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Xinyi Yuan

Publications and source records attributed to Xinyi Yuan.

At least 19 recordsLinked to original sources
arXiv2026

Equidistribution of small points over finitely generated fields

We study the equidistribution of small points over finitely generated fields, in connection with a conjecture of Yuan--Zhang. We first give a counterexample showing that numerical smallness, defined using Moriwaki heights for all polarizations, does not imply equidistribution at every valuation. We then prove that numerically small points do equidistribute at every fully transcendental valuation. In particular, when \(F\) is the function field of a curve \(B/\mathbb{Q}\), these valuations correspond to points of types \(2\), \(3\), and \(4\) in the Berkovich analytification of \(B_{\mathbb{Q}_p}\).

math.NT↗
arXiv2026

A Group-Theoretical Framework for Local k-Space Topology and Berry Phase in 2D Photonic Systems

Two-dimensional photonic crystals (2D PhCs) enable fine-grained control over a broad set of Bloch modes without the constraints of band occupancy and natural crystal structures, and, as intrinsically open systems, serve as versatile platforms for exploring diverse topological phenomena. Here, we develop a theoretical framework inspired by the irreducible-representation formalism in solid-state physics, while explicitly incorporating key characteristics of photonic Bloch systems, such as radiative coupling and transverse condition. Within this framework, we study the symmetry origins of local k-space topology, e.g., bound-states in the continuum and optical vortex beams, and Berry phase in two representative systems. We further analyze, from a group-theory perspective, how tailored structural designs and targeted symmetry perturbations can be exploited to manipulate these topological features. In particular, we showcase the application of the formalism to Bloch modes from distinct truncation approaches and specify the preferable regimes for each, both under a generic $n$-band configuration. The analysis can thereby be readily extended to a wide range of artificial wave crystals beyond scalar Schr\"odinger-like operators and two-level treatment.

physics.optics↗
arXiv2026

Prox: Training-Free FFN Activation Sparsity via Approximate Intermediate-Channel Salience in LLMs

Feed-forward networks (FFNs) dominate memory traffic and computation in large language model (LLM) inference, making them a primary target for activation sparsification. However, existing training-free methods suffer substantial model-quality degradation at high sparsity due to limitations in their channel-selection strategies. We observe that the SwiGLU intermediate state provides a highly effective channel-selection signal, but obtaining it requires costly dense computation. To address this, we present \emph{Prox}, a two-stage training-free framework for sparse SwiGLU FFNs. Prox hinges on the key insight: sparse execution requires only the channel mask induced by the intermediate state, which can be constructed from the magnitude ranking of its entries rather than their exact values. Specifically, Stage 1 uses input sparsity and quantized proxy weights to construct a shared mask; Stage 2 computes the selected channels exactly, enabling sparse execution of all three projections. Across ten LLMs from six model families, Prox outperforms training-free baselines at all sparsity levels, achieves up to a $1.99\times$ end-to-end decoding speedup at 70\% FFN sparsity, and is compatible with quantization and sparse attention.

cs.LG↗
arXiv2026

Demystifying Deep Learning Compiler Frontend Bugs: An LLM-Aided Empirical Study

Deep learning compilers (DLCs) are designed to translate deep learning programs into optimized, hardware-specific code. Typically, DLC frontends translate programs into graph-based intermediate representations (IRs) to enable optimizations. Defects introduced during this stage (termed \emph{fBug}s) are severe yet understudied, as prior work predominantly focuses on low-level APIs and operators or treats DLCs as monolithic entities. To bridge this gap, we conduct the first systematic empirical study of \emph{fBug}s in TorchDynamo, the default DLC frontend for PyTorch 2, the most popular DL framework. Leveraging a domain-knowledge-enhanced LLM-aided methodology, we analyze 123 \emph{fBug}s and construct a taxonomy comprising 7 root cause categories and 15 subcategories. Our findings provide actionable insights for DLC development and testing. Furthermore, we leverage the LLM to generate targeted, root cause-aware test cases to detect new bugs. We uncovered 23 previously unknown \emph{fBug}s in recent releases (15 confirmed) across eight (sub)categories, demonstrating the efficacy of our methodology in testing and hardening DLC frontends.

cs.PL↗
arXiv2026

Quantitativity in the Mordell Conjecture

The Mordell conjecture asserts that there are only finitely many rational points on a smooth projective curve of genus at least two over a number field. The uniform Mordell problem asks for suitable upper bounds on the number of rational points in the Mordell conjecture, and has been solved by combining works of Vojta, Dimitrov--Habegger--Gao and Kuhne. In this survey, we will introduce a quantitative version of the uniformity problem proved by the recent work of Yu--Yuan--Zhou.

