arXiv subjects
Publications and source records attributed to Can Wen.
We show that the Hochschild cohomology of higher Auslander algebras of type $\mathbb{A}$ vanishes in all positive degrees and is one-dimensional in degree zero. As a consequence, these algebras are rigid and intrinsically formal.
We present MagicSelector, a joint optimization framework integrating Counterfactual task decomposition, Progressive reranking, and Dynamic Top-K, designed to address the fundamental challenges of tool retrieval in agents. MagicSelector is a specialized framework capable of translating ambiguous user instructions into executable atomic subtasks and guiding high-precision tool retrieval, effectively mitigating redundant noise and severe context distraction in out-of-domain (OOD) scenarios. We empower MagicSelector with these capabilities through three key contributions: (1) a preference-guided counterfactual task decomposition mechanism that utilizes a counterfactual reward to quantify the marginal causal gain of decomposition on retrieval ranking, effectively imposing fine-grained structural supervision on logical coherence; (2) a progressive tool reranking method driven by self-distillation hard negative mining, which optimizes both point-wise and list-wise relevance to enhance fine-grained discrimination among highly similar tools; and (3) a dual semantic boundary-aware dynamic Top-K strategy that adaptively monitors reranking score cliffs and inter-tool semantic shifts to dynamically truncate the candidate list, maximizing relevant tool recall while filtering long-tail noise. Evaluated on MTDTool, the first task decomposition benchmark we constructed tailored for mobile multi-turn interactions with process-level annotations, MagicSelector yields promising performance. Extensive experiments demonstrate that MagicSelector significantly outperforms state-of-the-art methods in terms of tool retrieval accuracy, OOD generalization capability, and overall token efficiency, thereby demonstrating the effectiveness of our proposed framework.
In this paper we calculate the Hochschild cohomology of graded skew-gentle algebras, together with its structure as graded commutative algebra under the cup product and its Lie algebra structure given by the Gerstenhaber bracket. One of the results of this paper is that for graded skew-gentle algebras and thus also for partially wrapped Fukaya categories of orbifold surfaces with stops, their Hochschild cohomology is encoded in the underlying graded surface.
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.
We compare the first Hochschild cohomology groups of finite dimensional monomial algebras under gluing two idempotents. We also compare the fundamental groups and the Hochschild cohomology groups in other degrees. In particular, we will study the case of gluing a source and a sink, that is, when we obtain a stable equivalence.