arXiv subjects

Yonggang Hu

Publications and source records attributed to Yonggang Hu.

13 recordsLinked to original sources

arXiv2026

Quantum Weyl Relations arising from Two-Term Complexes

Let $Q$ be a Dynkin quiver over $k=\mathbb F_q$, let $A=kQ$, and let $\Ktwo(\cP)$ be the extriangulated category of two-term complexes of projective $A$-modules. We study the square-root normalized Hall algebra of $\Ktwo(\cP)$. We first establish a PBW-type vector-space factorization into the Ringel--Hall part and the shifted-projective part, and derive an explicit mixed multiplication formula. For the indecomposable projectives $P_i$, let $p_i$ and $z_i$ be the normalized Hall classes of $(0\to P_i)$ and $(P_i\to0)$, respectively. We prove \[ z_ip_i=q^{-1}p_iz_i+1, \] and determine all off-diagonal products $z_ip_j$ in terms of kernels and cokernels of maps $P_i\to P_j$. Hence each pair $(p_i,z_i)$ generates a rank-one quantum Weyl algebra, while every pairwise Hom-orthogonal family of projectives generates a higher-rank quantum Weyl subalgebra. For these subalgebras we construct explicit Hall--Fock modules, on which the $p_i$ act as creation operators and the $z_i$ act as $q$-annihilation operators. This provides a finite-field Hall model parallel to categorical Hall-type Weyl actions in Donaldson--Thomas theory. Finally, we show that BGP reflection transports the corresponding reflection subalgebras and preserves the mixed Hall coefficients.

math.RT↗

arXiv2025

Quantification of Electrolyte Degradation in Lithium-ion Batteries with Neutron Imaging Techniques

Non-destructive characterization of lithium-ion batteries provides critical insights for optimizing performance and lifespan while preserving structural integrity. Optimizing electrolyte design in commercial LIBs requires consideration of composition, electrolyte-to-capacity ratio, spatial distribution, and associated degradation pathways. However, existing non-destructive methods for studying electrolyte infiltration, distribution, and degradation in LIBs lack the spatiotemporal resolution required for precise observation and quantification of the electrolyte. In this study, we employ neutron imaging with sufficient spatial resolution ~150 um and large field of view 20x20 cm2 to quantitatively resolve the electrolyte inventory and distribution within LiFePO4/graphite pouch cells under high-temperature accelerated aging. Quantitative standard curves based on neutron transmission attenuation reveal a clear electrolyte dry-out threshold at 3.18 g Ah-1 and the two stages evolutions of EI during cell aging were quantified. By integrating non-destructive electrochemical diagnostics, accelerated graphite material loss and liquid phase Li+ diffusion degradation is observed during pore-drying. Further analysis, including operando cyclic aging, reveals that the neutron transmission below the saturation reference is due to the enrichment of hydrogen nuclei within the solid-electrolyte interphase. Assumed pore-drying does not occur, the SEI signal of the electrodes can be quantitatively decoupled during ageing. Combined analyses with NI, TOF-SIMS, and SEM reveal that high EI cells exhibit uniform SEI growth and reduced degradation, while low EI cells show uneven SEI formation, accelerating capacity loss. This study unveils a dynamic electrolyte infiltration-consumption-dry-out process in LIBs, offering non-destructive and quantitative insights to guide sustainable and durable battery development.

