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Yuming Liu

Publications and source records attributed to Yuming Liu.

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Classification of Brauer graph algebras under stable equivalence of Morita type

The classification of Brauer graph algebras under derived equivalence was recently given by Opper and Zvonareva. In this paper, we prove that two Brauer graph algebras are derived equivalent if and only if they are stably equivalent of Morita type. As an application, we show that every stable Picard group orbit of simple-images of Morita type contains a liftable representative. Moreover, we give a new proof of the fact that Brauer graph algebras are closed up to semisimple summands under stable equivalence of Morita type.

math.RT

Brauer graph algebras are closed under stable equivalence of Morita type

We study stable equivalences of Brauer graph algebras. In particular, we prove that Brauer graph algebras are closed up to semisimple summands under stable equivalence of Morita type. As a consequence, we reprove the result of Antipov and Zvonareva that Brauer graph algebras are closed under derived equivalence. As a byproduct, we get a solution of the reconstruction problem posed by Rickard and Rouquier for algebras stably equivalent of Morita type to Brauer graph algebras.

math.RT

ConnectionMind: Leveraging Social Networks and Large Language Models for Personalized Recommendation at Meta

Modern recommendation systems on social media platforms such as Meta must model complex social relationships, including friendships, group memberships, and creator interactions, alongside massive and heterogeneous content such as text and video. Traditional recommendation models, however, often omit these signals or treat them independently, lacking the reasoning capability to integrate multi-relational context for fine-grained personalization. We present ConnectionMind, a production-ready recommendation framework that tightly integrates the social network structure with large language models (LLMs) to enable scalable, interpretable, and reasoning-aware personalization in Meta. ConnectionMind constructs a heterogeneous graph connecting users, items, friends, groups, and creator pages, and formulates recommendation as a graph reasoning problem: discovering personalized paths from users to candidate items. An LLM-based policy is employed to reason over these graph structures and guide recommendation decisions. To train the system at scale, ConnectionMind adopts a two-stage learning strategy. We first perform supervised fine-tuning (SFT) on large-scale user-item interaction trajectories to initialize the reasoning policy, followed by end-to-end reinforcement learning (RL) to refine the model's ability to reason over social graphs for personalized recommendation. Extensive experiments on multiple real-world datasets demonstrate the effectiveness of ConnectionMind compared to representative baselines. More importantly, ConnectionMind has been deployed in Meta's large-scale recommendation pipeline and has been evaluated through online A/B tests, achieving a 0.43% improvement in video watch time. These results demonstrate measurable real-world impact in a production recommendation system.

cs.IR

NEXT: Reasoning-Driven Video Recommendation via a Vision-Language Model

We present NEXT (Next-interest EXploration Transformer), a reasoning-driven video recommendation framework that reasons over the video a user has just watched, infers the viewer's next intent, and retrieves concrete follow-up videos. Explicit continuations such as episodes are linked directly; implicit cases are handled by generating intent queries and searching for matching candidates. This Item-to-Intent-to-Item formulation produces directed recommendations beyond co-engagement correlation or semantic similarity. To make this framework reliable at scale, we train NEXT-8B, a purpose-trained 8B vision-language model with a three-stage recipe: Perception-Enhanced Reinforcement Learning for query-agnostic evidence extraction, Distribution-Aligned Supervised Fine-Tuning over real and synthetic visual QA mixtures, and Group Relative Policy Optimization for last-mile alignment. NEXT-8B achieves the best single-model DocVQA performance, ranking second overall only behind a multi-agent system while surpassing a substantially larger 200B+ scale model, and improves next-intent logic-wise quality by 3.3% over the base model in a task-specific LLM-as-a-judge evaluation. We deploy NEXT as an additional retrieval path in a large-scale social media recommendation system and observe statistically significant production gains, including +0.53% watch time and +0.51% distinct video exposure. Overall, NEXT shows that a carefully trained compact vision-language model can serve as a practical reasoning engine for next-interest exploration at production scale.

cs.IR

TriFusion-LLM: Prior-Guided Multimodal Fusion with LLM Arbitration for Fine-grained Code Clone Detection

