arXiv subjects

Niantao Xie

Publications and source records attributed to Niantao Xie.

3 recordsLinked to original sources

arXiv2026

A Certified Lower Bound for Lebesgue's Universal Cover Problem

Lebesgue's universal cover problem asks for the infimum of the areas of planar sets that contain a congruent copy of every planar set of diameter at most one. We work in the convex Brass$-$Sharifi three-test-set framework, where the test sets are a closed disk, an equilateral triangle, and a regular pentagon of diameter one. For each normalized placement $v$, let $A(v)$ denote the area of the convex hull of these three test sets. We construct a finite certificate proving $A(v)\ge 0.833$ throughout the admissible normalized domain. The threshold $0.833$ yields a certified improvement over the Brass$-$Sharifi lower bound $0.832$ within the same convex three-test-set framework. The proof is a finite-cover argument. The admissible domain is covered by finitely many parameter domains, and each domain carries a local lower-bound certificate. The non-witness domains are certified by supporting local records. On the witness domains, the local bound is obtained from an inner-witness polygon construction. The witness points lie in the three test sets and determine an ordered polygonal region certified to be simple and positively oriented. Its area is bounded below by interval orientation and shoelace estimates. Since this certified polygonal region lies inside the corresponding convex hull, its area gives a lower bound for the hull area. Combining the local inequalities with the finite cover yields $α_{cvx}\ge 0.833$, where $α_{cvx}$ is the infimum of the areas of convex universal covers.

cs.CG↗

arXiv2026

FadeMem: Biologically-Inspired Forgetting for Efficient Agent Memory

Large language models deployed as autonomous agents face critical memory limitations, lacking selective forgetting mechanisms that lead to either catastrophic forgetting at context boundaries or information overload within them. While human memory naturally balances retention and forgetting through adaptive decay processes, current AI systems employ binary retention strategies that preserve everything or lose it entirely. We propose FadeMem, a biologically-inspired agent memory architecture that incorporates active forgetting mechanisms mirroring human cognitive efficiency. FadeMem implements differential decay rates across a dual-layer memory hierarchy, where retention is governed by adaptive exponential decay functions modulated by semantic relevance, access frequency, and temporal patterns. Through LLM-guided conflict resolution and intelligent memory fusion, our system consolidates related information while allowing irrelevant details to fade. Experiments on Multi-Session Chat, LoCoMo, and LTI-Bench demonstrate superior multi-hop reasoning and retrieval with 45\% storage reduction, validating the effectiveness of biologically-inspired forgetting in agent memory systems.

cs.AI↗

arXiv2018

Abstractive Summarization Improved by WordNet-based Extractive Sentences

Recently, the seq2seq abstractive summarization models have achieved good results on the CNN/Daily Mail dataset. Still, how to improve abstractive methods with extractive methods is a good research direction, since extractive methods have their potentials of exploiting various efficient features for extracting important sentences in one text. In this paper, in order to improve the semantic relevance of abstractive summaries, we adopt the WordNet based sentence ranking algorithm to extract the sentences which are most semantically to one text. Then, we design a dual attentional seq2seq framework to generate summaries with consideration of the extracted information. At the same time, we combine pointer-generator and coverage mechanisms to solve the problems of out-of-vocabulary (OOV) words and duplicate words which exist in the abstractive models. Experiments on the CNN/Daily Mail dataset show that our models achieve competitive performance with the state-of-the-art ROUGE scores. Human evaluations also show that the summaries generated by our models have high semantic relevance to the original text.

cs.CL↗