8,462 research outputs found
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
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