展望使用代数环来描述卷积神经网络的操作

I. Suleimenov, A. Bakirov, Y. Vitulyova
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引用次数: 0

摘要

采用了一种新型的数字系统(整数编码系统)。在系统中,用一组数字,每个数字对应一个素数,来代替对应某个整数的幂的数字(例如,10),不同数字对应的所有素数都是不同的。这样的整数编码对应于一个离散信号模型,该模型对应的函数在某个代数环中取值。这种编码的优点是不同数字对应的数的独立乘法,这大大简化了计算,包括以离散形式表示的信号的卷积计算。在这种情况下,卷积运算可以简化为在伽罗瓦场中计算卷积的情况。在这种情况下,对所提出的数字系统中的信号进行的卷积运算是对每个数字独立进行的。提出了一种实现该方法的具体算法,并证明了其在描述卷积神经网络方面的优势。本文考虑了一个演示这些优点的具体示例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Prospects for the use of algebraic rings to describe the operation of convolutional neural networks
A new type of number systems (integer coding systems) is used. In the system a set of digits, each of which corresponds to a certain prime number, is used instead of digits corresponding to the powers of a certain integer (for example, ten), All the prime numbers corresponding to different digits are different. Such an encoding of integers corresponds to a discrete signal model, in which the function corresponding to this model takes values in some algebraic ring. The advantage of such an encoding is the independent multiplication of numbers corresponding to different digits, which provides a significant simplification of calculations, including calculation of convolutions of signals presented in a discrete form. It is shown that in this case the convolution operation can be reduced to a situation where the convolution is calculated in Galois fields. In this case, the convolution operations carried out for the signals presented in proposed number system are carried out independently for each digit. A specific algorithm that implements this approach is proposed and its advantages for describing convolutional neural networks are proved. A specific example demonstrating these advantages is considered.
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