基于熵空间理论理解深度学习
Understanding Deep Learning via Entropy Space Theory
- Changchun University of Science and Technology（长春理工大学）
- School of Electronic Information Engineering（电子信息工程学院）
- Zhongshan Institute of Changchun University of Science and Technology（长春理工大学中山研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对深度学习理论滞后于实践的问题，本文引入熵空间理论，证明其为赋范空间，提出统一坐标系，为深度学习数学基础提供新颖先验框架。
AI中文摘要：
深度学习常被批评理论研究滞后于实践。为便于理解深度学习，本文首次引入熵空间理论。熵空间可通过拓扑结构覆盖任意深度学习模型的所有可能性，且独立于网络参数。借助所设计的基本运算与范数，熵空间在形式公理框架内被证明为赋范空间。基于该理论，本文提出统一坐标系，可对模型的每种状态进行坐标化，并通过信息熵最大值的压缩程度对其排序。该理论为深度学习的数学基础提供了新颖的先验框架。
英文摘要：
Deep learning is often criticized for its theoretical research lagging behind practice. To make deep learning easier to understand, the entropy space theory is first introduced here. The entropy space can cover all the possibilities of any deep learning model by topological structure. It is independent of network parameters. Through the designed fundamental operations and norm, entropy space is proven to be a normed space within the formal axiomatic framework. Based on the theory, a unified coordinate system is proposed. It can coordinatize every state of a model and rank them by compression of the maximal value of information entropy. The theory offers a novel priori framework for mathematical fundamentals of deep learning.
