Where ordinary GSN frameworks are designed to be unsupervised, maximizing $p(\bold x)$ for observed data $\bold x$, **discriminant GSNs** are designed to be *supervised*, maximizing $p(\bold y | \bold x)$.

This means that the Markov chain in this architecture is over the *output* variable, and the input only acts to condition the chain, in contrast to ordinary GSNs. 

University of Connecticut

A **Generative Stochastic Network**, or **GSN**, is a generative model with latent or hidden variables $\bold h$ in the Markov chain, in addition to the ordinary visible random variables $\bold x$.

Generative Stochastic Networks (GSNs)

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

Deep Learning

The two parameters for a generative stochastic network are:

   1. $p(\bold x^{(k)} | \bold h ^ {(k)})$ defines how to generate the next visible variable given the current latent state. Similar to reconstruction in RBMs, DBNs, and DBMs.

2. $p(\bold h^{(k)} | \bold h ^{(k-1)}, \bold x ^{(k-1)})$ defines how to update the current latent variable state given the previous latent and visible varaible states.

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