physics.app-ph↗

arXiv2025

AutoTriton: Automatic Triton Programming with Reinforcement Learning in LLMs

Kernel development in deep learning requires optimizing computational units across hardware while balancing memory management, parallelism, and hardware-specific optimizations through extensive empirical tuning. Although domain-specific languages like Triton simplify GPU programming by abstracting low-level details, developers must still manually tune critical parameters such as tile sizes and memory access patterns through iterative experimentation, creating substantial barriers to optimal performance and wider adoption. In this work, we introduce AutoTriton, the first model dedicated to Triton programming powered by reinforcement learning (RL). AutoTriton performs supervised fine-tuning (SFT) to be equipped with essential Triton programming expertise using a high-quality data gathering pipeline, and conducts RL with Group Relative Policy Optimization (GRPO) algorithm, combining a rule-based reward and an execution-based reward to further improve Triton programming ability, sequentially. Experiments across five evaluation channels of TritonBench and KernelBench illustrate that our 8B model AutoTriton achieves performance comparable to mainstream large models, including Claude-4-Sonnet and DeepSeek-R1-0528. Further experimental analysis demonstrates the crucial role of each module within AutoTriton, including the SFT stage, the RL stage, and the reward design strategy. These findings underscore the promise of RL for automatically generating high-performance kernels, and since high-performance kernels are core components of AI systems, this breakthrough establishes an important foundation for building more efficient AI systems. The model and code will be available at https://github.com/AI9Stars/AutoTriton.

cs.LG↗

arXiv2025

Tensor Products of Flat Cotorsion Modules and Cotorsion Dimension

This paper studies the tensor product of flat cotorsion modules. Let~$R$~and $S$ be~$k$-algebras. We prove that both~$R$-module\ $M$ and~$S$-module\ $N$ are flat cotorsion modules if and only if~$M\otimes_{k} N$ is a flat cotorsion~$R\otimes_{k} S $-module. Based on this conclusion, we provide a lower bound for the global cotorsion dimension of the tensor product algebra~$R\otimes_{k}S $ under appropriate conditions.

math.RA↗

arXiv2021

One-sided n-suspended categories

Let $n$ be an integer greater or equal than $3$. We give a simultaneous generalization of $(n-2)$-exact categories and $n$-angulated categories, and we call it one-sided $n$-suspended categories. One-sided $n$-angulated categories are also examples of one-sided $n$-suspended categories. We provide a general framework for passing from one-sided $n$-suspended categories to one-sided $n$-angulated categories. Besides, we give a method to construct $n$-angulated quotient categories from Frobenius $n$-prile categories. These results generalize their works by Jasso for $n$-exact categories, Lin for $(n+2)$-angulated categories and Li for one-sided suspended categories.

math.RT↗

arXiv2021

s-Recollements and its localization

We introduce a new concept of s-recollements of extriangulated categories, which generalizes recollements of abelian categories, recollements of triangulated categories, as well as recollements of extriangulated categories. Moreover, some basic properties of s-recollements are presented. We also discuss the behavior of the localization theory on the adjoint pair of exact functors. Finally, we provide a method to obtain a recollement of triangulated categories from s-recollements of extriangulated categories via the localization theory.

math.RT↗

arXiv2021

Torsion pairs and recollements of extriangulated categories

In this article, we prove that if $(\mathcal A ,\mathcal B,\mathcal C)$ is a recollement of extriangulated categories, then torsion pairs in $\mathcal A$ and $\mathcal C$ can induce torsion pairs in $\mathcal B$, and the converse holds under natural assumptions. Besides, we give mild conditions on a cluster tilting subcategory on the middle category of a recollement of extriangulated categories, for the corresponding abelian quotients to form a recollement of abelian categories.

math.RT↗

arXiv2021

Cosilting modules arising from cotilting objects

Let $R$ be a ring. In this paper, we study the characterization of cosilting modules and establish a relation between cosilting modules and cotilting objects in a Grothendieck category. We proved that each cosilting right $R$-module $T$ can be described as a cotilting object in $σ[R/I]$, where $I$ is a right ideal of $R$ determined by $T$ and $σ[R/I]$ is the full subcategory of right $R$-modules, consisting of submodules of $R/I$-generated modules. Conversely, under some suitable conditions, if $T$ is a cotilting object in $σ[R/I]$, then $T$ is cosilting.

