arXiv subjects

Jiarui Song

Publications and source records attributed to Jiarui Song.

7 recordsLinked to original sources

arXiv2026

A geometric approach to the uniform boundedness of $\ell$-primary torsion points

We prove that for a non-isotrivial abelian scheme over a smooth curve, the genus of a generic sequence of multi-sections with small heights tends to infinity. As an application, we give a new proof of the uniform boundedness of $\ell$-primary torsion points on fibers of an abelian scheme over a smooth curve, a result originally proved by Cadoret and Tamagawa. Furthermore, our approach allows us to resolve a conjecture of Cadoret and Tamagawa without additional assumptions. Our approach is based on the theory of Betti foliations and the arithmetic equidistribution theorem.

math.NT↗

arXiv2025

Arithmetic Degrees are Cohomological Lyapunov Multipliers

For endomorphisms of projective varieties, we prove that the arithmetic degree of a point with Zariski dense orbit must be a cohomological Lyapunov multiplier of the dynamical system. We will apply our result to deduce a corollary towards the dynamical Mordell--Lang conjecture.

math.DS↗

arXiv2025

FedAGHN: Personalized Federated Learning with Attentive Graph HyperNetworks

Personalized Federated Learning (PFL) aims to address the statistical heterogeneity of data across clients by learning the personalized model for each client. Among various PFL approaches, the personalized aggregation-based approach conducts parameter aggregation in the server-side aggregation phase to generate personalized models, and focuses on learning appropriate collaborative relationships among clients for aggregation. However, the collaborative relationships vary in different scenarios and even at different stages of the FL process. To this end, we propose Personalized Federated Learning with Attentive Graph HyperNetworks (FedAGHN), which employs Attentive Graph HyperNetworks (AGHNs) to dynamically capture fine-grained collaborative relationships and generate client-specific personalized initial models. Specifically, AGHNs empower graphs to explicitly model the client-specific collaborative relationships, construct collaboration graphs, and introduce tunable attentive mechanism to derive the collaboration weights, so that the personalized initial models can be obtained by aggregating parameters over the collaboration graphs. Extensive experiments can demonstrate the superiority of FedAGHN. Moreover, a series of visualizations are presented to explore the effectiveness of collaboration graphs learned by FedAGHN.

cs.LG↗

arXiv2024

A Parameter Adaptive Trajectory Tracking and Motion Control Framework for Autonomous Vehicle

This paper studies the trajectory tracking and motion control problems for autonomous vehicles (AVs). A parameter adaptive control framework for AVs is proposed to enhance tracking accuracy and yaw stability. While establishing linear quadratic regulator (LQR) and three robust controllers, the control framework addresses trajectory tracking and motion control in a modular fashion, without introducing complexity into each controller. The robust performance has been guaranteed in three robust controllers by considering the parameter uncertainties, mismatch of unmodeled subsystem as well as external disturbance, comprehensively. Also, the dynamic characteristics of uncertain parameters are identified by Recursive Least Squares (RLS) algorithm, while the boundaries of three robust factors are determined through combining Gaussian Process Regression (GPR) and Bayesian optimization machine learning methods, reducing the conservatism of the controller. Sufficient conditions for closed-loop stability under the diverse robust factors are provided by the Lyapunov method analytically. The simulation results on MATLAB/Simulink and Carsim joint platform demonstrate that the proposed methodology considerably improves tracking accuracy, driving stability, and robust performance, guaranteeing the feasibility and capability of driving in extreme scenarios.

eess.SY↗

arXiv2024

Arithmetic degrees of dynamical systems over fields of characteristic zero

In this article, we generalize the arithmetic degree and its related theory to dynamical systems defined over an arbitrary field $\mathbf{k}$ of characteristic $0$. We first consider a dynamical system $(X,f)$ over a finitely generated field $K$ over $\mathbb{Q}$, we introduce the arithmetic degrees $\alpha(f,\cdot)$ for $\overline{K}$-points by using Moriwaki heights. We study the arithmetic dynamical degree of $(X,f)$ and establish the relative degree formula. The relative degree formula gives a proof of the fundamental inequality, that is, the upper arithmetic degree $\overline{\alpha}(f,x)$ is less than or equal to the first dynamical degree $\lambda_1(f)$ in this setting. By taking spread-outs, we extend the definition of arithmetic degrees to dynamical systems over the field $\mathbf k$. We demonstrate that our definition is independent of the choice of the spread-out. Moreover, in this setting, we prove certain special cases of the Kawaguchi-Silverman conjecture. A main novelty of this paper is that, we give a characterization of arithmetic degrees of "transcendental points" in the case $\mathbf{k}=\mathbb{C}$, from which we deduce that $\alpha(f,x)=\lambda_1(f)$ for very general $x\in X(\mathbb{C})$ when $f$ is an endomorphism.

math.NT↗

arXiv2023

A high-codimensional Yuan's inequality and its application to higher arithmetic degrees

In this article, we consider a dominant rational self-map $f:X \dashrightarrow X$ of a normal projective variety defined over a number field. We study the arithmetic degree $\alpha_k(f)$ for $f$ and $\alpha_k(f,V)$ of a subvariety $V$, which generalize the classical arithmetic degree $\alpha_1(f,P)$ of a point $P$. We generalize Yuan's arithmetic version of Siu's inequality to higher codimensions and utilize it to demonstrate the existence of the arithmetic degree $\alpha_k(f)$. Furthermore, we establish the relative degree formula $\alpha_k(f)=\max\{\lambda_k(f),\lambda_{k-1}(f)\}$. In addition, we prove several basic properties of the arithmetic degree $\alpha_k(f, V)$ and establish the upper bound $\overline{\alpha}_{k+1}(f, V)\leq \max\{\lambda_{k+1}(f),\lambda_{k}(f)\}$, which generalizes the classical result $\overline{\alpha}_f(P)\leq \lambda_1(f)$. Finally, we discuss a generalized version of the Kawaguchi-Silverman conjecture that was proposed by Dang et al, and we provide a counterexample to this conjecture.

math.NT↗

arXiv2021

Learning Non-Stationary Time-Series with Dynamic Pattern Extractions

The era of information explosion had prompted the accumulation of a tremendous amount of time-series data, including stationary and non-stationary time-series data. State-of-the-art algorithms have achieved a decent performance in dealing with stationary temporal data. However, traditional algorithms that tackle stationary time-series do not apply to non-stationary series like Forex trading. This paper investigates applicable models that can improve the accuracy of forecasting future trends of non-stationary time-series sequences. In particular, we focus on identifying potential models and investigate the effects of recognizing patterns from historical data. We propose a combination of \rebuttal{the} seq2seq model based on RNN, along with an attention mechanism and an enriched set features extracted via dynamic time warping and zigzag peak valley indicators. Customized loss functions and evaluating metrics have been designed to focus more on the predicting sequence's peaks and valley points. Our results show that our model can predict 4-hour future trends with high accuracy in the Forex dataset, which is crucial in realistic scenarios to assist foreign exchange trading decision making. We further provide evaluations of the effects of various loss functions, evaluation metrics, model variants, and components on model performance.

cs.LG↗