# What is the essential difference between neural network and linear regression

Well, I know this question can be a little bit stupid. But, still... a neural network is a several linear transormations $L_1,\ldots, L_m$ that are sequentialy appilied to feature vector $X$. A compositon of linear transformations is a linear transformation. So after all we get $L X$ where $L$ is a composition of $L_1,\ldots, L_m$.

The question is: if eventually we have that neural network is just applying a liner transformation to a feature vector what is the essential difference betwen neural networks and linear regression

• stackoverflow.com/questions/9782071/… – SmallChess Feb 4 '17 at 13:22
• Most common activation functions for neural networks are sigmoid and hyperbolic tangent, which are not linear transformations. – Łukasz Grad Feb 4 '17 at 13:22
• The transformation may be linear but the output is almost always transformed by a non-linear function. – SmallChess Feb 4 '17 at 13:24
• See en.wikipedia.org/wiki/Universal_approximation_theorem which states that you need at minimum 1 hidden layer to approximate any continuous function, so perceptron is not enough – Łukasz Grad Feb 4 '17 at 13:31
• – Franck Dernoncourt Feb 4 '17 at 15:32

• @FranckDernoncourt, thank you. Yes, a network may have $m\geq 1$ layers, so it is of course possible that $m=1$. – Richard Hardy Feb 4 '17 at 16:18