Jia Chen

T. Y. S. S. Santosh, Chen Jia, Patrick Goroncy et al.

This paper addresses the task of legal summarization, which involves distilling complex legal documents into concise, coherent summaries. Current approaches often struggle with content theme deviation and inconsistent writing styles due to their reliance solely on source documents. We propose RELexED, a retrieval-augmented framework that utilizes exemplar summaries along with the source document to guide the model. RELexED employs a two-stage exemplar selection strategy, leveraging a determinantal point process to balance the trade-off between similarity of exemplars to the query and diversity among exemplars, with scores computed via influence functions. Experimental results on two legal summarization datasets demonstrate that RELexED significantly outperforms models that do not utilize exemplars and those that rely solely on similarity-based exemplar selection.

JIa Chen, Heping Wang

In this paper, we obtain the preasymptotic and asymptotic behavior and strong equivalences of the approximation numbers of the embeddings from the anisotropic Sobolev spaces $W_2^{\bf R}(\Bbb T^d)$ to $L_2(\Bbb T^d)$. We also get the preasymptotic behavior of the approximation numbers of the embeddings from the limit spaces $W_2^{\infty}(\Bbb T^d)$ of the anisotropic Sobolev spaces $W_2^{\bf R}(\Bbb T^d)$ to $L_2(\Bbb T^d)$. We show that both the above embedding problems are intractable and do not suffer from the curse of dimensionality.