ProNetInfoGAN

We begin by introducing what we call Probabilistic Network InfoGAN, which is simply a variant of InfoGAN that uses general probabilistic dependency networks to characterize its latent variables.

Generative models such as InfoGAN are one type within the broader class of latent variable models. For use within SynerGAN, we want to choose a model that is flexible enough to model complex dependency structures between the variables in latent space, and also provides a tractable way of optimization. As a first step toward Compositional SynerGAN, we outline here general approaches to extending InfoGAN type modelling in this way.

We find InfoGAN specifically interesting in our case, because of their definition and use of mutual information as a regularization term for inducing latent code. Additionally, the auxiliary Q network in InfoGAN provides a convenient way to perform inference on data examples.

We outline an approach of iterative refinement of structure within the latent code, and provide examples for different operations on the structure and how they could be used. We present one possible implementation of a Probabilistic Network InfoGAN of this nature.

Operations on the Probabilistic Network

Probabilistic networks represent a set of random variables and their conditional dependencies. Many types of such networks could be used in this context. We want to find a suitable structure that has some semantic meaning, and fits the knowledge representation in our symbolic reasoning engine so that we can influence and reason about it in meaningful ways.

Initialization

Initially we define a probabilistic network either randomly by sampling from a distribution of possible structures, as the result of some symbolic reasoning process, or by explicitly providing system some human crafted structures. We can use knowledge previously available in the symbolic system to devise a number of hypothesis for possible structures.

Iterative Refinement

As described above, after performing inference using our model on some data we record the resulting latent variable values as vectors. We then use the frequent pattern miner to extract dependencies inside these graphs that occur most often. The results can be used in conjunction with probabilistic networks that can then devise new conclusions based on these. This leads to several new hypothesis of structures that explain the data in better, more disentangled ways. By applying this iteration over and over we hope to eventually reach structures that model features in the data explicitly via the latent variables.

These stored inferences can also be used for long term memory: We can attach timestamps to past inferences in the symbolic knowledge store for calculating dependencies between patterns over time. This is particularily interesting, but not limited in the context of Compositional SynerGAN.

Adding/splitting of nodes

In the case of adding latent variables to an existing probabilsitc network and trained model, we can retrain the model from scratch to let it find completely new dependencies based on this new structure, or start the training process from the old parameters and explicitly provide labels during training, supervised, in order to enforce a certain semantic meaning for the new node.