深度学习的谱几何：通过随机矩阵理论实现压缩与幻觉检测
Spectral Geometry for Deep Learning: Compression and Hallucination Detection via Random Matrix Theory
AI总结：
本文提出基于谱几何和随机矩阵理论的统一框架，通过分析隐藏激活的特征值结构，实现幻觉检测与模型压缩，提升深度学习的可靠性和效率。
摘要：
大型语言模型和深度神经网络虽然表现出色，但存在可靠性问题和高计算成本。本论文提出了一种基于谱几何和随机矩阵理论的统一框架，通过分析隐藏激活的特征值结构来解决这两个问题。第一项贡献，EigenTrack，是一种实时方法，利用谱特征及其时间动态性来检测语言和视觉-语言模型中的幻觉和分布外行为。第二项贡献，RMT-KD，是一种原理性的压缩方法，通过识别信息丰富的谱成分并应用迭代知识蒸馏，生成紧凑且高效的模型，同时保持准确性。这些结果表明，谱统计提供了可解释且稳健的信号，用于监控不确定性和指导大规模神经网络的压缩。
英文摘要：
Large language models and deep neural networks achieve strong performance but suffer from reliability issues and high computational cost. This thesis proposes a unified framework based on spectral geometry and random matrix theory to address both problems by analyzing the eigenvalue structure of hidden activations. The first contribution, EigenTrack, is a real-time method for detecting hallucinations and out-of-distribution behavior in language and vision-language models using spectral features and their temporal dynamics. The second contribution, RMT-KD, is a principled compression method that identifies informative spectral components and applies iterative knowledge distillation to produce compact and efficient models while preserving accuracy. Together, these results show that spectral statistics provide interpretable and robust signals for monitoring uncertainty and guiding compression in large-scale neural networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
