DeepAI AI Chat
Log In Sign Up

Derivation of the Backpropagation Algorithm Based on Derivative Amplification Coefficients

02/08/2021
by   Yiping Cheng, et al.
BEIJING JIAOTONG UNIVERSITY
0

The backpropagation algorithm for neural networks is widely felt hard to understand, despite the existence of some well-written explanations and/or derivations. This paper provides a new derivation of this algorithm based on the concept of derivative amplification coefficients. First proposed by this author for fully connected cascade networks, this concept is found to well carry over to conventional feedforward neural networks and it paves the way for the use of mathematical induction in establishing a key result that enables backpropagation for derivative amplification coefficients. Then we establish the connection between derivative amplification coefficients and error coefficients (commonly referred to as errors in the literature), and show that the same backpropagation procedure can be used for error coefficients. The entire derivation is thus rigorous, simple, and elegant.

READ FULL TEXT

page 1

page 2

page 3

page 4

05/19/2018

Neural networks with dynamical coefficients and adjustable connections on the basis of integrated backpropagation

We consider artificial neurons which will update their weight coefficien...
12/08/2016

Learning in the Machine: Random Backpropagation and the Learning Channel

Random backpropagation (RBP) is a variant of the backpropagation algorit...
08/10/2018

Quantum Algorithms for Autocorrelation Spectrum

In this paper we design quantum algorithms for studying the autocorrelat...
09/27/2022

A Derivation of Feedforward Neural Network Gradients Using Fréchet Calculus

We present a derivation of the gradients of feedforward neural networks ...
08/20/2003

Artificial Neural Networks for Beginners

The scope of this teaching package is to make a brief induction to Artif...
11/28/2019

Detection of Derivative Discontinuities in Observational Data

This paper presents a new approach to the detection of discontinuities i...
12/17/2015

Towards automating the generation of derivative nouns in Sanskrit by simulating Panini

About 1115 rules in Astadhyayi from A.4.1.76 to A.5.4.160 deal with gene...