arXiv subjects

Jinyuan Hu

Publications and source records attributed to Jinyuan Hu.

6 recordsLinked to original sources

arXiv2026

Todd's relation conjecture and binary relations for multiple zeta values in positive characteristic

We prove Todd's relation conjecture: all $\mathbb{F}_q(\theta)$-linear relations of Thakur's multiple zeta values are generated from the fundamental binary relation by the operators $\mathcal{B}^{\mathrm{S}}$, $\mathcal{C}^{\mathrm{S}}$, $\mathcal{B}^{\mathrm{S}}\circ \mathcal{C}^{\mathrm{S}}$; moreover they are also generated by $\mathcal{B}^{\ast\mathrm{S}}$, $\mathcal{C}^{\mathrm{S}}$, $\mathcal{B}^{\ast\mathrm{S}}\circ\mathcal{C}^{\mathrm{S}}$. The $\mathcal{B}^{\ast\mathrm{S}}$-part of this conjecture has been proved by Chang, Chen and Mishiba. We prove the whole conjecture for Carlitz multiple polylogarithm values, which implies the $\mathcal{B}^{\mathrm{S}}$-part for multiple zeta values. We also determine all fixed relations and binary relations. Let $\mathfrak{BR}^{\mathrm{S}}_w$ be the $\mathbb{F}_q(\theta)$-linear space spanned by binary relations of weight $w$, and let $\operatorname{Fix}^{\mathrm{S}}_w$ be the $\mathbb{F}_q(\theta)$-linear space spanned by fixed relations. We derive generating functions $\sum_{w\ge 1}\bigl(\dim_{\mathbb{F}_q(\theta)}\operatorname{Fix}^{\mathrm{S}}_w\bigr)x^w=\frac{x^{q+1}(1-x)}{(1-2x)(1-2x+x^{q+1})}$ and $\sum_{w\ge 1}\bigl(\dim_{\mathbb{F}_q(\theta)}\mathfrak{BR}^{\mathrm{S}}_w\bigr)x^w=\frac{x^q(1-x)}{(1-2x)(1-2x+x^{q+1})}.$ Our results are based on the recent work of Im-Kim-Ngo Dac on the $\mathbb{F}_q$-linear relations of Thakur's multiple zeta values, and a system of transfer theorems between multiple zeta values and multiple polylogarithm values.

math.NT↗

arXiv2026

$\mathbb{F}_q$-linear relations among Thakur's multiple zeta values in positive characteristic

Let $\mathcal{Z}_w^{(\mathbb{F}_q)}$ be the $\mathbb{F}_q$-linear subspace of $\mathbb{F}_q(\!(\theta^{-1})\!)$ spanned by Thakur's multiple zeta values $\zeta_A(\mathfrak{s})$ of weight $w$. We prove that $\sum_{w=1}^{\infty} \left(\dim_{\mathbb{F}_q} \mathcal{Z}_w^{(\mathbb{F}_q)}\right) x^w = \frac{x(1-x^q)(1-2x+x^q)}{(1-2x+x^{q+1})^2}$. Moreover, we construct an explicit $\mathbb{F}_q$-basis of $\mathcal{Z}_w^{(\mathbb{F}_q)}$, and prove that any $\mathbb{F}_q$-linear relation among Carlitz multiple polylogarithm values $\operatorname{Li}_A(\mathfrak{s})$ is an $\mathbb{F}_q$-linear combination of quadruple-carry relations. This result can be regarded as an $\mathbb{F}_q$-analogue of the corresponding $\mathbb{F}_q(\theta)$-theorem proved by Chang--Chen--Mishiba and independently by Im--Kim--Le--Ngo Dac--Pham. Our discovery of the quadruple-carry relations is inspired by the recent work of Im--Kim--Ngo Dac. These relations may be viewed as $\mathbb{F}_q$-analogues of the double-shuffle relations among classical multiple zeta values $\zeta(\mathfrak{s})$.

math.NT↗

arXiv2026

OpenGame: Open Agentic Coding for Games

Game development sits at the intersection of creative design and intricate software engineering, demanding the joint orchestration of game engines, real-time loops, and tightly coupled state across many files. While Large Language Models (LLMs) and code agents now solve isolated programming tasks with ease, they consistently stumble when asked to produce a fully playable game from a high-level design, collapsing under cross-file inconsistencies, broken scene wiring, and logical incoherence. We bridge this gap with OpenGame, the first open-source agentic framework explicitly designed for end-to-end web game creation. At its core lies Game Skill, a reusable, evolving capability composed of a Template Skill that grows a library of project skeletons from experience and a Debug Skill that maintains a living protocol of verified fixes - together enabling the agent to scaffold stable architectures and systematically repair integration errors rather than patch isolated syntax bugs. Powering this framework is GameCoder-27B, a code LLM specialized for game engine mastery through a three-stage pipeline of continual pre-training, supervised fine-tuning, and execution-grounded reinforcement learning. Since verifying interactive playability is fundamentally harder than checking static code, we further introduce OpenGame-Bench, an evaluation pipeline that scores agentic game generation along Build Health, Visual Usability, and Intent Alignment via headless browser execution and VLM judging. Across 150 diverse game prompts, OpenGame establishes a new state-of-the-art. We hope OpenGame pushes code agents beyond discrete software engineering problems and toward building complex, interactive real-world applications. Our framework will be fully open-sourced.

