Changing the weight parameter

[jw9357]

HI All

I have a question about
🗺 Chapter 1 – PyTorch Workflow

[5:49:31]
Video 44. Setting up a loss function and optimizer

In the Training loop, my starting random weight is 0.3367 and, after 1 epoch, the computer changes the weight to 0.3406

Can someone tell me if there is some mathematics behind this i.e. a formula/algorithm that the computer uses, that links 0.3367 to 0.3406, OR is the computer just picking a random value for weight (0.3406) close to the starting value of weight (0.3367) in the right direction (so increases the weight) in order to minimise the loss?

I think it's just a random number and there is no formula

Any advice would be greatly appreciated

Thanks

Jonathan

[ZephyrusBlaze]

Gradient descent is a fundamental optimization algorithm used in machine learning that involves calculus. The update rule for the weights is given by:

w_new = w_old - alpha * ∇L(w_old)

Where:

• w_new is the new weight vector,
• w_old is the old weight vector,
• alpha is the learning rate (a small positive scalar),
• ∇L(w_old) is the gradient of the loss function with respect to the weights.

The gradient ∇L(w_old) represents the direction of steepest ascent of the loss function at the point w_old. By subtracting this gradient scaled by the learning rate from the old weights, we move in the direction that minimizes the loss function. This process is repeated iteratively until convergence.

This GIF visually explains the convergence process in gradient descent. You can see how the algorithm iteratively adjusts the weights to minimize the loss function.