Earlier quoted context omitted.
> That's the only non-linearity I'm aware of. "only" is doing a lot work here because that non-linearity is enough to vastly expand the landscape of functions that an NN can approximate. If the NN was linear, you could greatly simplify the computational needs of the whole thing (as was implied by another commenter above) but you'd also not get a GPT out of it.
All the trainable parameters are just slopes of lines tho. Training NNs doesn't involve adjusting any inputs to non-linear functions. The tanh smashing function just makes sure nothing can blow up into large numbers and all outputs are in a range of less than 1. There's no "magic" or "knowledge" in the tanh smashing. All the magic is 100% in the weights. They're all linear. The amazing thing is that all weights are l…
That's not the main point even though it probably helps. As OkayPhysicist said above, without a nonlinearity, you could collapse all the weight matrices into a single matrix. If you have 2 layers (same size, for simplicity) described by weight matrices A and B, you could multiply them and get C, which you could use for inference.
Now, you can do this same trick not only with 2 layers but 100 million, all collapsing into a single matrix after multiplication. If the nonlinearities weren't there, the effective information content of the whole NN would collapse into that of a single-layer NN.