Galin Georgiev

Galin Georgiev

We introduce a version of a variational auto-encoder (VAE), which can generate good perturbations of images, when trained on a complex dataset (in our experiments, CIFAR-10). The net is using only two latent generative dimensions per class, with uni-modal probability density. The price one has to pay for good generation is that not all training images are well reconstructed. An additional classifier is required to determine which training image is well reconstructed and generally the weights of training images. Only training images which are well reconstructed, can be perturbed. For good perturbations, we use the tentative empirical drifts of well reconstructed images. The construct is not predictive in the usual statistical sense.

Galin Georgiev

Bases, mappings, projections and metrics, natural for Neural network training, are introduced. Graph-theoretical interpretation is offered. Non-Gaussianity naturally emerges, even in relatively simple datasets. Training statistics, hierarchies and energies are analyzed, from physics point of view. Duality between observables (for example, pixels) and observations is established. Relationship between exact and numerical solutions is studied. Physics and financial mathematics interpretations of a key problem are offered. Examples support all new concepts.

Galin Georgiev

We study generative nets which can control and modify observations, after being trained on real-life datasets. In order to zoom-in on an object, some spatial, color and other attributes are learned by classifiers in specialized attention nets. In field-theoretical terms, these learned symmetry statistics form the gauge group of the data set. Plugging them in the generative layers of auto-classifiers-encoders (ACE) appears to be the most direct way to simultaneously: i) generate new observations with arbitrary attributes, from a given class, ii) describe the low-dimensional manifold encoding the "essence" of the data, after superfluous attributes are factored out, and iii) organically control, i.e., move or modify objects within given observations. We demonstrate the sharp improvement of the generative qualities of shallow ACE, with added spatial and color symmetry statistics, on the distorted MNIST and CIFAR10 datasets.

Galin Georgiev

We study from a physics viewpoint a class of generative neural nets, Gibbs machines, designed for gradual learning. While including variational auto-encoders, they offer a broader universal platform for incrementally adding newly learned features, including physical symmetries. Their direct connection to statistical physics and information geometry is established. A variational Pythagorean theorem justifies invoking the exponential/Gibbs class of probabilities for creating brand new objects. Combining these nets with classifiers, gives rise to a brand of universal generative neural nets - stochastic auto-classifier-encoders (ACE). ACE have state-of-the-art performance in their class, both for classification and density estimation for the MNIST data set.