本文从数学的角度探讨了外部输入信息与过完备字典之间的关系问题即相关性问题，研究了过完备字典与稀 疏表示的内在联系，在此基础上对过完备字典进行分析和修正，以提高深度学习的层次且增加对环境的适应性，为今后对字典 的设计奠定了基础。

The paper inquiries into the relativity problem between input information and over-complete dictionary from the mathematical viewpoint and their inner relationships. On this foundation, we analyze and revise the over- complete dictionaries to enhance the level and adaptability of deep learning, and lay the foundations of the dictionary design in the future.