Machine learning spatial geometry from entanglement features

On Machine Learning applications with algebraic geometry

In this article, we briefly describe various tools and approaches that algebraic geometry has to offer to straighten bent objects. throughout this article we will consider a specific example of a bent or curved piece of paper which in our case acts very much like an elastica curve. We generalize this model to various shapes of paper which are stretched and bent and then finally implement it on ...

Riemannian Geometry and Statistical Machine Learning

Statistical machine learning algorithms deal with the problem of selecting an appropriate statistical model from a model space Θ based on a training set {xi}i=1 ⊂ X or {(xi, yi)}i=1 ⊂ X × Y. In doing so they either implicitly or explicitly make assumptions on the geometries of the model space Θ and the data space X . Such assumptions are crucial to the success of the algorithms as different geo...

Constructing Relational Features from Background Knowledge for Inductive Machine Learning

Most existing inductive learning systems form concept descriptions in propositional languages from vectors of basic features. However, many concepts are characterized by the relationships of individual examples to general domain knowledge. We describe a system that constructs relational terms e ciently to augment the description language of standard inductive systems. In our approach, examples ...

Learning Line Features in 3D Geometry

Feature detection in geometric datasets is a fundamental tool for solving shape matching problems such as partial symmetry detection. Traditional techniques usually employ a priori models such as crease lines that are unspecific to the actual application. Our paper examines the idea of learning geometric features. We introduce a formal model for a class of linear feature constellations based on...

Quantum Entanglement and Geometry