Neural_Networks

Understanding Neural Networking with basics of Keras.

Diagram of a Nth Neural Network

Topics	Links
Keras Activation Functions:	https://keras.io/activations/
Keras Models:	https://keras.io/models/about-keras-models/#about-keras-models
Keras Optimizers:	https://keras.io/optimizers/
Keras Metrics:	https://keras.io/metrics/
Keras - Functions	https://keras.io/api/models/sequential/

Important Partial Derivatives for Backpropagation

(experimenting with LaTeX for GitHub for full equations sheet check out)

https://raw.githubusercontent.com/adgsenpai/Neural_Networks/main/Partial_Derivatives_Backpropagation.pdf

Equation 1

$$ z_{1} = x_{1}*w_{1}+b_{1} $$

Equation 2

$$ a_{1} = f(z_{1}) = {1 \over 1+e^{-z_{1}}} $$

Equation 3

$$ z_{2} = a_{1} * w_{2} + b_{2} $$

Equation 4

$$ a_{2} = f(z_{2}) = {1 \over 1+e^{-z_{2}}}$$

Equation 5

$$ E = {1 \over 2}{(T-a_{2})^2} $$

Doing one partial differential equation

using Equation 5

$$ E = {1 \over 2}{(T-a_{2})^2} $$

1. for

$$ {\partial{E} \over \partial{w_2}} $$

$$ {\partial{E} \over \partial{w_2}} = {\partial{E} \over \partial{a_2}}{\partial{a_{2}} \over \partial{z_{2}}} {\partial{z_{2}} \over \partial{w_{2}}} $$

$$ {\partial{E} \over \partial{w_2}} = 2{1 \over 2}{(T-a_{2})}{(-1)} $$ $$ = -{(T-a_{2})}$$