How random sign matrix works in compression algorithm

Question

The video introduce a compression algorithm in 6:15s,

The compression algorithm stated as below

For a weight matrix A,

1. generate $k$ random sign matrices $M_1,...,M_k$

2. return $\hat{A}=\frac{1}{k}\sum^k_{t=1}<A, M_t> M_t$

And the result $\hat{A}$ reduced number of parameters to $k$

I fail to understand how the compression is done here. Any suggestion?