To optimize the loss means to adjust the model’s parameters (weights and biases) to minimize the overall error in predictions, which the loss function quantifies. This process is the core of training a neural network, and it involves finding the combination of parameters that reduces the loss as much as possible, ideally to a minimum.
Here’s a breakdown of how this process works:
1. Loss Function: Measuring Error
First, we define a loss function, which is a mathematical formula that measures the difference between the model’s predictions and the actual target values. The choice of loss function depends on the problem:
• Mean Squared Error (MSE) for regression tasks
• Cross-Entropy Loss for classification tasks
The loss function calculates a single value (the “loss”) that represents the model’s performance on a batch or an entire dataset.
2. Gradient Descent: The Optimization Process
The process of optimizing the loss function involves finding the minimum value of the loss. Gradient descent is a commonly used optimization algorithm for this purpose. Here’s how it works:
• Compute Gradients: During backpropagation, the model computes the gradient of the loss with respect to each parameter (weight and bias). This gradient tells us the direction and rate at which the loss would change if we adjusted each parameter.
• Update Parameters: Using the gradients, we adjust each parameter in the direction that reduces the loss. Specifically, each parameter is updated by subtracting a fraction of its gradient:
Here:
• is the learning rate, which controls the step size for each update.
• is the gradient of the loss with respect to .
3. Iteratively Reducing Loss
By repeating the steps above—calculating the loss, computing gradients, and updating weights—over many training iterations (epochs), the model gradually reduces the loss, or “optimizes” it. Ideally, the model will converge to a point where the loss is minimized, and the parameters are close to their optimal values for making accurate predictions.
Why Optimizing the Loss Matters
Minimizing the loss function is how the model learns patterns in the data and improves its predictive accuracy. The lower the loss, the closer the model’s predictions are to the actual values, meaning it’s performing better.