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Aaron Chan

Aaron Chan contributes to research discovery and scholarly infrastructure.

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Published work

4 published item(s)

preprint2026arXiv

LATTICE: Evaluating Decision Support Utility of Crypto Agents

We introduce LATTICE, a benchmark for evaluating the decision support utility of crypto agents in realistic user-facing scenarios. Prior crypto agent benchmarks mainly focus on reasoning-based or outcome-based evaluation, but do not assess agents' ability to assist user decision-making. LATTICE addresses this gap by: (1) defining six evaluation dimensions that capture key decision support properties; (2) proposing 16 task types that span the end-to-end crypto copilot workflow; and (3) using LLM judges to automatically score agent outputs based on these dimensions and tasks. Crucially, the dimensions and tasks are designed to be evaluable at scale using LLM judges, without relying on ground truth from expert annotators or external data sources. In lieu of these dependencies, LATTICE's LLM judge rubrics can be continually audited and updated given new dimensions, tasks, criteria, and human feedback, thus promoting reliable and extensible evaluation. While other benchmarks often compare foundation models sharing a generic agent framework, we use LATTICE to assess production-level agents used in actual crypto copilot products, reflecting the importance of orchestration and UI/UX design in determining agent quality. In this paper, we evaluate six real-world crypto copilots on 1,200 diverse queries and report breakdowns across dimensions, tasks, and query categories. Our experiments show that most of the tested copilots achieve comparable aggregate scores, but differ more significantly on dimension-level and task-level performance. This pattern suggests meaningful trade-offs in decision support quality: users with different priorities may be better served by different copilots than the aggregate rankings alone would indicate. To support reproducible research, we open-source all LATTICE code and data used in this paper.

preprint2020arXiv

Classifying torsion classes of gentle algebras

For a finite-dimensional gentle algebra, it is already known that the functorially finite torsion classes of its category of finite-dimensional modules can be classified using a combinatorial interpretation, called maximal non-crossing sets of strings, of the corresponding support $τ$-tilting module (or equivalently, two-term silting complexes). In the topological interpretation of gentle algebras via marked surfaces, such a set can be interpreted as a dissection (or partial triangulation), or equivalently, a lamination that does not contain a closed curve. We will refine this combinatorics, which gives us a classification of torsion classes in the category of finite length modules over a (possibly infinite-dimensional) gentle algebra. As a consequence, our result also unifies the functorially finite torsion class classification of finite-dimensional gentle algebras with certain classes of special biserial algebras - such as Brauer graph algebras.

preprint2020arXiv

Irreducible representations of the symmetric groups from slash homologies of p-complexes

In the 40s, Mayer introduced a construction of (simplicial) $p$-complex by using the unsigned boundary map and taking coefficients of chains modulo $p$. We look at such a $p$-complex associated to an $(n-1)$-simplex; in which case, this is also a $p$-complex of representations of the symmetric group of rank $n$ - specifically, of permutation modules associated to two-row compositions. In this article, we calculate the so-called slash homology - a homology theory introduced by Khovanov and Qi - of such a $p$-complex. We show that every non-trivial slash homology group appears as an irreducible representation associated to two-row partitions, and how this calculation leads to a basis of these irreducible representations given by the so-called $p$-standard tableaux.

preprint2020arXiv

On representation-finite gendo-symmetric algebras with only one non-injective projective module

Motivated by the relation between Schur algebra and the group algebra of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang and Steffen Koenig addressed some behaviour of the endomorphism algebra of a generator over a symmetric algebra, which they called gendo-symmetric algebra. Continuing this line of works, we classify in this article the representation-finite gendo-symmetric algebras that have at most one isomorphism class of indecomposable non-injective projective module. We also determine their almost ν-stable derived equivalence classes in the sense of Wei Hu and Changchang Xi. It turns out that a representative can be chosen as the quotient of a representation-finite symmetric algebra by the socle of a certain indecomposable projective module.