# descramble.m

Generates a weight matrix descrambler for a particular layer in a neural network using Tikhonov smoothness criterion. The particulars are described in https://arxiv.org/abs/1912.01498

## Syntax

    P=descramble(S,n_iter,guess)


## Arguments

   S       - a matrix containing, in its columns, the outputs
of the preceding layers of the neural network for
a (preferably large) number of reasonable inputs

n_iter  - maximum number of Newton-Raphson interations, 400
is generally sufficient

guess   - [optional] the initial guess for the descrambling
transform generator (lower triangle is used), a
reasonable choice is a zero matrix (default)


## Outputs

   P       - descrambling matrix. In the case when the network
is wiretapped before the activation function, i.e.

S = Wf(W...f(Wf(WX)))

matrix P descrambles the output dimension of the
left-most W. In the case when the network is wire
tapped after the activation function, i.e.

S = f(Wf(W...f(Wf(WX))))

matrix inv(P) descrambles the input dimension of
the weight matrix of the subsequent layer.


## Examples

An example of this function being applied to DEERNet is published in https://arxiv.org/abs/1912.01498