going to evaluate basically the derivative of g with respect to all the internal nodes like e, d, and c but also with respect to the inputs a and b. And then we can actually query this derivative of g with respect to a, for example that's a.grad, in this case it happens to be 138, and the derivative of g with respect to b which also happens to be here 645. And this derivative we'll see soon is very important information because it's telling us how a and b are affecting g through this mathematical expression. So in particular a.grad is 138, so if we slightly nudge a and make it slightly larger, 138 is telling us that g will grow and the slope of that growth is going to be 138 and the slope of growth of b is going to be 645. So that's going to tell us about how g will respond if a and b get tweaked a tiny amount in a positive direction. Now you might be confused about what this expression is that we built out here and this expression by the way is completely meaningless. I just made it up, I'm just flexing about the kinds of operations that are supported by micrograd. What we actually really care about are neural networks but it turns out that neural networks are just mathematical expressions just like this one but actually slightly a bit less crazy even. Neural networks are just a mathematical expression, they take the input data as an input and they take the weights of a neural network as an input and it's a mathematical expression and the output are your predictions of your neural net or the loss function, we'll see this in a bit. But basically neural networks just happen to be a certain class of mathematical expressions but back propagation is actually significantly more general. It doesn't actually care about neural networks at all, it only cares about arbitrary mathematical expressions and then we happen to use that machinery for training of neural networks. Now one more note I would like to make at this stage is
rtdocs_stable/api.python.langchain.com/en/stable/modules/indexes/document_loaders/examples/audio.html