The Eman Network $($without output activation function and bias units$)$ can be defined as

$s(t)=Wx(t)+a(t-1)$

$a(t)=f(s(t))$

hat$(y)(t)=Va(t)$

with input vectors $x(t),$ hidden pre$-$activation vectors $s(t),$ hidden activation vectors $a(t),$ activation function $f(*),$ and parameter matrices $W,V.$ Which of the following statements are true?

a$.$ The hidden units of the Elman network are disconnected in the sense that they cannot exchange information from one time step to another.

b$.$ The recurrent weights are equal to the identity matrix.

c$.$ Elman propsed to train this netwerk locally in time, i$.$e$.,$ on each time step separately.

d$.$ The recurrent Jacobian of the hidden activations is $\frac{\text{d}\text{e}\text{l}\text{a}(t)}{\text{d}\text{e}\text{l}\text{a}(t-1)}=$diag$(f^{\text{'}}(s(t-1))).$

e$.$ The recurrent weights are variable.