From Perception to Programs: Regularize, Overparameterize, and Amortize

Toward combining inductive reasoning with perception abilities, we develop techniques for neurosymbolic program synthesis where perceptual input is first parsed by neural nets into a low-dimensional interpretable representation, which is then processed by a synthesized program. We explore several techniques for relaxing the problem and jointly learning all modules end-to-end with gradient descent: multitask learning; amortized inference; overparameterization; and a differentiable strategy for penalizing lengthy programs. Collectedly this toolbox improves the stability of gradient-guided program search, and suggests ways of learning both how to perceive input as discrete abstractions, and how to symbolically process those abstractions as programs.Comment: ICML 202

Duality Symmetries and Noncommutative Geometry of String Spacetime

We examine the structure of spacetime symmetries of toroidally compactified string theory within the framework of noncommutative geometry. Following a proposal of Frohlich and Gawedzki, we describe the noncommutative string spacetime using a detailed algebraic construction of the vertex operator algebra. We show that the spacetime duality and discrete worldsheet symmetries of the string theory are a consequence of the existence of two independent Dirac operators, arising from the chiral structure of the conformal field theory. We demonstrate that these Dirac operators are also responsible for the emergence of ordinary classical spacetime as a low-energy limit of the string spacetime, and from this we establish a relationship between T-duality and changes of spin structure of the target space manifold. We study the automorphism group of the vertex operator algebra and show that spacetime duality is naturally a gauge symmetry in this formalism. We show that classical general covariance also becomes a gauge symmetry of the string spacetime. We explore some larger symmetries of the algebra in the context of a universal gauge group for string theory, and connect these symmetry groups with some of the algebraic structures which arise in the mathematical theory of vertex operator algebras, such as the Monster group. We also briefly describe how the classical topology of spacetime is modified by the string theory, and calculate the cohomology groups of the noncommutative spacetime. A self-contained, pedagogical introduction to the techniques of noncommmutative geometry is also included.Comment: 70 pages, Latex, No Figures. Typos and references corrected. Version to appear in Communications in Mathematical Physic

Massive quiver matrix models for massive charged particles in AdS

We present a new class of ${\cal N}=4$ supersymmetric quiver matrix models and argue that it describes the stringy low-energy dynamics of internally wrapped D-branes in four-dimensional anti-de Sitter (AdS) flux compactifications. The Lagrangians of these models differ from previously studied quiver matrix models by the presence of mass terms, associated with the AdS gravitational potential, as well as additional terms dictated by supersymmetry. These give rise to dynamical phenomena typically associated with the presence of fluxes, such as fuzzy membranes, internal cyclotron motion and the appearance of confining strings. We also show how these models can be obtained by dimensional reduction of four-dimensional supersymmetric quiver gauge theories on a three-sphere.Comment: 43 pages + appendices, 4 figure

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

Taking shape: The data science of elastic shape analysis with practical applications

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London.A mathematical curve can represent many different objects, both physical and abstract, from the outline curve of an artefact in an image to the weight of growing animal to the set of frequencies used in a sound. Regardless of these variations, the curves can almost always vary non-linearly. One way to study shapes and their potential variations is elastic shape analysis, a rich theory of which has developed over the past twenty years. However, methods of elastic shape analysis are seldom utilized in practical applications on real-world data, especially outside of the mathematical shape analysis community. Our aim in this thesis is to explore some practical applications of elastic shape analysis. To do this, we work with various types of shape data, the majority of which are based on image datasets. As our focus is on two-dimensional curves, it is important to be able to robustly extract contours from images, before we can apply elastic shape analysis tools. In order to analyse the shapes in a dataset, we turn to methods of machine learning, to investigate the applications of elastic shape analysis in classification. In this thesis, we introduce an anthology of projects, in order to emphasise and under- stand the potential of elastic shape analysis in practical applications. There are four main projects in this thesis: (i) Classification of objects using outlines and the comparisons between methods of elastic shape analysis, geometric morphometrics, and human experts, with a focus on ancient Greek vases, (ii) Mussel species identification and a demonstra- tion that shape may not be enough in some applications, (iii) A novel tool to monitor the development of k ̄ak ̄ap ̄o chicks, and (iv) Classifying individual kiwi based on acoustic data from their calls. By combining tools from computer vision and machine learning with methods of elastic shape analysis, we introduce a practical framework for the application of elastic shape analysis, through a data science lens

Similarity, Retrieval, and Classification of Motion Capture Data

Three-dimensional motion capture data is a digital representation of the complex spatio-temporal structure of human motion. Mocap data is widely used for the synthesis of realistic computer-generated characters in data-driven computer animation and also plays an important role in motion analysis tasks such as activity recognition. Both for efficiency and cost reasons, methods for the reuse of large collections of motion clips are gaining in importance in the field of computer animation. Here, an active field of research is the application of morphing and blending techniques for the creation of new, realistic motions from prerecorded motion clips. This requires the identification and extraction of logically related motions scattered within some data set. Such content-based retrieval of motion capture data, which is a central topic of this thesis, constitutes a difficult problem due to possible spatio-temporal deformations between logically related motions. Recent approaches to motion retrieval apply techniques such as dynamic time warping, which, however, are not applicable to large data sets due to their quadratic space and time complexity. In our approach, we introduce various kinds of relational features describing boolean geometric relations between specified body points and show how these features induce a temporal segmentation of motion capture data streams. By incorporating spatio-temporal invariance into the relational features and induced segments, we are able to adopt indexing methods allowing for flexible and efficient content-based retrieval in large motion capture databases. As a further application of relational motion features, a new method for fully automatic motion classification and retrieval is presented. We introduce the concept of motion templates (MTs), by which the spatio-temporal characteristics of an entire motion class can be learned from training data, yielding an explicit, compact matrix representation. The resulting class MT has a direct, semantic interpretation, and it can be manually edited, mixed, combined with other MTs, extended, and restricted. Furthermore, a class MT exhibits the characteristic as well as the variational aspects of the underlying motion class at a semantically high level. Classification is then performed by comparing a set of precomputed class MTs with unknown motion data and labeling matching portions with the respective motion class label. Here, the crucial point is that the variational (hence uncharacteristic) motion aspects encoded in the class MT are automatically masked out in the comparison, which can be thought of as locally adaptive feature selection