The Riemannian Geometry of Deep Generative Models

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate the Riemannian geometry of these generated manifolds. First, we develop efficient algorithms for computing geodesic curves, which provide an intrinsic notion of distance between points on the manifold. Second, we develop an algorithm for parallel translation of a tangent vector along a path on the manifold. We show how parallel translation can be used to generate analogies, i.e., to transport a change in one data point into a semantically similar change of another data point. Our experiments on real image data show that the manifolds learned by deep generative models, while nonlinear, are surprisingly close to zero curvature. The practical implication is that linear paths in the latent space closely approximate geodesics on the generated manifold. However, further investigation into this phenomenon is warranted, to identify if there are other architectures or datasets where curvature plays a more prominent role. We believe that exploring the Riemannian geometry of deep generative models, using the tools developed in this paper, will be an important step in understanding the high-dimensional, nonlinear spaces these models learn.Comment: 9 page

An improved approach for automatic process plan generation of complex borings

The authors are grateful for funding provided to this project by the French Ministry of Industry, Dassault Aviation, Dassault Systemes, and F. Vernadat for his review and recommendations.The research concerns automated generation of process plans using knowledge formalization and capitalization. Tools allowing designers to deal with issues and specifications of the machining domain are taken into account. The main objective of the current work is to prevent designers from designing solutions that would be expensive and difficult to machine. Among all available solutions to achieve this goal, two are distinguished: the generative approach and the analogy approach. The generative approach is more adapted to generate the machining plans of parts composed of numerous boring operations in interaction. However, generative systems have two major problems: proposed solutions are often too numerous and are only geometrically but not technologically relevant. In order to overcome these drawbacks, two new concepts of feature and three control algorithms are developed. The paper presents the two new features: the Machining Enabled Geometrical Feature (MEGF) and the Machinable Features (MbF). This development is the result of the separation of the geometrical and the technological data contained in one machining feature. The second objective of the paper is to improve the current Process Ascending Generation (PAG) system with control algorithms in order to limit the combinatorial explosion and disable the generation of unusable or not machinable solutions

Kevoree Modeling Framework (KMF): Efficient modeling techniques for runtime use

The creation of Domain Specific Languages(DSL) counts as one of the main goals in the field of Model-Driven Software Engineering (MDSE). The main purpose of these DSLs is to facilitate the manipulation of domain specific concepts, by providing developers with specific tools for their domain of expertise. A natural approach to create DSLs is to reuse existing modeling standards and tools. In this area, the Eclipse Modeling Framework (EMF) has rapidly become the defacto standard in the MDSE for building Domain Specific Languages (DSL) and tools based on generative techniques. However, the use of EMF generated tools in domains like Internet of Things (IoT), Cloud Computing or Models@Runtime reaches several limitations. In this paper, we identify several properties the generated tools must comply with to be usable in other domains than desktop-based software systems. We then challenge EMF on these properties and describe our approach to overcome the limitations. Our approach, implemented in the Kevoree Modeling Framework (KMF), is finally evaluated according to the identified properties and compared to EMF.Comment: ISBN 978-2-87971-131-7; N° TR-SnT-2014-11 (2014