Skrrubs
0
So I read somewhere that we as humans don't understand what exactly happens in a neural network, we just know that a neuron does something using the biases and the inputs given to it and leads us to a specific output.
My question here is, do we understand (mathematically speaking) how X input leads the computer to give Y input? If we don't, then why don't we understand it?
Let X be an input Matrix and Y be the associated output vector (our target). Let theta be the parameter of our model, representing the weights and the bias of each neuron. Mathematically, a neural network can be represented as a function f such as f(X, theta) = Y + epsilon. Epsilon is the error of the model. The goal is to find the value of theta that is minimizing epsilon. To do so, we just have to find the global minimum of the multivariate function epsilon(theta) = f(X, theta) - Y. This is an optimization problem that can be solved thanks to gradient descent. So yes, mathematically, we understand how X input leads the computer to give output Y: it is just a matter of finding the minimum of a function. Additionally, as the structure of a neural network is quite simple (linear layers + activation functions), we are able to calculate easily the derivatives of epsilon() and propagate them throw the network. However, it's not because we can explain mathematically a neural network that we can interpret it. It's very difficult to know the specific role played by each neuron in the prediction. In contrary, decision trees are much more interpretable, as we know which feature was used to make a split at each node of the tree.