LSTM Calculations

$1$ point possible $($graded$)$

Let all the neural network's weight matrices, the hidden state, and the memory cell be a scalar $1.$ Let the new

$x-$value be $5.$ Calculate the value of the new hidden state. Round sigmoid to $1$ or $0,$ and round tanh to $-1$ or

$1.$

$f_t=$sigmoid$(W^{f,h}{h}_{t-1}+W^{f,x}{x}_t)$ forget gate

$i_t=$sigmoid$(W^{i,h}{h}_{t-1}+W^{i,x}{x}_t)$ input gate

$o_t=$sigmoid$(W^{o,h}{h}_{t-1}+W^{o,x}{x}_t)$ output gate

$c_t=f_{t}o.c_{t-1}+i_{t}o.tanh(W^{c,h}{h}_{t-1}+W^{c,x}{x}_t)$ memory

$h_t=o_{t}o.tanh(c_t)$ visible state

$-1$

$1$

$0$

$5$