Andrey A. Bagrov

Anna Kravchenko, Andrey A. Bagrov, Mikhail I. Katsnelson et al.

While intuitive for humans, the concept of visual complexity is hard to define and quantify formally. We suggest adopting the multi-scale structural complexity (MSSC) measure, an approach that defines structural complexity of an object as the amount of dissimilarities between distinct scales in its hierarchical organization. In this work, we apply MSSC to the case of visual stimuli, using an open dataset of images with subjective complexity scores obtained from human participants (SAVOIAS). We demonstrate that MSSC correlates with subjective complexity on par with other computational complexity measures, while being more intuitive by definition, consistent across categories of images, and easier to compute. We discuss objective and subjective elements inherently present in human perception of complexity and the domains where the two are more likely to diverge. We show how the multi-scale nature of MSSC allows further investigation of complexity as it is perceived by humans.

I. Schurov, D. Alforov, M. Katsnelson et al.

Success of machine learning (ML) in the modern world is largely determined by abundance of data. However at many industrial and scientific problems, amount of data is limited. Application of ML methods to data-scarce scientific problems can be made more effective via several routes, one of them is equivariant neural networks possessing knowledge of symmetries. Here we suggest that combination of symmetry-aware invariant architectures and stacks of dilated convolutions is a very effective and easy to implement receipt allowing sizable improvements in accuracy over standard approaches. We apply it to representative physical problems from different realms: prediction of bandgaps of photonic crystals, and network approximations of magnetic ground states. The suggested invariant multiscale architectures increase expressibility of networks, which allow them to perform better in all considered cases.