Where ordinary Generative Stochastic Network (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

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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 of a Generative Stochastic Network (GSN) are:
1. $$p(\bold x^{(k)} | \bold h^{(k)})$$, which defines how to generate the next visible variable given the current latent state. This process is similar to reconstruction in Restricted Boltzmann Machines (RBMs), Deep Belief Networks (DBNs), and Deep Boltzmann Machines (DBMs).
2. $$p(\bold h^{(k)} | \bold h^{(k-1)}, \bold x^{(k-1)})$$, which defines how to update the current latent variable state given the previous latent and visible variable states.

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