Neural Network Toolbox

Mathematical Notation for Equations and Figures

Basic Concepts

Scalars -- small italic letters.....a,b,c

Vectors -- small bold nonitalic letters.....a,b,c

Matrices -- capital BOLD nonitalic letters.....A,B,C

Language

Vector means a column of numbers.

Weight Matrices

Scalar Element

     - row, - column, - time or iteration

Matrix

Column Vector

Row Vector ...vector made of ith row of weight matrix W

Bias Vector

Scalar Element

Vector

Layer Notation

A single superscript is used to identify elements of layer. For instance, the net input of layer 3 would be shown as n³.

Superscripts are used to identify the source (l) connection and the destination (k) connection of layer weight matrices and input weight matrices. For instance, the layer weight matrix from layer 2 to layer 4 would be shown as LW^4,2.

Input Weight Matrix

Layer Weight Matrix

Figure and Equation Examples

The following figure, taken from Chapter 12, illustrates notation used in such advanced figures.

Basic Chapters

Mathematics and Code Equivalents

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