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I am dealing with restricted boltzmann machines to model distributuins in my final degree project and some question has come to my mind.

A restricted boltzmann machine with v visible binary neurons and h hidden neurons models a distribution in the following manner:

## f_i= e^{ \sum_k b[k] \sigma^i[k] + \sum_s \log(c[ s ] + e^{\sum_k w[ s ][ k ] b[ k ] })} ##

## Z = \sum_i f_i ##

## p_i = f_i/Z ##

Where b[ k ] and c[ s ] are, respectively, the k-th and the s-th bias of, again respectively, the visible and hidden layer.

w[ s ][k] is the component s, k of the weight matrix of the network.

"i" here refers to a certain binary vector with components ##\sigma^i[k]##.

My question is:

Given a certain restricted boltzmann machine (i.e. a certain set of biases and weights) that models a certain distribution ##p_i##, is it possible to find another configuration (i.e. a different set of parameters and weights) such that it gives the same distribution?

Thanks in advance.

A restricted boltzmann machine with v visible binary neurons and h hidden neurons models a distribution in the following manner:

## f_i= e^{ \sum_k b[k] \sigma^i[k] + \sum_s \log(c[ s ] + e^{\sum_k w[ s ][ k ] b[ k ] })} ##

## Z = \sum_i f_i ##

## p_i = f_i/Z ##

Where b[ k ] and c[ s ] are, respectively, the k-th and the s-th bias of, again respectively, the visible and hidden layer.

w[ s ][k] is the component s, k of the weight matrix of the network.

"i" here refers to a certain binary vector with components ##\sigma^i[k]##.

My question is:

Given a certain restricted boltzmann machine (i.e. a certain set of biases and weights) that models a certain distribution ##p_i##, is it possible to find another configuration (i.e. a different set of parameters and weights) such that it gives the same distribution?

Thanks in advance.

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