Code clone detection (CCD) supports software maintenance, refactoring, and security analysis. Although pre-trained models capture code semantics, most work reduces CCD to binary classification, overlooking the heterogeneity of clone types and the seven fine-grained categories in BigCloneBench. We present Full Model, a multimodal fusion framework that jointly integrates heuristic similarity priors from classical machine learning, structural signals from abstract syntax trees (ASTs), and deep semantic embeddings from CodeBERT into a single predictor. By fusing structural, statistical, and semantic representations, Full Model improves discrimination among fine-grained clone types while keeping inference cost practical. On the seven-class BigCloneBench benchmark, Full Model raises Macro-F1 from 0.695 to 0.875. Ablation studies show that using the primary model's probability distribution as a prior to guide selective arbitration by a large language model (LLM) substantially outperforms blind reclassification; arbitrating only ~0.2% of high-uncertainty samples yields an additional 0.3 absolute Macro-F1 gain. Overall, Full Model achieves an effective performance-cost trade-off for fine-grained CCD and offers a practical solution for large-scale industrial deployment.

cs.SE

Rethinking Zero-Shot Time Series Classification: From Task-specific Classifiers to In-Context Inference

The zero-shot evaluation of time series foundation models (TSFMs) for classification typically uses a frozen encoder followed by a task-specific classifier. However, this practice violates the training-free premise of zero-shot deployment and introduces evaluation bias due to classifier-dependent training choices. To address this issue, we propose TIC-FM, an in-context learning framework that treats the labeled training set as context and predicts labels for all test instances in a single forward pass, without parameter updates. TIC-FM pairs a time series encoder and a lightweight projection adapter with a split-masked latent memory Transformer. We further provide theoretical justification that in-context inference can subsume trained classifiers and can emulate gradient-based classifier training within a single forward pass. Experiments on 128 UCR datasets show strong accuracy, with consistent gains in the extreme low-label situation, highlighting training-free transfer for time series classification.The source code is publicly available at https://github.com/fangjuntao/TIC-FM.

cs.LG

The second Hochschild cohomology and deformations of Brauer graph algebras

In this paper, we give an explicit description about the second Hochschild cohomology groups of bipartite Brauer graph algebras with trivial grading. Based on this, we provide geometric interpretations of deformations associated to some standard cocycles in terms of the surface models of Brauer graph algebras.

math.RA

$A_{\infty}$-structures on the additive decomposition of the Tate-Hochschild cohomology of a finite group algebra

Firstly, for a finite group algebra, we provide a computational framework $\widehat{m}_n$ for the Tate-Hochschild cochain complex in terms of the additive decomposition, by decomposing each planar n-ary tree into local two children and local three children. Secondly, we give all $\widehat{m}_2$ formulas of the Tate-Hochschild cochain complex in terms of the additive decomposition. Thirdly, we give explicit $A_{\infty}$-multiplication formulas for both the Hochschild cochain complex and the Hochschild chain complex under additive decompositions. Finally, we give $A_{\infty}$-multiplication formulas in the context of abelian groups.

math.KT

Disentangling Long-Short Term State Under Unknown Interventions for Online Time Series Forecasting

Current methods for time series forecasting struggle in the online scenario, since it is difficult to preserve long-term dependency while adapting short-term changes when data are arriving sequentially. Although some recent methods solve this problem by controlling the updates of latent states, they cannot disentangle the long/short-term states, leading to the inability to effectively adapt to nonstationary. To tackle this challenge, we propose a general framework to disentangle long/short-term states for online time series forecasting. Our idea is inspired by the observations where short-term changes can be led by unknown interventions like abrupt policies in the stock market. Based on this insight, we formalize a data generation process with unknown interventions on short-term states. Under mild assumptions, we further leverage the independence of short-term states led by unknown interventions to establish the identification theory to achieve the disentanglement of long/short-term states. Built on this theory, we develop a long short-term disentanglement model (LSTD) to extract the long/short-term states with long/short-term encoders, respectively. Furthermore, the LSTD model incorporates a smooth constraint to preserve the long-term dependencies and an interrupted dependency constraint to enforce the forgetting of short-term dependencies, together boosting the disentanglement of long/short-term states. Experimental results on several benchmark datasets show that our \textbf{LSTD} model outperforms existing methods for online time series forecasting, validating its efficacy in real-world applications.

