Weights and Bias in Neural Networks

Neural networks learn from data and identify complex patterns that makes them important in areas such as image recognition, natural language processing and autonomous systems. Neural networks has two fundamental components: weights and biases that help in how neural networks learn and make predictions.

1. Weights

Weights are numerical values assigned to the connections between neurons. Weights determine how much influence an input has on a neuron's output.

• Purpose: During forward propagation, inputs are multiplied by their respective weights before being passed through an activation function. This influences how strongly each input contributes to the final output.
• Learning Mechanism: During training, weights are updated iteratively through optimization algorithms like gradient descent to minimize the difference between predicted and actual outcomes.
• Generalization: Properly tuned weights allow the network to generalize beyond training data making accurate predictions on new, unseen inputs.

2. Biases

A bias is a constant added to a neuron's weighted input. It is not linked to any specific input but shifts the activation function to fit the data. Biases enhance the flexibility and learning capacity of neural networks. While weights control the influence of inputs, biases act as offsets that allow neurons to activate under a wider range of conditions.

• Purpose: Biases allow neurons to learn even when the weighted sum of inputs is insufficient, providing a mechanism to recognize patterns that don't pass through the origin.
• Functionality: If biases are not present, neurons can only activate when the input reaches a specific threshold. Activation becomes more flexible when biases are present.
• Training: Both weights, biases are updated during backpropagation to minimize prediction error. They help fine-tune neuron outputs, contributing to more accurate model performance.

Learning Process: Forward and Back Propagation

Forward Propagation

Forward propagation is the initial phase of processing input data through the neural network to produce an output or prediction. Here's how it works:

1. Input Layer: The input data is fed into the neural network's input layer.
2. Weighted Sum: Each neuron calculates a weighted sum of the inputs it receives, where the weights are the adjustable parameters.
3. Adding Biases: To this weighted sum, the bias associated with each neuron is added. This introduces a threshold for activation.
4. Activation Function: The result of the weighted sum plus bias is passed through an activation function. This function determines whether the neuron should activate or remain as is based on the calculated value.
5. Propagation: The output of one layer becomes the input for the next layer and the process repeats until the final layer produces the network's prediction.

Backpropagation

Once the network has made a prediction, it's essential to evaluate how accurate that prediction is and make adjustments to improve future predictions. This is where backpropagation comes into play:

1. Error Calculation: The prediction made by the network is compared to the actual target. The loss or cost, measures the difference between prediction and reality.
2. Gradient Descent: Backward propagation involves minimizing this error using Gradient Descent. The network calculates the gradient of the error with respect to the weights and biases. This gradient points in the direction of the steepest decrease in error.
3. Weight and Bias Updates: The network uses the gradient information to update the weights and biases in the network. The goal is to find the values that minimize the error.
4. Iterative Process: This process of forward and backward propagation is repeated multiple times on batches of training data. With each iteration, the network's weights and biases get closer to values that minimize the error.

Real-World Applications

1. Image Recognition: Neural networks are efficient at tasks like object and handwriting recognition. For example, to detect cats in images :

• Weights determine which pixels (those showing ears or whiskers) have more influence on the output.
• Biases allow neurons to activate despite slight variations in lighting or position, which improves generalization.

During training, the network adjusts these parameters to recognize patterns, enabling it to classify unseen images accurately.

For more details regarding it you can refer to: Cat & Dog Classification using Convolutional Neural Network in Python

2. Natural Language Processing (NLP): In sentiment analysis or language translation:

• Weights assign importance to words within context.
• Biases help the network handle variation and tone, enhancing its adaptability.

Refining these parameters through training allows NLP models to interpret and generate human language effectively.

For more details regarding it you can refer to: Flipkart Reviews Sentiment Analysis using Python

Weights control the influence of inputs between neurons, while biases allow the model to adjust and improve flexibility. Together weights and biases, enable neural networks to capture patterns through forward and backward propagation.