arXiv subjects
Publications and source records attributed to Hongbo Yin.
In \cite{Yin26}, the author constructed some CM points on the elliptic curves $E_{p^i}:y^2=x^3+\frac{p^{2i}}{4}$ for primes $p\equiv 4,7\mod 9$ and $i=1,2$, which give rational points on the curves $x^3+y^3=p^i$. This solves the $4,7$ cases of Sylvester's conjecture. In this paper, we prove the explicit Gross-Zagier formula relating the height of our CM points and the derivative of the $L$-functions of $E_{p^i}$.
In this paper, we prove that every prime $p$ which is congruent to $4,7$ modulo $9$ is the sum of two rational cubes. This is $2/3$ of Sylvester's conjecture which has a history of nearly 150 years since 1879. In the proof, we use recent progress on Full BSD conjecture of rank $0$ elliptic curves in \cite{BF} to deduce that the Manin-Stevens constants of some families of elliptic curves are units. We also use recent solutions of Unbounded Denominators Conjecture in \cite{CDT} to prove that some cubic roots of modular functions are invariant under some congruence subgroups. Instead of using the Unbounded Denominators Conjecuture, we also give another conditional proof assuming the GRH for number fields or Artin's primitive root conjecture for arithmetic progressions.
Effective autonomous driving hinges on robust reasoning across perception, prediction, planning, and behavior. However, conventional end-to-end models fail to generalize in complex scenarios due to the lack of structured reasoning. While recent vision-language models (VLMs) have been applied to driving tasks, they typically rely on isolated modules and static supervision, limiting their ability to support multi-stage decision-making. We present AutoDriveRL, a unified training framework that formulates autonomous driving as a structured reasoning process over four core tasks. Each task is independently modeled as a vision-language QA problem and optimized using task-specific reward models, enabling fine-grained reinforcement signals at different reasoning stages. Within this framework, we train DriveRX, a cross-task reasoning VLM designed for multi-stage decision-making. DriveRX achieves strong performance on the public benchmark, outperforming GPT-4o in behavior reasoning and demonstrating robustness under complex or corrupted driving conditions. DriveRX serves as a high-level semantic reasoning backbone, producing structured stage-wise reasoning chains that enhance decision consistency. These outputs also provide high-quality supervisory signals for annotation and downstream planning/control models. We release the AutoDriveRL framework and DriveRX to support future research.
Let $E_n$ be the congruent number elliptic curve $y^2=x^3-n^2x$, where $n$ is square-free and not divisible by primes $p\equiv 3\pmod 4$. In this paper, we prove that $L(E_n,1)$ can be expressed as the square of CM values of some simple theta functions, generalizing two classical formulas of Gauss. Our result is meaningful in both theory and practical computation.
This paper introduces a new Transformer, called MS$^2$Dformer, that can be used as a generalized backbone for multi-modal sequence spammer detection. Spammer detection is a complex multi-modal task, thus the challenges of applying Transformer are two-fold. Firstly, complex multi-modal noisy information about users can interfere with feature mining. Secondly, the long sequence of users' historical behaviors also puts a huge GPU memory pressure on the attention computation. To solve these problems, we first design a user behavior Tokenization algorithm based on the multi-modal variational autoencoder (MVAE). Subsequently, a hierarchical split-window multi-head attention (SW/W-MHA) mechanism is proposed. The split-window strategy transforms the ultra-long sequences hierarchically into a combination of intra-window short-term and inter-window overall attention. Pre-trained on the public datasets, MS$^2$Dformer's performance far exceeds the previous state of the art. The experiments demonstrate MS$^2$Dformer's ability to act as a backbone.
Graph neural networks (GNNs) are a type of deep learning models that are trained on graphs and have been successfully applied in various domains. Despite the effectiveness of GNNs, it is still challenging for GNNs to efficiently scale to large graphs. As a remedy, distributed computing becomes a promising solution of training large-scale GNNs, since it is able to provide abundant computing resources. However, the dependency of graph structure increases the difficulty of achieving high-efficiency distributed GNN training, which suffers from the massive communication and workload imbalance. In recent years, many efforts have been made on distributed GNN training, and an array of training algorithms and systems have been proposed. Yet, there is a lack of systematic review on the optimization techniques for the distributed execution of GNN training. In this survey, we analyze three major challenges in distributed GNN training that are massive feature communication, the loss of model accuracy and workload imbalance. Then we introduce a new taxonomy for the optimization techniques in distributed GNN training that address the above challenges. The new taxonomy classifies existing techniques into four categories that are GNN data partition, GNN batch generation, GNN execution model, and GNN communication protocol. We carefully discuss the techniques in each category. In the end, we summarize existing distributed GNN systems for multi-GPUs, GPU-clusters and CPU-clusters, respectively, and give a discussion about the future direction on distributed GNN training.
Let $p\equiv 8\mod 9$ be a prime. In this paper we give a sufficient condition such that at least one of $p$ and $p^2$ is the sum of two rational cubes. This is the first general result on the $8$ case of the so-called Sylvester conjecture.
Nowadays, there are ubiquitousness of GPS sensors in various devices collecting, transmitting and storing tremendous trajectory data. However, such an unprecedented scale of GPS data has posed an urgent demand for not only an effective storage mechanism but also an efficient query mechanism. Line simplification in online mode, searving as a mainstream trajectory compression method, plays an important role to attack this issue. But for the existing algorithms, either their time cost is extremely high, or the accuracy loss after the compression is completely unacceptable. To attack this issue, we propose $ε\_$Region based Online trajectory Compression with Error bounded (ROCE for short), which makes the best balance among the accuracy loss, the time cost and the compression rate. The range query serves as a primitive, yet quite essential operation on analyzing trajectories. Each trajectory is usually seen as a sequence of discrete points, and in most previous work, a trajectory is judged to be overlapped with the query region R iff there is at least one point in this trajectory falling in R. But this traditional criteria is not suitable when the queried trajectories are compressed, because there may be hundreds of points discarded between each two adjacent points and the points in each compressed trajectory are quite sparse. And many trajectories could be missing in the result set. To address this, in this paper, a new criteria based on the probability and an efficient Range Query processing algorithm on Compressed trajectories RQC are proposed. In addition, an efficient index \emph{ASP\_tree} and lots of novel techniques are also presented to accelerate the processing of trajectory compression and range queries obviously. Extensive experiments have been done on multiple real datasets, and the results demonstrate superior performance of our methods.
