Simplified Explanation of Gradients and Neural Networks

1. Gradient
   • Definition: A measure of how much a function changes if you change the input a little bit. Think of this like trails when you’re hiking; the gradient points to the steepest slope, and you want to go in the opposite direction to decrease the loss.
2. In Neural Networks
   • Context: The function we’re interested in is the loss function, which measures how well the network’s predictions match the targets. The inputs to this function are the weights in the network.
3. Loss Function
   • Purpose: Tells us how bad the model’s predictions are. We want to minimize the loss to improve the model.
4. Parameters (Weights)
   • Definition: These are the values in the network that are adjusted during training to make better predictions.
5. Partial Derivatives
   • Definition: Measure how much the loss changes if you change one parameter slightly, keeping all other parameters constant. This helps to understand the impact of each parameter on the overall loss.
6. Vector of Partial Derivatives
   • Definition: A vector is just a list of numbers. In this case, it’s a list of the partial derivatives with respect to each parameter.

Putting It All Together

As we train neural networks, we want to update the parameters (weights) to make the model better and reduce the loss. This is achieved by calculating how each weight affects the loss, which is done through partial derivatives. The result of these calculations (a list of partial derivatives) is what we call the gradient. The process of calculating the gradients throughout the neural network is called backpropagation.