.DS↗

arXiv2024

On Sylvester equations in Banach subalgebras

Let ${\mathcal B}$ be a Banach algebra and ${\mathcal A}$ be a Banach subalgebra that admits norm-controlled inversion in ${\mathcal B}$. In this work, we take $A, B$ in the Banach subalgebra ${\mathcal A}$ with their spectra in the Banach algebra ${\mathcal B}$ being disjoint, and show that the operator Sylvester equation $ BX-XA=Q$ has a unique solution $X\in {\mathcal A}$ for every $Q\in {\mathcal A}$. Under the additional assumptions that ${\mathcal B}$ is the operator algebra ${\mathcal B}(H)$ on a Hilbert space $H$ and that $A$ and $B$ are normal in ${\mathcal B}(H)$, an explicit norm estimate for the solution $X$ of the above operator Sylvester equation is provided in this work. In addition, the above conclusion on norm control is applied to Banach subalgebras of localized infinite matrices and integral operators.

math.FA↗

arXiv2024

Computer vision tasks for intelligent aerospace missions: An overview

Computer vision tasks are crucial for aerospace missions as they help spacecraft to understand and interpret the space environment, such as estimating position and orientation, reconstructing 3D models, and recognizing objects, which have been extensively studied to successfully carry out the missions. However, traditional methods like Kalman Filtering, Structure from Motion, and Multi-View Stereo are not robust enough to handle harsh conditions, leading to unreliable results. In recent years, deep learning (DL)-based perception technologies have shown great potential and outperformed traditional methods, especially in terms of their robustness to changing environments. To further advance DL-based aerospace perception, various frameworks, datasets, and strategies have been proposed, indicating significant potential for future applications. In this survey, we aim to explore the promising techniques used in perception tasks and emphasize the importance of DL-based aerospace perception. We begin by providing an overview of aerospace perception, including classical space programs developed in recent years, commonly used sensors, and traditional perception methods. Subsequently, we delve into three fundamental perception tasks in aerospace missions: pose estimation, 3D reconstruction, and recognition, as they are basic and crucial for subsequent decision-making and control. Finally, we discuss the limitations and possibilities in current research and provide an outlook on future developments, including the challenges of working with limited datasets, the need for improved algorithms, and the potential benefits of multi-source information fusion.

cs.CV↗

arXiv2024

Scalable Networked Feature Selection with Randomized Algorithm for Robot Navigation

We address the problem of sparse selection of visual features for localizing a team of robots navigating an unknown environment, where robots can exchange relative position measurements with neighbors. We select a set of the most informative features by anticipating their importance in robots localization by simulating trajectories of robots over a prediction horizon. Through theoretical proofs, we establish a crucial connection between graph Laplacian and the importance of features. We show that strong network connectivity translates to uniformity in feature importance, which enables uniform random sampling of features and reduces the overall computational complexity. We leverage a scalable randomized algorithm for sparse sums of positive semidefinite matrices to efficiently select the set of the most informative features and significantly improve the probabilistic performance bounds. Finally, we support our findings with extensive simulations.

cs.RO↗

arXiv2023

Barron Space for Graph Convolution Neural Networks

Graph convolutional neural network (GCNN) operates on graph domain and it has achieved a superior performance to accomplish a wide range of tasks. In this paper, we introduce a Barron space of functions on a compact domain of graph signals. We prove that the proposed Barron space is a reproducing kernel Banach space, it can be decomposed into the union of a family of reproducing kernel Hilbert spaces with neuron kernels, and it could be dense in the space of continuous functions on the domain. Approximation property is one of the main principles to design neural networks. In this paper, we show that outputs of GCNNs are contained in the Barron space and functions in the Barron space can be well approximated by outputs of some GCNNs in the integrated square and uniform measurements. We also estimate the Rademacher complexity of functions with bounded Barron norm and conclude that functions in the Barron space could be learnt from their random samples efficiently.

stat.ML↗

arXiv2023

GasMono: Geometry-Aided Self-Supervised Monocular Depth Estimation for Indoor Scenes

This paper tackles the challenges of self-supervised monocular depth estimation in indoor scenes caused by large rotation between frames and low texture. We ease the learning process by obtaining coarse camera poses from monocular sequences through multi-view geometry to deal with the former. However, we found that limited by the scale ambiguity across different scenes in the training dataset, a naïve introduction of geometric coarse poses cannot play a positive role in performance improvement, which is counter-intuitive. To address this problem, we propose to refine those poses during training through rotation and translation/scale optimization. To soften the effect of the low texture, we combine the global reasoning of vision transformers with an overfitting-aware, iterative self-distillation mechanism, providing more accurate depth guidance coming from the network itself. Experiments on NYUv2, ScanNet, 7scenes, and KITTI datasets support the effectiveness of each component in our framework, which sets a new state-of-the-art for indoor self-supervised monocular depth estimation, as well as outstanding generalization ability. Code and models are available at https://github.com/zxcqlf/GasMono

cs.CV↗