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Ziyang Gao

Publications and source records attributed to Ziyang Gao.

At least 19 recordsLinked to original sources
arXiv2026

Uniformity in rational torsion and small points on abelian varieties

In this paper, we propose a method to study the {\it Uniform Boundedness Conjecture} and the {\it Lang-Silverman Conjecture} for abelian varieties $A$ defined over a global field $K$; the latter is a uniform lower bound on the heights of non-torsion rational points. Our method is inspired by Vojta's proof of the Mordell Conjecture (Faltings's Theorem). Over function fields of characteristic $0$, a recent breakthrough of Looper-Yap (arXiv:2603.23396) proves both conjectures with inexplicit bounds. In our paper, we give a new proof of both conjectures with explicit bounds, which also depend polynomially on the field $K$ unless $A/K$ admits a factor of good reduction everywhere. We also prove explicit bounds for elliptic curves over function fields of characteristic $p>0$. Over number fields, we prove both conjectures under a suitable high-dimensional Szpiro conjecture (weaker than Hindry's version, Conjecture 3.4 of https://webusers.imj-prg.fr/~marc.hindry/MW-size.pdf) that we propose.

math.NT↗
arXiv2026

Rank of normal functions and Betti strata

In a recent work of the authors, we proved the generic positivity of the Beilinson-Bloch heights of the Gross-Schoen and Ceresa cycles. The geometric part of the proof was to prove the maximality of the rank of the associated normal function and the Zariski closedness of the Betti strata. In this paper, we generalize these geometric results to an arbitrary family of homologically trivial cycles. More generally, we prove a formula to compute the Betti rank and prove the Zariski closedness of the Betti strata, for any admissible normal function of a variation of Hodge structures of weight $-1$. We also define and prove results about degeneracy loci. In the end, we go back to the arithmetic setting and ask some questions about the rationality of the Betti strata and the torsion loci.

math.AG↗
arXiv2026

DiCoR: Decoupled Referent Disambiguation and Contour Recalibration for Efficient Referring Remote Sensing Image Segmentation

Referring remote sensing image segmentation (RRSIS) aims to delineate targets specified by natural language expressions in remote sensing imagery. Existing methods mainly follow joint fusion segmentation (JFS) or decoupled prompt segmentation (DPS). JFS is efficient but often suffers from limited accuracy because referent localization and mask delineation are optimized under a unified objective, whereas DPS separates localization from mask generation using spatial prompts and foundation segmenters at the cost of higher memory consumption and inference latency. To bridge this gap, we propose DiCoR, a decoupled referent disambiguation and contour recalibration framework built on an efficient JFS pipeline. DiCoR addresses two key challenges: distinguishing the correct referent from ambiguous candidates and refining coarse masks after localization. A disambiguation-aware localization guidance strategy ranks salient candidate regions with adaptive linguistic cues and injects the resulting localization prior into fused features. A lightweight contour recalibration module further predicts residual corrections to coarse logits under localized contour supervision, improving mask quality with limited computational overhead. Experiments on RefSegRS, RRSIS-D, and RISBench show that DiCoR achieves the best segmentation accuracy across all three benchmarks. On RefSegRS, it improves mIoU and gIoU by 5.28% and 2.87% over a competitive JFS method while running 4.7% faster than a representative DPS method, demonstrating a favorable accuracy-efficiency trade-off. Code is available at https://github.com/zyGao1126/DiCoR.

cs.CV↗
arXiv2026

The Relative Manin-Mumford Conjecture

We prove the Relative Manin-Mumford Conjecture for families of abelian varieties in characteristic 0. We follow the Pila-Zannier method to study special point problems, and we use the Betti map which goes back to work of Masser and Zannier in the case of curves. The key new ingredients compared to previous applications of this approach are a height inequality proved by both authors of the current paper and Dimitrov, and the first-named author's study of certain degeneracy loci in subvarieties of abelian schemes. We also strengthen this result and prove a criterion for torsion points to be dense in a subvariety of an abelian scheme over $\mathbb{C}$. The Uniform Manin-Mumford Conjecture for curves embedded in their Jacobians was first proved by Kühne. We give a new proof, as a corollary to our main theorem, that does not use equidistribution.