math.NT↗
arXiv2026

Extreme Motion Generation via Hybrid Null-Space Control for Straight-Line Path Following

This work studies ``extreme motion generation'', which aims to maximize the Cartesian path length along a pre-defined trajectory within the manipulator's workspace. This objective is important in industry as long as path-following is fundamental to a large variety of tasks such as surface coating and welding. More critically, extreme motion enables a fixed-base manipulator to exploit the kinematic capability under limited reachability. However, such exploitation is challenging in practice, as the manipulator must actively avoid the safety boundary through execution, which is inherently a long-horizon problem. Accordingly, we claim that long-horizon decision-making should be delegated to a learning-based policy to maximize exploitation, while a classical model-based controller covers the near-boundary region, where the learning policy degrades sharply due to sparse data coverage. In detail, our proposed method is a step-level hybrid controller that switches between an RL-based and a model-based controller according to the normalized joint-limit distance. The initial joint configuration is sampled through conditional diffusion-based sampling, which improves the achievable path length based on the learned motion prior. We evaluate the proposed framework on 10,000 straight-line path-following tasks with a 7-DoF Franka FR3, extending the average rollout length by 27\% over the model-based baseline. Notably, certain tasks yield a pronounced extension toward the motion extreme, as reflected in the maximum improvement reported in the statistical results. The project website and related videos of this paper can be found at https://yuan-xinyi.github.io/extreme-motion-generation/.

cs.RO↗
arXiv2026

Effective Reinforcement Learning Control using Conservative Soft Actor-Critic

Reinforcement Learning (RL) has shown great potential in complex control tasks, particularly when combined with deep neural networks within the Actor-Critic (AC) framework. However, in practical applications, balancing exploration, learning stability, and sample efficiency remains a significant challenge. Traditional methods such as Soft Actor-Critic (SAC) and Proximal Policy Optimization (PPO) address these issues by incorporating entropy or relative entropy regularization, but often face problems of instability and low sample efficiency. In this paper, we propose the Conservative Soft Actor-Critic (CSAC) algorithm, which seamlessly integrates entropy and relative entropy regularization within the AC framework. CSAC improves exploration through entropy regularization while avoiding overly aggressive policy updates with the use of relative entropy regularization. Evaluations on benchmark tasks and real-world robotic simulations demonstrate that CSAC offers significant improvements in stability and efficiency over existing methods. These findings suggest that CSAC provides strong robustness and application potential in control tasks under dynamic environments.

cs.RO↗
arXiv2026

Nef cone and successive minima: an example

In this paper, we compute the nef cone and the pseudo-effective cone of $C\times J$ for a smooth projective curve $C$ and its Jacobian variety $J$ such that $C\times J$ has the minimal Picard number. As a consequence, we also compute the successive minima of a height function for the relative setting $C\times J\to J$, and our result shows that Zhang's theorem of successive minima does not hold in this case.

math.AG↗
arXiv2026

Quantitativity on the number of rational points in the Mordell conjecture

In this paper, we prove an explicit upper bound on the number of rational points on a smooth projective curve of genus at least two over a number field. This gives explicit constants in the uniform Mordell conjecture proposed by Mazur and proved by Vojta, Dimitrov-Gao-Habegger, and Kühne. The main body of this paper consists of two parts: Part I for arithmetic estimates and Part II for analytic estimates.

math.NT↗
arXiv2025

On Vojta's proof of the Mordell conjecture

This paper re-organizes Vojta's proof of the Mordell conjecture (i.e. Faltings' theorem) in terms of Arakelov geometry. A new ingredient is to replace an application of Gillet--Soule's arithmetic Riemannn--Roch theorem by that of Yuan's arithmetic Siu inequality.

