Search arXiv⌕ Search

arXiv subjects

Chih-Chi Chou

Publications and source records attributed to Chih-Chi Chou.

7 recordsLinked to original sources

CatalogAgent: A Supervisor-mediated Self-Learning System Enabling Context Engineering for GenAI Models

Product catalogs are the backbone of e-commerce sites, yet a large number of structured attributes (SAs) -- such as material, color, and shape -- often have missing values. Typically, SA values are extracted from product information, including titles and descriptions. While LLM-based generator-evaluator frameworks have demonstrated effectiveness for SA prediction -- where an LLM generates SA values and another evaluates them -- they face challenges when the Generator and Evaluator produce conflicting outputs, as either component can make mistakes. We introduce \texttt{CatalogAgent}, a novel agentic system that continuously improves Generator and Evaluator models for e-commerce catalog enrichment. When disagreements arise from (1) internal conflicts between the LLM-based Generator and Evaluator, or (2) external feedback from sellers on LLM outputs, a Supervisor Agent intervenes to mediate these conflicts and make final decisions. The system also incorporates a Memory Base and a Memory Summarizer that stores Supervisor Agent activities from individual cases and aggregates patterns into learnings. These learnings are fed back to the worker Generator and Evaluator LLMs, enabling self-improvement without human intervention. Through context engineering -- injecting learnings and insights into worker LLMs' contexts -- the system successfully transfers the Supervisor's capabilities to the Generator and Evaluator, improving their performance by 15.24\% and 13.98\%, respectively. Our experiments demonstrate a new paradigm of Supervisor Agent-mediated self-learning systems for improving generative AI model accuracy.

cs.AI↗

On direct images of twisted pluricanonical sheaves on normal varieties

We study the depth properties of certain direct image sheaves on normal varieties. Let $f: Y\rightarrow X$ be a proper morphism of relative dimension $d$ from a smooth variety onto a normal variety such that the preimage $E$ of the singular locus of $X$ is a divisor. We show that for any integer $m>0$, the higher direct image $R^df_*ω^{\otimes m}_Y(aE)$ modulo the torsion subsheaf is $S_2$, provided that $a$ is sufficiently large. In case $f$ is birational, we give criteria on $a$ for the direct image $f_*ω_Y(aE)$ to coincide with $ω_X$. We also introduce an index measuring the singularities of normal varieties.

math.AG↗

Singularities of secant varieties

We study the singularities of the secant variety $Σ(X,L)$ associated to a smooth variety $X$ embedded by a sufficiently positive adjoint bundle $L$. We show that $Σ(X,L)$ is always Du Bois singular. Examples of secant varieties with worse singularities when $L$ has weak positivity are provided. We also give a necessary and sufficient condition for $Σ(X, L)$ to have rational singularities.

math.AG↗

Some applications of Grothendieck Duality Theorem

In this paper, we systematically apply Grothendieck duality theorem to simplify the proofs of several theorems in different papers: Including a vanishing theorem in KMM, a theorem of Kollár's paper, a vanishing theorem due to Kovács and a theorem of Fujino. We remark that all of the above are achieved by the same trick.

math.AG↗

On isolated log canonical centers

In this paper, we show that the depth of an isolated log canonical center is determined by the cohomology of the -1 discrepancy diviors over it. A similar result also holds for normal isolated Du Bois singularities.

math.AG↗

A Transversality Theorem for some Classical Varieties

In 2009, de Fernex and Hacon proposed a generalization of the notion of the singularities to normal varieties that are not Q-Gorenstein. Based on their work, we generalize Kleiman's transversality theorem to subvarieties with log terminal or log canonical singularities. We also show that some classical varieties, such as generic determinantal varieties, W^r_d for general smooth curves, and certain Schubert varieties in G(k, n) are log terminal.

math.AG↗