math.NT↗
arXiv2026

MA$^{2}$P: A Meta-Cognitive Autonomous Intelligent Agents Framework for Complex Persuasion

Persuasive dialogue generation plays a vital role in decision-making, negotiation, counseling, and behavior change, yet it remains a challenging problem. In complex persuasion where the persuadee's internal states are not expressed clearly, the persuader must interpret responses, infer the persuadee's latent mental states (e.g., beliefs and desires), and translate them into targeted, strategy-consistent actions; however, current approaches often produce generic or weakly grounded responses even when such cues are identified. Moreover, although large language models (LLMs) can generate persuasive content, their performance varies substantially across domains due to uneven knowledge coverage and limited reasoning generalization. To address these challenges, we propose MA$^{2}$P, a meta-cognitive autonomous intelligent agent framework for complex persuasion. Specifically, we develop an autonomous multi-agent architecture that coordinates perception management, mental-state inference, strategy execution, memory maintenance, and performance evaluation. To mitigate cross-domain performance variation, we further design a meta-cognitive configurator that selects an appropriate meta-strategy from a structured knowledge base at the outset, thereby guiding subsequent reasoning and planning. Experimental results show that our approach achieves a higher persuasion success rate than baselines.

cs.CL↗
arXiv2026

The Uniform Mordell-Lang Conjecture

The Mordell--Lang conjecture for abelian varieties states that the intersection of an algebraic subvariety $X$ with a subgroup of finite rank is contained in a finite union of cosets contained in $X$. In this article, we prove a uniform version of this conjecture, meaning that that the number of cosets necessary does not depend on the ambient abelian variety. To achieve this, we prove a general gap principle on algebraic points that extends the gap principle for curves embedded into their Jacobians, previously obtained by Dimitrov--Gao--Habegger and Kühne. Our new gap principle also implies the full uniform Bogomolov conjecture in abelian varieties.

math.NT↗
arXiv2026

Heights of Ceresa and Gross-Schoen cycles

We study the Beilinson-Bloch heights of Ceresa and Gross-Schoen cycles in families. We construct that for any $g\ge 3$, a Zariski open dense subset $\mathcal{M}_g^{\mathrm{amp}}$ of $\mathcal{M}_g$, the coarse moduli of curves of genus $g$ over $\mathbb{Q}$, such that the heights of Ceresa cycles and Gross-Schoen cycles over $\mathcal{M}_g^{\mathrm{amp}}$ have a lower bound and satisfy the Northcott property.

math.NT↗
arXiv2025

GastroDL-Fusion: A Dual-Modal Deep Learning Framework Integrating Protein-Ligand Complexes and Gene Sequences for Gastrointestinal Disease Drug Discovery

Accurate prediction of protein-ligand binding affinity plays a pivotal role in accelerating the discovery of novel drugs and vaccines, particularly for gastrointestinal (GI) diseases such as gastric ulcers, Crohn's disease, and ulcerative colitis. Traditional computational models often rely on structural information alone and thus fail to capture the genetic determinants that influence disease mechanisms and therapeutic responses. To address this gap, we propose GastroDL-Fusion, a dual-modal deep learning framework that integrates protein-ligand complex data with disease-associated gene sequence information for drug and vaccine development. In our approach, protein-ligand complexes are represented as molecular graphs and modeled using a Graph Isomorphism Network (GIN), while gene sequences are encoded into biologically meaningful embeddings via a pre-trained Transformer (ProtBERT/ESM). These complementary modalities are fused through a multi-layer perceptron to enable robust cross-modal interaction learning. We evaluate the model on benchmark datasets of GI disease-related targets, demonstrating that GastroDL-Fusion significantly improves predictive performance over conventional methods. Specifically, the model achieves a mean absolute error (MAE) of 1.12 and a root mean square error (RMSE) of 1.75, outperforming CNN, BiLSTM, GIN, and Transformer-only baselines. These results confirm that incorporating both structural and genetic features yields more accurate predictions of binding affinities, providing a reliable computational tool for accelerating the design of targeted therapies and vaccines in the context of gastrointestinal diseases.

