471 research outputs found

    Taylor University Catalog 2023-2024

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    The 2023-2024 academic catalog of Taylor University in Upland, Indiana.https://pillars.taylor.edu/catalogs/1128/thumbnail.jp

    Undergraduate and Graduate Course Descriptions, 2023 Spring

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    Wright State University undergraduate and graduate course descriptions from Spring 2023

    Neural function approximation on graphs: shape modelling, graph discrimination & compression

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    Graphs serve as a versatile mathematical abstraction of real-world phenomena in numerous scientific disciplines. This thesis is part of the Geometric Deep Learning subject area, a family of learning paradigms, that capitalise on the increasing volume of non-Euclidean data so as to solve real-world tasks in a data-driven manner. In particular, we focus on the topic of graph function approximation using neural networks, which lies at the heart of many relevant methods. In the first part of the thesis, we contribute to the understanding and design of Graph Neural Networks (GNNs). Initially, we investigate the problem of learning on signals supported on a fixed graph. We show that treating graph signals as general graph spaces is restrictive and conventional GNNs have limited expressivity. Instead, we expose a more enlightening perspective by drawing parallels between graph signals and signals on Euclidean grids, such as images and audio. Accordingly, we propose a permutation-sensitive GNN based on an operator analogous to shifts in grids and instantiate it on 3D meshes for shape modelling (Spiral Convolutions). Following, we focus on learning on general graph spaces and in particular on functions that are invariant to graph isomorphism. We identify a fundamental trade-off between invariance, expressivity and computational complexity, which we address with a symmetry-breaking mechanism based on substructure encodings (Graph Substructure Networks). Substructures are shown to be a powerful tool that provably improves expressivity while controlling computational complexity, and a useful inductive bias in network science and chemistry. In the second part of the thesis, we discuss the problem of graph compression, where we analyse the information-theoretic principles and the connections with graph generative models. We show that another inevitable trade-off surfaces, now between computational complexity and compression quality, due to graph isomorphism. We propose a substructure-based dictionary coder - Partition and Code (PnC) - with theoretical guarantees that can be adapted to different graph distributions by estimating its parameters from observations. Additionally, contrary to the majority of neural compressors, PnC is parameter and sample efficient and is therefore of wide practical relevance. Finally, within this framework, substructures are further illustrated as a decisive archetype for learning problems on graph spaces.Open Acces

    Brain Computations and Connectivity [2nd edition]

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    This is an open access title available under the terms of a CC BY-NC-ND 4.0 International licence. It is free to read on the Oxford Academic platform and offered as a free PDF download from OUP and selected open access locations. Brain Computations and Connectivity is about how the brain works. In order to understand this, it is essential to know what is computed by different brain systems; and how the computations are performed. The aim of this book is to elucidate what is computed in different brain systems; and to describe current biologically plausible computational approaches and models of how each of these brain systems computes. Understanding the brain in this way has enormous potential for understanding ourselves better in health and in disease. Potential applications of this understanding are to the treatment of the brain in disease; and to artificial intelligence which will benefit from knowledge of how the brain performs many of its extraordinarily impressive functions. This book is pioneering in taking this approach to brain function: to consider what is computed by many of our brain systems; and how it is computed, and updates by much new evidence including the connectivity of the human brain the earlier book: Rolls (2021) Brain Computations: What and How, Oxford University Press. Brain Computations and Connectivity will be of interest to all scientists interested in brain function and how the brain works, whether they are from neuroscience, or from medical sciences including neurology and psychiatry, or from the area of computational science including machine learning and artificial intelligence, or from areas such as theoretical physics

    Lessons from Formally Verified Deployed Software Systems (Extended version)

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    The technology of formal software verification has made spectacular advances, but how much does it actually benefit the development of practical software? Considerable disagreement remains about the practicality of building systems with mechanically-checked proofs of correctness. Is this prospect confined to a few expensive, life-critical projects, or can the idea be applied to a wide segment of the software industry? To help answer this question, the present survey examines a range of projects, in various application areas, that have produced formally verified systems and deployed them for actual use. It considers the technologies used, the form of verification applied, the results obtained, and the lessons that can be drawn for the software industry at large and its ability to benefit from formal verification techniques and tools. Note: a short version of this paper is also available, covering in detail only a subset of the considered systems. The present version is intended for full reference.Comment: arXiv admin note: text overlap with arXiv:1211.6186 by other author

