A lot of times I've read that with a Single Layer Perceptron (SLP), you can only learn linear functions. But what if we use a generalized linear model?
Imagine we only have one input feature $x_1$. The function the SLP would learn would be of the shape: $$ y = w_0 + w_1*x_1 $$ Here the SLP has 2 input neurons and one output neuron (we do regression). But what if we create a new feature $x_2$ which we generate from $x_1^2$. We simply add another input neuron to the SLP. The function the SLP would now learn looks like: $$ y = w_0 + w_1*x_1 + w_2*x_1^2 $$ This is a quadratic function and not a linear function anymore?
Can anyone explain this to me?
Can we say that with a SLP we can learn non-linear function if we define the base-functions (e.g. $x_1^2$) ourselves. In contrast, a MLP would learn these on its own? Thanks.