cs.SE↗

arXiv2026

NMRPeak: a ready-to-use intelligent system for molecular structure elucidation enabled by synergistic cross-modal learning

One-dimensional nuclear magnetic resonance (NMR) spectroscopy is essential for molecular structure elucidation in organic synthesis, drug discovery, natural product characterization, and metabolomics, yet its interpretation remains heavily dependent on expert knowledge and difficult to scale. Although machine learning has been applied to NMR spectrum prediction, library retrieval, and structure generation, these tasks have evolved in isolation using simulated data and incompatible spectral representations, limiting their utility under real experimental scenarios. Here we present NMRPeak, a unified cross-modal learning system that integrates these three tasks through experimentally grounded design. We curate approximately 1.8 million experimental and simulated spectra to construct the largest benchmark for NMR-based structure elucidation and systematically quantify the distribution shift between these domains. We introduce a chemically-aware adaptive tokenizer that dynamically balances discretization granularity to preserve spectral semantics while controlling vocabulary size, and an assignment-free peak-aware similarity metric that enables direct comparison between predicted and experimental spectra. Through a unified molecule-to-spectrum paradigm and synergistic coupling of prediction, retrieval, and generation modules, NMRPeak achieves transformative performance on experimental benchmarks: it overcomes the longstanding simulation-to-experiment gap in spectrum prediction while delivering over 95% top-1 accuracy in molecular retrieval and approximately 75% top-1 accuracy in stereochemistry-aware de novo structure generation. These capabilities establish a foundation for automated, high-throughput molecular structure elucidation in organic synthesis, drug discovery, and chemical biology.

cond-mat.mtrl-sci↗

arXiv2025

MixAR: Mixture Autoregressive Image Generation

Autoregressive (AR) approaches, which represent images as sequences of discrete tokens from a finite codebook, have achieved remarkable success in image generation. However, the quantization process and the limited codebook size inevitably discard fine-grained information, placing bottlenecks on fidelity. Motivated by this limitation, recent studies have explored autoregressive modeling in continuous latent spaces, which offers higher generation quality. Yet, unlike discrete tokens constrained by a fixed codebook, continuous representations lie in a vast and unstructured space, posing significant challenges for efficient autoregressive modeling. To address these challenges, we introduce MixAR, a novel framework that leverages mixture training paradigms to inject discrete tokens as prior guidance for continuous AR modeling. MixAR is a factorized formulation that leverages discrete tokens as prior guidance for continuous autoregressive prediction. We investigate several discrete-continuous mixture strategies, including self-attention (DC-SA), cross-attention (DC-CA), and a simple approach (DC-Mix) that replaces homogeneous mask tokens with informative discrete counterparts. Moreover, to bridge the gap between ground-truth training tokens and inference tokens produced by the pre-trained AR model, we propose Training-Inference Mixture (TI-Mix) to achieve consistent training and generation distributions. In our experiments, we demonstrate a favorable balance of the DC-Mix strategy between computational efficiency and generation fidelity, and consistent improvement of TI-Mix.

cs.CV↗

arXiv2025

Large Language Models as AI Agents for Digital Atoms and Molecules: Catalyzing a New Era in Computational Biophysics

In computational biophysics, where molecular data is expanding rapidly and system complexity is increasing exponentially, large language models (LLMs) and agent-based systems are fundamentally reshaping the field. This perspective article examines the recent advances at the intersection of LLMs, intelligent agents, and scientific computation, with a focus on biophysical computation. Building on these advancements, we introduce ADAM (Agent for Digital Atoms and Molecules), an innovative multi-agent LLM-based framework. ADAM employs cutting-edge AI architectures to reshape scientific workflows through a modular design. It adopts a hybrid neural-symbolic architecture that combines LLM-driven semantic tools with deterministic symbolic computations. Moreover, its ADAM Tool Protocol (ATP) enables asynchronous, database-centric tool orchestration, fostering community-driven extensibility. Despite the significant progress made, ongoing challenges call for further efforts in establishing benchmarking standards, optimizing foundational models and agents, building an open collaborative ecosystem and developing personalized memory modules. ADAM is accessible at https://sidereus-ai.com.

physics.comp-ph↗