Introduction to Deep Learning: Mathematical Explanation of Multi-Layer Perceptron and Backpropagation

In recent decades, machine learning techniques have been increasingly applied to biological data, including functional magnetic resonance imaging, electroencephalography, and electromyography. A growing number of physiological psychology and psychophysiological studies now utilize deep learning, a machine learning method actively employed across various fields. However, understanding such research can be difficult without understanding the underlying mathematics. This paper introduces the essential mathematics required to understand the operating principles of the multi-layer perceptron, a fundamental deep learning model. It aims to provide a foundation for further exploring deep learning techniques.