Let $p\equiv 2,5\mod 9$ be a prime. We prove that both $3p$ and $3p^2$ are cube sums. We also establish some explicit Gross-Zagier formulae and investigate the 3 part full BSD conjecture of the related elliptic curves.
In this paper we discuss Waldspurger's local period integral for newforms in new cases. The main ingredient is the work \cite{HN18} on Waldspurger's period integral using the minimal vectors, and the explicit relation between the newforms and the minimal vectors. We use a representation theoretical trick to simplify computations for newforms. As an example, we compute the local integral coming from a special arithmetic setting which was used to study 3-part full BSD conjecture in \cite{HSY}.
In the paper, we show that $λ(z_1) -λ(z_2)$, $λ(z_1)$ and $1-λ(z_1)$ are all Borcherds products in $X(2) \times X(2)$. We then use the big CM value formula of Bruinier, Kudla, and Yang to give explicit factorization formulas for the norms of $λ(\frac{d+\sqrt d}2)$, $1-λ(\frac{d+\sqrt d}2)$, and $λ(\frac{d_1+\sqrt{d_1}}2) -λ(\frac{d_2+\sqrt{d_2}}2)$, with the latter under the condition $(d_1, d_2)=1$. Finally, we use these results to show that $λ(\frac{d+\sqrt d}2)$ is always an algebraic integer and can be easily used to construct units in the ray class field of $\mathbb{Q}(\sqrt{d})$ of modulus $2$. In the process, we also give explicit formulas for a whole family of local Whittaker functions, which are of independent interest.
Let $p\equiv 4,7\mod 9$ be a rational prime number such that $3\mod p$ is not a cubic residue. In this paper we prove the 3-part of the product of the full BSD conjectures for $E_p$ and $E_{3p^3}$ is true using an explicit Gross-Zagier formula, where $E_p: x^3+y^3=p$ and $E_{3p^2}: x^3+y^3=3p^2$ are the elliptic curves related to the Sylvester conjecture and cube sum problems.
Let $p\equiv 2,5\mod 9$ be an odd prime. In this paper, we prove that at least one of $3p$ and $3p^2$ is a cube sum by constructing certain nontrivial Heegner points. We also establish the explicit Gross-Zagier formulae for these Heegner points and give variants of the Birch and Swinnerton-Dyer conjecture of the related elliptic curves.
In this paper, we use Borcherds lifting and the big CM value formula of Bruinier, Kudla, and Yang to give an explicit factorization formula for the norm of $Ψ(\frac{d_1+\sqrt{d_1}}2) -Ψ(\frac{d_2+\sqrt{d_2}}2)$, where $Ψ$ is the $j$-invariant or the Weber invariant $ω_2$. The $j$-invariant case gives another proof of the well-known Gross-Zagier factorization formula of singular moduli, while the Weber invariant case gives a proof of the Yui-Zagier conjecture for $ω_2$. The method used here could be extended to deal with other modular functions on a genus zero modular curve.
In this paper, we consider some CM fields which we call of dihedral type and compute the Artin $L$-functions associated to all CM types of these CM fields. As a consequence of this calculation, we see that the Colmez conjecture in this case is very closely related to understanding the log derivatives of certain Hecke characters of real quadratic fields. Recall that the `abelian case' of the Colmez conjecture, proved by Colmez himself, amounts to understanding the log derivatives of Hecke characters of $\Q$ (cyclotomic characters). In this paper, we also prove that the Colmez conjecture holds for `unitary CM types of signature $(n-1, 1)$' and holds on average for `unitary CM types of a fixed CM number field of signature $(n-r, r)$'.
Let $Q$ be a finite quiver of Dynkin type and $Λ=Λ_Q$ be the preprojective algebra of $Q$ over an algebraically closed field $k$. Let $\mathcal {T}_Λ$ be the mutation graph of maximal rigid $Λ$ modules. Geiss, Leclerc and Schr$\ddot{\rm o}$er conjectured that $\mathcal {T}_Λ$ is connected, see [C.Geiss, B.Leclerc, J.Schröer, Rigid modules over preprojective algebras, Invent.Math., 165(2006), 589-632]. In this paper, we prove that this conjecture is true when $Λ$ is of representation finite type or tame type. Moreover, we also prove that $\mathcal {T}_Λ$ is isomorphic to the tilting graph of ${\rm End}_ΛT$ for each maximal rigid $Λ$-module $T$ if $Λ$ is representation-finite.
Let $A$ be a finite dimensional algebra over an algebraically closed field $k$, $\mathcal {D}^b(A)$ be the bounded derived category of $A$-mod and $A^{(m)}$ be the $m$-replicated algebra of $A$. In this paper, we investigate the structure properties of endomorphism algebras arising from silting mutation in $\mathcal {D}^b(A)$ and tilting mutation in $A^{(m)}$-mod.
In this paper, we prove that the matrix between a special PBW basis and the semicanonical basis of $U^+(sl_n(\mathbb{C}))$ is upper triangular unipotent under any order which is compatible with the partial order $\leq_{deg}$.