cs.LG↗
arXiv2025

Cross-Lingual Sponsored Search via Dual-Encoder and Graph Neural Networks for Context-Aware Query Translation in Advertising Platforms

Cross-lingual sponsored search is crucial for global advertising platforms, where users from different language backgrounds interact with multilingual ads. Traditional machine translation methods often fail to capture query-specific contextual cues, leading to semantic ambiguities that negatively impact click-through rates (CTR) and conversion rates (CVR). To address this challenge, we propose AdGraphTrans, a novel dual-encoder framework enhanced with graph neural networks (GNNs) for context-aware query translation in advertising. Specifically, user queries and ad contents are independently encoded using multilingual Transformer-based encoders (mBERT/XLM-R), and contextual relations-such as co-clicked ads, user search sessions, and query-ad co-occurrence-are modeled as a heterogeneous graph. A graph attention network (GAT) is then applied to refine embeddings by leveraging semantic and behavioral context. These embeddings are aligned via contrastive learning to reduce translation ambiguity. Experiments conducted on a cross-lingual sponsored search dataset collected from Google Ads and Amazon Ads (EN-ZH, EN-ES, EN-FR pairs) demonstrate that AdGraphTrans significantly improves query translation quality, achieving a BLEU score of 38.9 and semantic similarity (cosine score) of 0.83, outperforming strong baselines such as mBERT and M2M-100. Moreover, in downstream ad retrieval tasks, AdGraphTrans yields +4.67% CTR and +1.72% CVR improvements over baseline methods. These results confirm that incorporating graph-based contextual signals with dual-encoder translation provides a robust solution for enhancing cross-lingual sponsored search in advertising platforms.

stat.ME↗
arXiv2025

Bi-$\overline{\mathbb{Q}}$-structures on Hermitian symmetric spaces and quadratic relations between CM periods

In this paper, we introduce the notion of a bi-$\overline{\mathbb{Q}}$-structure on the tangent space at a CM point on a locally Hermitian symmetric domain. We prove that this bi-$\overline{\mathbb{Q}}$-structure decomposes into the direct sum of $1$-dimensional bi-$\overline{\mathbb{Q}}$-subspaces, and make this decomposition explicit for the moduli space of abelian varieties $\mathbb{A}_g$. We propose an Analytic Subspace Conjecture, which is the analogue of the Wüstholz's Analytic Subgroup Theorem in this context. We show that this conjecture, applied to $\mathbb{A}_g$, implies that all quadratic $\overline{\mathbb{Q}}$-relations among the holomorphic periods of CM abelian varieties arise from elementary ones.

math.NT↗
arXiv2025

Hodge cycles and quadratic relations between holomorphic periods on CM abelian varieties

In this paper, we prove the following result advocating the importance of monomial quadratic relations between holomorphic CM periods. For any simple CM abelian variety $A$, we can construct a CM abelian variety $B$ such that all non-trivial Hodge relations between the holomorphic periods of the product $A\times B$ are generated by monomial quadratic ones which are also explicit. Moreover, $B$ splits over the Galois closure of the CM field associated with $A$.

math.NT↗
arXiv2025

Explainable Depression Detection in Clinical Interviews with Personalized Retrieval-Augmented Generation

Depression is a widespread mental health disorder, and clinical interviews are the gold standard for assessment. However, their reliance on scarce professionals highlights the need for automated detection. Current systems mainly employ black-box neural networks, which lack interpretability, which is crucial in mental health contexts. Some attempts to improve interpretability use post-hoc LLM generation but suffer from hallucination. To address these limitations, we propose RED, a Retrieval-augmented generation framework for Explainable depression Detection. RED retrieves evidence from clinical interview transcripts, providing explanations for predictions. Traditional query-based retrieval systems use a one-size-fits-all approach, which may not be optimal for depression detection, as user backgrounds and situations vary. We introduce a personalized query generation module that combines standard queries with user-specific background inferred by LLMs, tailoring retrieval to individual contexts. Additionally, to enhance LLM performance in social intelligence, we augment LLMs by retrieving relevant knowledge from a social intelligence datastore using an event-centric retriever. Experimental results on the real-world benchmark demonstrate RED's effectiveness compared to neural networks and LLM-based baselines.

