Andrey Voynov

The literature has proposed several methods to finetune pretrained GANs on new datasets, which typically results in higher performance compared to training from scratch, especially in the limited-data regime. However, despite the apparent empirical benefits of GAN pretraining, its inner mechanisms were not analyzed in-depth, and understanding of its role is not entirely clear. Moreover, the essential practical details, e.g., selecting a proper pretrained GAN checkpoint, currently do not have rigorous grounding and are typically determined by trial and error. This work aims to dissect the process of GAN finetuning. First, we show that initializing the GAN training process by a pretrained checkpoint primarily affects the model's coverage rather than the fidelity of individual samples. Second, we explicitly describe how pretrained generators and discriminators contribute to the finetuning process and explain the previous evidence on the importance of pretraining both of them. Finally, as an immediate practical benefit of our analysis, we describe a simple recipe to choose an appropriate GAN checkpoint that is the most suitable for finetuning to a particular target task. Importantly, for most of the target tasks, Imagenet-pretrained GAN, despite having poor visual quality, appears to be an excellent starting point for finetuning, resembling the typical pretraining scenario of discriminative computer vision models.

Multiplicative matrix semigroups with constant spectral radius (c.s.r.) are studied and applied to several problems of algebra, combinatorics, functional equations, and dynamical systems. We show that all such semigroups are characterized by means of irreducible ones. Each irreducible c.s.r. semigroup defines walks on Euclidean sphere, all its nonsingular elements are similar (in the same basis) to orthogonal. We classify all nonnegative c.s.r. semigroups and arbitrary low-dimensional semigroups. For higher dimensions, we describe five classes and leave an open problem on completeness of that list. The problem of algorithmic recognition of c.s.r. property is proved to be polynomially solvable for irreducible semigroups and undecidable for reducible ones.

We disprove a well-known conjecture of D. Vallete (1978), which states that every d-dimensional self-affine convex body is a direct product of a polytope with a convex body of lower dimension. It is shown that there are counterexamples for dimension d = 4. Additional assumptions under which the conjecture is true are discussed.

We give a complete characterization of finite-dimensional compact sets with the following property: all of their images under affine operators are symmetric (that is, have symmetry planes of certain d