math.NT↗
arXiv2025

Breakdown of Bulk-Radiation Correspondence in Radiative Photonic Lattices

The topological characteristics of energy bands in crystalline systems are encapsulated in the Berry curvature of the bulk Bloch states. In photonic crystal slabs, far-field emission from guided resonances naturally provides a non-invasive way to probe the embedded wavefunctions, raising the question of how the information carried by escaping photons relates to the band topology. We develop a non-Hermitian model to describe the guided and leaky modes of photonic crystal slabs with long-range couplings and non-local responses. Within this framework, radiation Berry curvature is defined from the far-field polarization and compared to the conventional bulk Berry curvature of the crystal Bloch modes. We investigate this bulk-radiation correspondence in the vicinity of the $Γ$-point of the square lattice and the $K$-point of the honeycomb lattice. The results show that the comparability between the bulk topology and the radiation topology is not universal; the validity is contingent upon the specific bulk Bloch states. Notably, the correspondence completely breaks down surrounding the far-field singularities, while it can hold in smooth regions under special symmetry conditions, e.g., rotational symmetry. Besides, net Berry curvature concentration is captured at the valleys of the non-local honeycomb lattice, facilitating further exploration on generalized topological phases in photonic lattices beyond the regimes with localized couplings and Hermiticity.

physics.optics↗
arXiv2025

Adelic line bundles on quasi-projective varieties

In this book, we establish a theory of adelic line bundles over quasi-projective varieties over finitely generated fields. Besides definitions of adelic line bundles, we consider their intersection theory, volume theory, and height theory, and apply these to study heights of algebraic points of quasi-projective varieties.

math.NT↗
arXiv2025

IKSel: Selecting Good Seed Joint Values for Fast Numerical Inverse Kinematics Iterations

This paper revisits the numerical inverse kinematics (IK) problem, leveraging modern computational resources and refining the seed selection process to develop a solver that is competitive with analytical-based methods. The proposed seed selection strategy consists of three key stages: (1) utilizing a K-Dimensional Tree (KDTree) to identify seed candidates based on workspace proximity, (2) sorting candidates by joint space adjustment and attempting numerical iterations with the one requiring minimal adjustment, and (3) re-selecting the most distant joint configurations for new attempts in case of failures. The joint space adjustment-based seed selection increases the likelihood of rapid convergence, while the re-attempt strategy effectively helps circumvent local minima and joint limit constraints. Comparison results with both traditional numerical solvers and learning-based methods demonstrate the strengths of the proposed approach in terms of success rate, time efficiency, and accuracy. Additionally, we conduct detailed ablation studies to analyze the effects of various parameters and solver settings, providing practical insights for customization and optimization. The proposed method consistently exhibits high success rates and computational efficiency. It is suitable for time-sensitive applications.

cs.RO↗
arXiv2025

Preference Aligned Diffusion Planner for Quadrupedal Locomotion Control

Diffusion models demonstrate superior performance in capturing complex distributions from large-scale datasets, providing a promising solution for quadrupedal locomotion control. However, the robustness of the diffusion planner is inherently dependent on the diversity of the pre-collected datasets. To mitigate this issue, we propose a two-stage learning framework to enhance the capability of the diffusion planner under limited dataset (reward-agnostic). Through the offline stage, the diffusion planner learns the joint distribution of state-action sequences from expert datasets without using reward labels. Subsequently, we perform the online interaction in the simulation environment based on the trained offline planner, which significantly diversified the original behavior and thus improves the robustness. Specifically, we propose a novel weak preference labeling method without the ground-truth reward or human preferences. The proposed method exhibits superior stability and velocity tracking accuracy in pacing, trotting, and bounding gait under different speeds and can perform a zero-shot transfer to the real Unitree Go1 robots. The project website for this paper is at https://shangjaven.github.io/preference-aligned-diffusion-legged.

cs.RO↗
arXiv2024

Modular Heights of Quaternionic Shimura Curves

The goal of this paper is to prove a formula expressing the modular height of a quaternionic Shimura curve over a totally real number field in terms of the logarithmic derivative of the Dedekind zeta function of the totally real number field. Our proof is based on the work of Yuan-Zhang-Zhang on the Gross-Zagier formula and the work of Yuan-Zhang on the averaged Colmez conjecture. All these works are in turn inspired by the Pioneering work of Gross-Zagier and some philosophies of Kudla's program.

math.NT↗
arXiv2024

Arithmetic bigness and a uniform Bogomolov-type result

In this paper, we prove that the admissible canonical bundle of the universal family of curves is a big adelic line bundle, and apply it to prove a uniform Bogomolov-type theorem for curves over global fields of all characteristics. This gives a different approach to the uniform Mordell-Lang type of result of Dimitrov-Gao-Habegger and Kuhne. The treatment is based on the recent theory of adelic line bundles of Yuan-Zhang.

math.NT↗
arXiv2024

Explicit Kodaira-Spencer map over Shimura Curves

The goal of this paper is to explicitly compute the Kodaira-Spencer map for a quaternionic Shimura curve over Q and its effect on the metrics of the Hodge bundle. The results are known to experts.

math.NT↗