We prove super-linear lower bounds for the number of edges
in constant depth circuits with $n$ inputs and up to $n$ outputs.
Our lower bounds are proved for all types of constant depth
circuits, e.g., constant depth arithmetic circuits, constant depth
threshold circuits and constant depth Boolean circuits with
arbitrary gates. The bounds apply for several explicit functions,
and, most importantly, for matrix product.

We prove super-linear lower bounds for the number of edges
in constant depth circuits with $n$ inputs and up to $n$ outputs.
Our lower bounds are proved for all types of constant depth
circuits, e.g., constant depth arithmetic circuits, constant depth
threshold circuits and constant depth Boolean circuits with
arbitrary gates. The bounds apply for several explicit functions,
and, most importantly, for matrix product.