    A distributional investigation of German verbs

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    Diese Dissertation bietet eine empirische Untersuchung deutscher Verben auf der Grundlage statistischer Beschreibungen, die aus einem großen deutschen Textkorpus gewonnen wurden. In einem kurzen Überblick über linguistische Theorien zur lexikalischen Semantik von Verben skizziere ich die Idee, dass die Verbbedeutung wesentlich von seiner Argumentstruktur (der Anzahl und Art der Argumente, die zusammen mit dem Verb auftreten) und seiner Aspektstruktur (Eigenschaften, die den zeitlichen Ablauf des vom Verb denotierten Ereignisses bestimmen) abhängt. Anschließend erstelle ich statistische Beschreibungen von Verben, die auf diesen beiden unterschiedlichen Bedeutungsfacetten basieren. Insbesondere untersuche ich verbale Subkategorisierung, Selektionspräferenzen und Aspekt. Alle diese Modellierungsstrategien werden anhand einer gemeinsamen Aufgabe, der Verbklassifikation, bewertet. Ich zeige, dass im Rahmen von maschinellem Lernen erworbene Merkmale, die verbale lexikalische Aspekte erfassen, für eine Anwendung von Vorteil sind, die Argumentstrukturen betrifft, nämlich semantische Rollenkennzeichnung. Darüber hinaus zeige ich, dass Merkmale, die die verbale Argumentstruktur erfassen, bei der Aufgabe, ein Verb nach seiner Aspektklasse zu klassifizieren, gut funktionieren. Diese Ergebnisse bestätigen, dass diese beiden Facetten der Verbbedeutung auf grundsätzliche Weise zusammenhängen.This dissertation provides an empirical investigation of German verbs conducted on the basis of statistical descriptions acquired from a large corpus of German text. In a brief overview of the linguistic theory pertaining to the lexical semantics of verbs, I outline the idea that verb meaning is composed of argument structure (the number and types of arguments that co-occur with a verb) and aspectual structure (properties describing the temporal progression of an event referenced by the verb). I then produce statistical descriptions of verbs according to these two distinct facets of meaning: In particular, I examine verbal subcategorisation, selectional preferences, and aspectual type. All three of these modelling strategies are evaluated on a common task, automatic verb classification. I demonstrate that automatically acquired features capturing verbal lexical aspect are beneficial for an application that concerns argument structure, namely semantic role labelling. Furthermore, I demonstrate that features capturing verbal argument structure perform well on the task of classifying a verb for its aspectual type. These findings suggest that these two facets of verb meaning are related in an underlying way

    Evaluating syntactic proposals using minimalist grammars and minimum description length

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    Many patterns found in natural language syntax have multiple pos-sible explanations or structural descriptions. Even within the cur-rently dominant Minimalist framework (Chomsky 1995, 2000), it is not uncommon to encounter multiple types of analyses for the same phenomenon proposed in the literature. A natural question, then, is whether one could evaluate and compare syntactic proposals from a quantitative point of view. In this paper, we show how an evaluation measure inspired by the minimum description length principle (Rissa-nen 1978) can be used to compare accounts of syntactic phenomena implemented as minimalist grammars (Stabler 1997), and how argu-ments for and against this kind of analysis translate into quantitative differences

    Designing similarity functions

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    The concept of similarity is important in many areas of cognitive science, computer science, and statistics. In machine learning, functions that measure similarity between two instances form the core of instance-based classifiers. Past similarity measures have been primarily based on simple Euclidean distance. As machine learning has matured, it has become obvious that a simple numeric instance representation is insufficient for most domains. Similarity functions for symbolic attributes have been developed, and simple methods for combining these functions with numeric similarity functions were devised. This sequence of events has revealed three important issues, which this thesis addresses. The first issue is concerned with combining multiple measures of similarity. There is no equivalence between units of numeric similarity and units of symbolic similarity. Existing similarity functions for numeric and symbolic attributes have no common foundation, and so various schemes have been devised to avoid biasing the overall similarity towards one type of attribute. The similarity function design framework proposed by this thesis produces probability distributions that describe the likelihood of transforming between two attribute values. Because common units of probability are employed, similarities may be combined using standard methods. It is empirically shown that the resulting similarity functions treat different attribute types coherently. The second issue relates to the instance representation itself. The current choice of numeric and symbolic attribute types is insufficient for many domains, in which more complicated representations are required. For example, a domain may require varying numbers of features, or features with structural information. The framework proposed by this thesis is sufficiently general to permit virtually any type of instance representation-all that is required is that a set of basic transformations that operate on the instances be defined. To illustrate the framework’s applicability to different instance representations, several example similarity functions are developed. The third, and perhaps most important, issue concerns the ability to incorporate domain knowledge within similarity functions. Domain information plays an important part in choosing an instance representation. However, even given an adequate instance representation, domain information is often lost. For example, numeric features that are modulo (such as the time of day) can be perfectly represented as a numeric attribute, but simple linear similarity functions ignore the modulo nature of the attribute. Similarly, symbolic attributes may have inter-symbol relationships that should be captured in the similarity function. The design framework proposed by this thesis allows domain information to be captured in the similarity function, both in the transformation model and in the probability assigned to basic transformations. Empirical results indicate that such domain information improves classifier performance, particularly when training data is limited

    Fundamentals

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    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
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