ANN Series - 10 - Backpropagation of Errors

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Watch the video to understand the forward pass in an ANN.



Backpropagation, short for "backward propagation of errors," is a fundamental algorithm used for training artificial neural networks. It efficiently computes the gradient of the loss function with respect to the weights of the network, which is essential for adjusting the weights and minimizing the loss through gradient descent or other optimization techniques. The process involves two main phases: a forward pass and a backward pass.

  Forward Pass

 1. Input Layer: 

The input features are fed into the network.

2. Hidden Layers: 

Each neuron in these layers computes a weighted sum of its inputs (from the previous layer or the input layer) plus a bias term. This sum is then passed through an activation function to produce the neuron's output. This process repeats layer by layer until the output layer is reached.

3. Output Layer: 

The final output of the network is computed, which is then used to calculate the loss (or error) by comparing the network's prediction against the true target values using a loss function.

 Backward Pass (Backpropagation)

1. Compute the Gradient of the Loss Function: 

The gradient of the loss function with respect to the output of the neural network is calculated. This indicates how changes in the output layer's activations can decrease the loss.

2. Propagate the Error Backwards: 

The gradient of the loss is propagated back through the network, layer by layer, using the chain rule of calculus. At each layer, the process involves:

   - Computing the gradient of the loss with respect to the weights and biases, based on the gradient of the loss with respect to the output of the neurons in that layer.

   - Computing the gradient of the loss with respect to the output of the previous layer's neurons, to continue propagating the error back through the network.

3. Update Weights and Biases: 

Once the gradients are computed, the weights and biases of the network are updated, typically using a gradient descent step.

Let us see how to calculate the error using backpropagation.

Python Code:

Check the below Pytorch code to check the working of the backpropagation algorithm.

ml-course/Pytorch_hidden nodes.ipynb at main · lovelynrose/ml-course (github.com) 

Key Concepts

 - Chain Rule: 

The core mathematical principle behind backpropagation, allowing the gradient of the loss to be computed with respect to any weight or bias in the network, regardless of its position.

- Learning Rate : 

Determines the size of the steps taken during the gradient descent update of the weights and biases.

- Activation Functions: 

Non-linear functions (e.g., sigmoid, ReLU) applied at each neuron, enabling the network to capture complex patterns and relationships in the data.

 Backpropagation is an efficient and powerful mechanism that enables neural networks to learn from data by iteratively reducing the error between the predicted and actual outputs, thereby improving the network's performance on a given task.



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