math.RT↗

arXiv2020

The representation invariants of 2-term silting complexes

Let $A$ be a finite dimensional algebra over a field $k$ and $\textbf{P}$ be a 2-term silting complex in $K^{b}(\text{proj}A)$. In this paper, we investigate the representation dimension of $\text{End}_{D^{b}(A)} (\textbf{P})$ by using the silting theory. We show that if $\textbf{P}$ is a separating silting complex with certain homological restriction, then rep.dim $A=$rep.dim $\text{End}_{D^{b}(A)}(\textbf{P})$. This gives a proper generalization of the classical compare theorem of representation dimensions showed by Chen and Hu. It is well-known that $\text{H}^{0}(\textbf{P})$ is a tilting $A/\text{ann}_{A} (\textbf{P})$-module. We also show that rep.dim $\text{End}_{A} (\text{H}^{0}(\textbf{P})) = $rep.dim $A/\text{ann}_{A} (\textbf{P})$ if $\textbf{P}$ is a separating and splitting silting complex.

math.RT↗

arXiv2020

Elastic Bulk Synchronous Parallel Model for Distributed Deep Learning

The bulk synchronous parallel (BSP) is a celebrated synchronization model for general-purpose parallel computing that has successfully been employed for distributed training of machine learning models. A prevalent shortcoming of the BSP is that it requires workers to wait for the straggler at every iteration. To ameliorate this shortcoming of classic BSP, we propose ELASTICBSP a model that aims to relax its strict synchronization requirement. The proposed model offers more flexibility and adaptability during the training phase, without sacrificing on the accuracy of the trained model. We also propose an efficient method that materializes the model, named ZIPLINE. The algorithm is tunable and can effectively balance the trade-off between quality of convergence and iteration throughput, in order to accommodate different environments or applications. A thorough experimental evaluation demonstrates that our proposed ELASTICBSP model converges faster and to a higher accuracy than the classic BSP. It also achieves comparable (if not higher) accuracy than the other sensible synchronization models.

cs.LG↗

arXiv2019

Recollements arising from cotorsion pairs on extriangulated categories

This paper is devoted to constructing some recollements of additive categories associated to concentric twin cotorsion pairs on an extriangulated category. As an application, this result generalizes the work by Chen-Liu-Yang in a triangulated case. Moreover, it highlights new phenomena when it applied to an exact category. Finally, we give some applications to illustrate our main results. In particular, we obtain the Krause's recollement whose the proofs are both elementary and very general.

math.RT↗

arXiv2019

Dynamic Graph Embedding via LSTM History Tracking

Many real world networks are very large and constantly change over time. These dynamic networks exist in various domains such as social networks, traffic networks and biological interactions. To handle large dynamic networks in downstream applications such as link prediction and anomaly detection, it is essential for such networks to be transferred into a low dimensional space. Recently, network embedding, a technique that converts a large graph into a low-dimensional representation, has become increasingly popular due to its strength in preserving the structure of a network. Efficient dynamic network embedding, however, has not yet been fully explored. In this paper, we present a dynamic network embedding method that integrates the history of nodes over time into the current state of nodes. The key contribution of our work is 1) generating dynamic network embedding by combining both dynamic and static node information 2) tracking history of neighbors of nodes using LSTM 3) significantly decreasing the time and memory by training an autoencoder LSTM model using temporal walks rather than adjacency matrices of graphs which are the common practice. We evaluate our method in multiple applications such as anomaly detection, link prediction and node classification in datasets from various domains.

cs.LG↗

arXiv2012

Tensor-based projection depth

The conventional definition of a depth function is vector-based. In this paper, a novel projection depth (PD) technique directly based on tensors, such as matrices, is instead proposed. Tensor projection depth (TPD) is still an ideal depth function and its computation can be achieved through the iteration of PD. Furthermore, we also discuss the cases for sparse samples and higher order tensors. Experimental results in data classification with the two projection depths show that TPD performs much better than PD for data with a natural tensor form, and even when the data have a natural vector form, TPD appears to perform no worse than PD.

math.ST↗