cs.CL↗
arXiv2025

A CT Image Classification Network Framework for Lung Tumors Based on Pre-trained MobileNetV2 Model and Transfer learning, And Its Application and Market Analysis in the Medical field

In the medical field, accurate diagnosis of lung cancer is crucial for treatment. Traditional manual analysis methods have significant limitations in terms of accuracy and efficiency. To address this issue, this paper proposes a deep learning network framework based on the pre-trained MobileNetV2 model, initialized with weights from the ImageNet-1K dataset (version 2). The last layer of the model (the fully connected layer) is replaced with a new fully connected layer, and a softmax activation function is added to efficiently classify three types of lung cancer CT scan images. Experimental results show that the model achieves an accuracy of 99.6% on the test set, with significant improvements in feature extraction compared to traditional models.With the rapid development of artificial intelligence technologies, deep learning applications in medical image processing are bringing revolutionary changes to the healthcare industry. AI-based lung cancer detection systems can significantly improve diagnostic efficiency, reduce the workload of doctors, and occupy an important position in the global healthcare market. The potential of AI to improve diagnostic accuracy, reduce medical costs, and promote precision medicine will have a profound impact on the future development of the healthcare industry.

eess.IV↗
arXiv2023

Degeneracy loci in the universal family of abelian varieties

Recent developments on the uniformity of the number of rational points on curves and subvarieties in a moving abelian variety rely on the geometric concept of the degeneracy locus. The first-named author investigated the degeneracy locus in certain mixed Shimura varieties. In this expository note we revisit some of these results while minimizing the use of mixed Shimura varieties while working in a family of principally polarized abelian varieties. We also explain their relevance for applications in diophantine geometry.

math.NT↗
arXiv2021

Recent developments of the Uniform Mordell-Lang Conjecture

This expository survey is based on my online talk at the ICCM 2020. It aims to sketch key steps of the recent proof of the uniform Mordell-Lang conjecture for curves embedded into Jacobians (a question of Mazur). The full version of this conjecture is proved by combining Dimitrov-Gao-Habegger (https://annals.math.princeton.edu/articles/17715) and Kühne (arXiv:2101.10272). We include in this survey a detailed proof on how to combine these two results, which was implicitly done in another short paper of Dimitrov-Gao-Habegger (arXiv:2009.08505) but not explicitly written in existing literature. At the end of the survey we state some future aspects.

math.NT↗
arXiv2021

Generic rank of Betti map and unlikely intersections

Let $\mathcal{A} \rightarrow S$ be an abelian scheme over an irreducible variety over $\mathbb{C}$ of relative dimension $g$. For any simply-connected subset $Δ$ of $S^{\mathrm{an}}$ one can define the Betti map from $\mathcal{A}_Δ$ to $\mathbb{T}^{2g}$, the real torus of dimension $2g$, by identifying each closed fiber of $\mathcal{A}_Δ \rightarrow Δ$ with $\mathbb{T}^{2g}$ via the Betti homology. Computing the generic rank of the Betti map restricted to a subvariety $X$ of $\mathcal{A}$ is useful to study Diophantine problems, e.g. proving the Geometric Bogomolov Conjecture over characteristic $0$ and studying the relative Manin-Mumford conjecture. In this paper we give a geometric criterion to detect this rank. As an application we show that it is maximal after taking a large enough fibered power (if $X$ satisfies some conditions): it is an important step to prove the bound for the number of rational points on curves [DGH20]. Another application is to answer a question of André-Corvaja-Zannier and improve a result of Voisin. We also systematically study its link with the relative Manin-Mumford conjecture, reducing the latter to a simpler conjecture. Our tools are functional transcendence and unlikely intersections for mixed Shimura varieties.

math.NT↗
arXiv2021

A consequence of the relative Bogomolov conjecture

We propose a formulation of the relative Bogomolov conjecture and show that it gives an affirmative answer to a question of Mazur's concerning the uniformity of the Mordell-Lang conjecture for curves. In particular we show that the relative Bogomolov conjecture implies the uniform Manin-Mumford conjecture for curves. The proof is built up on our previous work "Uniformity in Mordell-Lang for curves".

math.NT↗