用高阶张量重构稀疏卷积网络的回归机制
High-Order Tensor Regression in Sparse Convolutional Neural Networks
- 基于高阶张量建立通用卷积框架
- 重新定义反向传播算法，实现最简通用形式
- 为稀疏卷积神经网络提供统一理论基础
本文提出一种与当前机器学习主流方法显著不同的通用卷积方法。从数学角度看，该方法在处理高阶张量时尤为清晰简洁。在此基础上，构建了神经网络中回归的理性理论，作为对稀疏卷积神经网络的通用视角框架。作为直接成果，经典反向传播算法被重新定义，以契合这一基于张量的理性方法，并呈现为最简、最通用的形式。
原文摘要 · Abstract (English)
This article presents a generic approach to convolution that significantly differs from conventional methodologies in the current Machine Learning literature. The approach, in its mathematical aspects, proved to be clear and concise, particularly when high-order tensors are involved. In this context, a rational theory of regression in neural networks is developed, as a framework for a generic view of sparse convolutional neural networks, the primary focus of this study. As a direct outcome, the classic Backpropagation Algorithm is redefined to align with this rational tensor-based approach and presented in its simplest, most generic form.
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