cs.LG

Fractional Brauer configuration algebras II: covering theory

In this paper, we develop a covering theory for the fractional Brauer configurations and connect it with the coverings of the associated quivers with relations in the sense of Mart\'inez-Villa and de la Pe\~na. Among the results, we show the following: (1) The universal cover of any fractional Brauer configuration is simply connected and we construct explicitly the universal cover of fractional Brauer configurations of type MS; (2) The fundamental group of a fractional Brauer configuration $E$ of type S is isomorphic to the fundamental group of the associated quiver with relations $(Q_E,I_E)$; (3) A (regular) covering of fractional Brauer configurations induces a (Galois) covering of the associated fractional Brauer configuration categories; (4) Set up an analogy of Van Kampen theorem for fractional Brauer configurations and apply it to calculate the fundamental group of any connected Brauer configuration.

math.RT

Fractional Brauer configuration algebras III: fractional Brauer graph algebras of type MS

In previous two papers, we defined fractional Brauer configuration algebras and developed their covering theory. In this paper, we study the representation theory of fractional Brauer graph algebras of type MS, a special class of fractional Brauer configuration algebras that properly generalizes Brauer graph algebras. We first introduce the notion of Brauer $G$-set, which is a generalization of fractional Brauer graph of type MS. Then we develop a covering theory for Brauer $G$-sets and use it to characterize the representation types of fractional Brauer graph algebras of type MS. Moreover, we describe the AR-components of representation-finite and domestic fractional Brauer graph algebras of type MS respectively.

math.RT

Trivial extensions of monomial algebras are symmetric fractional Brauer configuration algebras

By providing equivalent definitions of fractional Brauer configuration algebras in certain special cases, we associate to each monomial algebra some combinatorial data called a fractional Brauer configuration, from which we construct a corresponding fractional Brauer configuration algebra. We show that this algebra is isomorphic to the trivial extension of the given monomial algebra. Furthermore, we establish a one-to-one correspondence between the isomorphism classes of monomial algebras and the equivalence classes of pairs consisting of a symmetric fractional Brauer configuration algebra of type S with a free fractional-degree function and an admissible cut on it.

math.RA

Fractional Brauer configuration algebras I: definitions and examples

In 2017, Green and Schroll introduced a generalization of Brauer graph algebras which they call Brauer configuration algebras. In the present paper, we further generalize Brauer configuration algebras to fractional Brauer configuration algebras by generalizing Brauer configurations to fractional Brauer configurations. The fractional Brauer configuration algebras are locally bounded but neither finite-dimensional nor symmetric in general. We show that if the fractional Brauer configuration is of type S (resp. of type MS), then the corresponding fractional Brauer configuration algebra is a locally bounded Frobenius algebra (resp. a locally bounded special multiserial Frobenius algebra). Moreover, we show that over an algebraically closed field, the class of finite-dimensional indecomposable representation-finite fractional Brauer configuration algebras in type S coincides with the class of basic indecomposable finite-dimensional standard representation-finite self-injective algebras.

math.RT

Algebraic Morse theory via Homological Perturbation Lemma

As a generalization of the classical killing-contractible-complexes lemma, we present algebraic Morse theory via homological perturbation lemma, in a form more general than existing presentations in the literature. Two-sided Anick resolutions due to E.~Sk\"{o}ldberg are generalised to algebras given by quivers with relations and a minimality criterion is provided as well. Two applications of algebraic Morse theory are presented. It is shown that the Chinese algebra of rank $n\geq 1$ is homologically smooth and of global dimension $\frac{n(n+1)}{2}$, and the minimal two-sided projective resolution of a Koszul algebra is constructed.

math.KT

The Hochschild cohomology groups under gluing arrows

In a previous paper arXiv:2211.05435 we have compared the Hochschild cohomology groups of finite dimensional monomial algebras under gluing two idempotents. In the present paper, we compare the Hochschild cohomology groups of finite dimensional monomial algebras under gluing two arrows.

math.KT

A note on higher structures on the complexes associated to quiver algebras with applications to toupie algebras

In this paper, we summarize a general method of transforming DG structures into higher structures on the various complexes related to the reduced bar resolution of a given quiver algebra using algebraic Morse theory. As an application, we describe the $A_\infty$-structures of toupie algebras. Additionally, for certain special toupie algebras, we also prove that their double homological duals are isomorphic to their associated graded algebras.

math.RT