updated content

contrib/machine-learning/ArtificialNeuralNetwork.md

@@ -26,7 +26,6 @@ This guide will walk you through a fundamental neural network implementation in
 
 | `Neuron` cells forming the humand nervous system | `Perceptron` inspired from human brain |
 | :----------------------------------------------- | -------------------------------------: |
-| <img align="left" width="300" height="150" src="https://bit.ly/neu-ron"> | <img align="right" width="300" height="150" src="https://bit.ly/nn-perceptron"> |
 | Neurons are nerve cells that send messages all over your body to allow you to do everything from breathing to talking, eating, walking, and thinking. |  The perceptron is a mathematical model of a biological neuron. Performing heavy computations to think like humans. |
 | Neuron collects signals from dendrites. | The first layer is knownn as Input Layer, acting like dendritres to receive the input signal. |
 | Synapses are the connections between neurons where signals are transmitted. | Weights represent synapses. |
@@ -44,28 +43,17 @@ Neurons in ANNs are organized into layers:
 * **Input Layer:** Receives the raw data.
 * **(n) Hidden Layers:** (Optional) Intermediate layers where complex transformations occur. They learn to detect patterns and features in the data.
 * **Output Layer:** Produces the final result (prediction or classification).
-<p align="center">
-  <img width="400" height="250" src="https://bit.ly/nn-architecture">
-</p>
 
 ### Weights and Biases
 - For each input $(x_i)$, a weight $(w_i)$ is associated with it. Weights, multiplied with input units $(w_i \cdot x_i)$, determine the influence of one neuron's output on another.
 - A bias $(b_i)$ is added to help influence the end product, giving the equation as $(w_i \cdot x_i + b_i)$.
 - During training, the network adjusts these weights and biases to minimize errors and improve its predictions.
 
-<p align="center">
-  <img width="300" height="300" src="https://bit.ly/nn-WnB">
-</p>
-
 ### Activation Functions
 - An activation function is applied to the result to introduce non-linearity in the model, allowing ANNs to learn more complex relationships from the data.
 - The resulting equation: $y = f(g(x))$, determines whether the neuron will "fire" or not, i.e., if its output will be used as input for the next neuron.
 - Common activation functions include the sigmoid function, tanh (hyperbolic tangent), and ReLU (Rectified Linear Unit).
 
-<p align="center">
-  <img width="400" height="200" src="https://miro.medium.com/max/1280/1*xYCVODGB7RwJ9RynebB2qw.gif">
-</p>
-
 ### Forward and Backward Propagation
 - **Flow of Information:** All the above steps are part of Forward Propagation. It gives the output equation as $y = f\left(\sum_{i=1}^n w_i x_i + b_i\right)$
 - **Error Correction:** Backpropagation is the algorithm used to train ANNs by calculating the gradient of error at the output layer and then propagating this error backward through the network. This allows the network to adjust its weights and biases in the direction that reduces the error.
@@ -75,10 +63,6 @@ Neurons in ANNs are organized into layers:
   $
   where $E$ is the error, $\hat{y}_j$ is the predicted output, $\theta_j$ is the input to the activation function of the $j^{th}$ neuron, and $w_{ij}$ is the weight from neuron $i$ to neuron $j$.
 
-<p align="center">
-  <img width="400" height="200" src="https://bit.ly/nn-FnB">
-</p>
-
 
 ## Building From Scratch
 
@@ -167,6 +151,3 @@ To understand how well our model is learning, let's visualize the training loss
 model = NeuralNetwork(input_size, hidden_layers, hidden_neurons, output_size)
 model.train(X, y, 100)
 ```
-<p align="center">
-  <img width="500" height="300" src="https://bit.ly/nn-output">
-</p>