A Tutorial on Neural Networks and Gradient-free Training

• URL: http://arxiv.org/abs/2211.17217v1
• Date: Sat, 26 Nov 2022 15:33:11 GMT
• Title: A Tutorial on Neural Networks and Gradient-free Training
• Authors: Turibius Rozario, Arjun Trivedi, Ankit Goel
• Abstract summary: This paper presents a compact, matrix-based representation of neural networks in a self-contained tutorial fashion. neural networks are mathematical nonlinear functions constructed by composing several vector-valued functions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: This paper presents a compact, matrix-based representation of neural networks in a self-contained tutorial fashion. Specifically, we develop neural networks as a composition of several vector-valued functions. Although neural networks are well-understood pictorially in terms of interconnected neurons, neural networks are mathematical nonlinear functions constructed by composing several vector-valued functions. Using basic results from linear algebra, we represent a neural network as an alternating sequence of linear maps and scalar nonlinear functions, also known as activation functions. The training of neural networks requires the minimization of a cost function, which in turn requires the computation of a gradient. Using basic multivariable calculus results, the cost gradient is also shown to be a function composed of a sequence of linear maps and nonlinear functions. In addition to the analytical gradient computation, we consider two gradient-free training methods and compare the three training methods in terms of convergence rate and prediction accuracy.

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