[SOLVED] LING570 Hw9: Math basics

Q1 (8 points): Logistic function: (see https://en.wikipedia.org/wiki/Logistic function) 1a (3 pts): What’s a logistic function? Write down the formula. 1b (2 pts): What is the standard logistic function? Write down the formula. 1c (3 pts): What is the derivative of the standard logistic function f(x)? Write down the formula. Q2 (8 points): Sigmoid function: See https://en.wikipedia.org/wiki/Sigmoid function 1 2a (4 pts): What is a sigmoid function? Write down the definition. 2b (4 pts): What is the relation between sigmoid function and logistic function? Q3 (8 points): Tanh function: (see https://en.wikipedia.org/wiki/Hyperbolic function and https://en.wikipedia.org/wiki/Sigmoid function) 3a (4 pts): Write down the formula for the tanh function. 3b (4 pts): What is the relation between sigmoid function and tanh function? Q4 (8 points): The softmax function: 4a (4 pts): What is the softmax function? Write down the formula. See https://en.wikipedia.org/wiki/Softmax function 4b (4 pts): If a vector x is [1, 2, 3], what is the value of softmax(x)? Q5 (18 points): Matrix: see Sect 1-3 of https://en.wikipedia.org/wiki/Matrix (mathematics) 5a (12 points): Let A =   1 2 3 4 5 6 7 8 9   and B =   2 1 3   what is A × B? 2 what is B × A? what is the transpose of A? what is the tranpose of B? what are the dimensions of B? what are the dimensions of the transpose of B? 5b (6 points): Let A =  1 2 3 4 and B =  2 0 1 2 . What is A × B? what is B × A? Is matrix multiplication communtative? Submission: submit only one file named hw.pdf or hw.jpeg to Canvas. 3