Expressiveness of perceptrons Consider a perceptron with g=step function(Rosenblatt,1957,1960) Can represent AND,OR,NOT,majority,etc.,but not XOR Represents a linear separator in input space: ∑，Wz)>0orW·x>0 0( 00 0 0 (a)xi and x2 (b)x1 orx2 (c)x1 xor x2 Minsky Papert (1969)pricked the neural network balloon Chapter 20,Section 5 10 Expressiveness of perceptrons Consider a perceptron with g = step function (Rosenblatt, 1957, 1960) Can represent AND, OR, NOT, majority, etc., but not XOR Represents a linear separator in input space: ΣjWjxj > 0 or W · x > 0 (a) x1 and x2 1 0 0 1 x1 x2 (b) x1 or x2 0 1 1 0 x1 x2 (c) x1 xor x2 ? 0 1 1 0 x1 x2 Minsky & Papert (1969) pricked the neural network balloon Chapter 20, Section 5 10