Searching for Hyperbolicity

This is an expository paper, based on by a talk given at the AWM Research Symposium 2017. It is intended as a gentle introduction to geometric group theory with a focus on the notion of hyperbolicity, a theme that has inspired the field from its inception to current-day research

Topological regluing of rational functions

Regluing is a topological operation that helps to construct topological models for rational functions on the boundaries of certain hyperbolic components. It also has a holomorphic interpretation, with the flavor of infinite dimensional Thurston--Teichm\"uller theory. We will discuss a topological theory of regluing, and trace a direction in which a holomorphic theory can develop.Comment: 38 page

Domain Generalization by Solving Jigsaw Puzzles

Human adaptability relies crucially on the ability to learn and merge knowledge both from supervised and unsupervised learning: the parents point out few important concepts, but then the children fill in the gaps on their own. This is particularly effective, because supervised learning can never be exhaustive and thus learning autonomously allows to discover invariances and regularities that help to generalize. In this paper we propose to apply a similar approach to the task of object recognition across domains: our model learns the semantic labels in a supervised fashion, and broadens its understanding of the data by learning from self-supervised signals how to solve a jigsaw puzzle on the same images. This secondary task helps the network to learn the concepts of spatial correlation while acting as a regularizer for the classification task. Multiple experiments on the PACS, VLCS, Office-Home and digits datasets confirm our intuition and show that this simple method outperforms previous domain generalization and adaptation solutions. An ablation study further illustrates the inner workings of our approach.Comment: Accepted at CVPR 2019 (oral

Few-Shot Bayesian Imitation Learning with Logical Program Policies

Humans can learn many novel tasks from a very small number (1--5) of demonstrations, in stark contrast to the data requirements of nearly tabula rasa deep learning methods. We propose an expressive class of policies, a strong but general prior, and a learning algorithm that, together, can learn interesting policies from very few examples. We represent policies as logical combinations of programs drawn from a domain-specific language (DSL), define a prior over policies with a probabilistic grammar, and derive an approximate Bayesian inference algorithm to learn policies from demonstrations. In experiments, we study five strategy games played on a 2D grid with one shared DSL. After a few demonstrations of each game, the inferred policies generalize to new game instances that differ substantially from the demonstrations. Our policy learning is 20--1,000x more data efficient than convolutional and fully convolutional policy learning and many orders of magnitude more computationally efficient than vanilla program induction. We argue that the proposed method is an apt choice for tasks that have scarce training data and feature significant, structured variation between task instances.Comment: AAAI 202