[uh_uh]

> 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.

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.

[quantadev]

You can explain the "effect" of tanh at any level of abstraction you like, up to including describing things that happen in Semantic Space itself, but my description of what tanh is doing is 100% accurate in the context I used it. All it's doing is squashing a number down to below one. My understanding of how the Perceptron works is fully correct, and isn't missing any details. I've implemented many of them.

[beckhamc]

Your description of tanh isn't even correct, it squashes a real number to `(-1, 1)`, not "less than one".

You're curious about whether there is gain in parameterising activation functions and learning them instead, or rather, why it's not used much in practice. That's an interesting and curious academic question, and it seems like you're already experimenting with trying out your own kinds of activation functions. However, people in this thread (including myself) wanted to clarify some perceived misunderstandings you had about nonlinearities and "why" they are used in DNNs. Or how "squashing functions" is a misnomer because `g(x) = x/1000` doesn't introduce any nonlinearities. Yet you continue to fixate and double down on your knowledge of "what" a tanh is, and even that is incorrect.

[quantadev]

When discussing `tanh squashing` among other AI experts it's generally assumed that even the most pedantic and uncharitable parsing of words won't be able to misinterpret "smashing to less than one" as an incorrect sentence fragment, because the "one", in that context, obviously refers to distance from zero.