arXiv subjects

Galin Georgiev

Publications and source records attributed to Galin Georgiev.

6 recordsLinked to original sources

arXiv2019

Generating new pictures in complex datasets with a simple neural network

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.

cs.CV↗

arXiv2018

Linear Algebra and Duality of Neural Networks

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.

cs.CV↗

arXiv2016

Towards universal neural nets: Gibbs machines and ACE

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.

cs.CV↗

arXiv2016

Symmetries and control in generative neural nets

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.

cs.CV↗

arXiv1995

Combinatorial constructions of modules for infinite-dimensional Lie algebras, II. Parafermionic space

The standard modules for an affine Lie algebra $\ga$ have natural subquotients called parafermionic spaces -- the underlying spaces for the so-called parafermionic conformal field theories associated with $\ga.$ We study the case $\ga = \widehat{sl}(n+1,\C)$ for any positive integral level $k \geq 2.$ Generalizing the $\cal Z$-algebra approach of Lepowsky, Wilson and Primc, we construct a combinatorial basis for the parafermionic spaces in terms of colored partitions. The parts of these partitions represent ''Fourier coefficients'' of generalized vertex operators (parafermionic currents) and can be interpreted as statistically interacting quasi-particles of color $i,\;1\leq i \leq n,$ and charge $s,\; 1\leq s \leq k-1.$ From a combinatorial point of view, these bases are essentially identical with the bases for level $k-1$ principal subspaces constructed by the author in [GeI]. In the particular case of the vacuum module, the character (string function) associated with our basis is the formula of Kuniba, Nakanishi and Suzuki [KNS] conjectured in a Bethe Ansatz layout. New combinatorial characters are established for the whole standard vacuum $\ga$-modules.

q-alg↗

arXiv1995

Combinatorial constructions of modules for infinite-dimensional Lie algebras, I. Principal subspace

This is the first of a series of papers studying combinatorial (with no ``subtractions'') bases and characters of standard modules for affine Lie algebras, as well as various subspaces and ``coset spaces'' of these modules. In part I we consider certain standard modules for the affine Lie algebra $\ga,\;\g := sl(n+1,\C),\;n\geq 1,$ at any positive integral level $k$ and construct bases for their principal subspaces (introduced and studied recently by Feigin and Stoyanovsky [FS]). The bases are given in terms of partitions: a color $i,\;1\leq i \leq n,$ and a charge $s,\; 1\leq s \leq k,$ are assigned to each part of a partition, so that the parts of the same color and charge comply with certain difference conditions. The parts represent ``Fourier coefficients'' of vertex operators and can be interpreted as ``quasi-particles'' enjoying (two-particle) statistical interaction related to the Cartan matrix of $\g.$ In the particular case of vacuum modules, the character formula associated with our basis is the one announced in [FS]. New combinatorial characters are proposed for the whole standard vacuum $\ga$-modules at level one.

hep-th↗