797 research outputs found

    Classical and quantum algorithms for scaling problems

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    This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Farming out : a study.

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    Farming is one of severals ways of arranging for a group of individuals to perform work simultaneously. Farming is attractive. It is a simple concept, and yet it allocates work dynamically, balancing the load automatically. This gives rise to potentially great efficiency; yet the range of applications that can be farmed efficiently and which implementation strategies are the most effective has not been classified. This research has investigated the types of application, design and implementation that farm efficiently on computer systems constructed from a network of communicating parallel processors. This research shows that all applications can be farmed and identifies those concerns that dictate efficiency. For the first generation of transputer hardware, extensive experiments have been performed using Occam, independent of any specific application. This study identified the boundary conditions that dictate which design parameters farm efficiently. These boundary conditions are expressed in a general form that is directly amenable to other architectures. The specific quantitative results are of direct use to others who wish to implement farms on this architecture. Because of farming’s simplicity and potential for high efficiency, this work concludes that architects of parallel hardware should consider binding this paradigm into future systems so as to enable the dynamic allocation of processes to processors to take place automatically. As well as resulting in high levels of machine utilisation for all programs, this would also permanently remove the burden of allocation from the programmer

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    What does explainable AI explain?

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    Machine Learning (ML) models are increasingly used in industry, as well as in scientific research and social contexts. Unfortunately, ML models provide only partial solutions to real-world problems, focusing on predictive performance in static environments. Problem aspects beyond prediction, such as robustness in employment, knowledge generation in science, or providing recourse recommendations to end-users, cannot be directly tackled with ML models. Explainable Artificial Intelligence (XAI) aims to solve, or at least highlight, problem aspects beyond predictive performance through explanations. However, the field is still in its infancy, as fundamental questions such as “What are explanations?”, “What constitutes a good explanation?”, or “How relate explanation and understanding?” remain open. In this dissertation, I combine philosophical conceptual analysis and mathematical formalization to clarify a prerequisite of these difficult questions, namely what XAI explains: I point out that XAI explanations are either associative or causal and either aim to explain the ML model or the modeled phenomenon. The thesis is a collection of five individual research papers that all aim to clarify how different problems in XAI are related to these different “whats”. In Paper I, my co-authors and I illustrate how to construct XAI methods for inferring associational phenomenon relationships. Paper II directly relates to the first; we formally show how to quantify uncertainty of such scientific inferences for two XAI methods – partial dependence plots (PDP) and permutation feature importance (PFI). Paper III discusses the relationship between counterfactual explanations and adversarial examples; I argue that adversarial examples can be described as counterfactual explanations that alter the prediction but not the underlying target variable. In Paper IV, my co-authors and I argue that algorithmic recourse recommendations should help data-subjects improve their qualification rather than to game the predictor. In Paper V, we address general problems with model agnostic XAI methods and identify possible solutions

    Bounded-depth Frege complexity of Tseitin formulas for all graphs

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    We prove that there is a constant K such that Tseitin formulas for a connected graph G requires proofs of size 2tw(G)javax.xml.bind.JAXBElement@531a834b in depth-d Frege systems for [Formula presented], where tw(G) is the treewidth of G. This extends HĂ„stad's recent lower bound from grid graphs to any graph. Furthermore, we prove tightness of our bound up to a multiplicative constant in the top exponent. Namely, we show that if a Tseitin formula for a graph G has size s, then for all large enough d, it has a depth-d Frege proof of size 2tw(G)javax.xml.bind.JAXBElement@25a4b51fpoly(s). Through this result we settle the question posed by M. Alekhnovich and A. Razborov of showing that the class of Tseitin formulas is quasi-automatizable for resolution

    Eddy current defect response analysis using sum of Gaussian methods

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    This dissertation is a study of methods to automatedly detect and produce approximations of eddy current differential coil defect signatures in terms of a summed collection of Gaussian functions (SoG). Datasets consisting of varying material, defect size, inspection frequency, and coil diameter were investigated. Dimensionally reduced representations of the defect responses were obtained utilizing common existing reduction methods and novel enhancements to them utilizing SoG Representations. Efficacy of the SoG enhanced representations were studied utilizing common Machine Learning (ML) interpretable classifier designs with the SoG representations indicating significant improvement of common analysis metrics

    Symmetry and Topology in Disordered Systems

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    Global symmetries greatly enrich the landscape of topological quantum phases, playing an essential role from symmetry-protection of topological insulators to symmetry charge fractionalization on anyons in fractional quantum Hall effect. Topological phases in mixed quantum states, originating from decoherence in open quantum systems or disorders in imperfect crystalline solids, have recently garnered significant interest. Unlike pure states, mixed quantum states can exhibit average symmetries -- symmetries that keep the total ensemble invariant but not on each individual state. It was realized that symmetry-protected topological phases could be well-defined for such mixed states carrying average symmetries. In this thesis I present a systematic classification and characterization of average symmetry-protected topological (ASPT) phases applicable to generic symmetry groups, encompassing both average and exact symmetries, for bosonic and fermionic systems. Moreover, I formulate the theory of average symmetry-enriched topological (ASET) orders in disordered bosonic systems. This research demonstrates that numerous concepts from pure state symmetry-enriched topological (SET) phases, such as anyon permutation, symmetry fractionalization, and 't Hooft anomaly, are well-defined for ASET phases but with various intriguing twists. Our systematic approach helps clarify nuanced issues in previous literature and uncovers compelling new physics. Then the focus of our investigation shifts towards the study of open quantum systems governed by non-unitary dynamics. Specifically, I investigate the effects of measurements and decoherence on long distance behaviors of quantum critical systems. We demonstrate that measurements and decoherence can be viewed as dynamic generalizations of the two aforementioned types of disorders in equilibrium. We classify different measurements and decoherence based on their timescales and symmetry properties, and show that they can be described by replicated Keldysh field theories with distinct physical and replica symmetries. Low energy effective theories for various scenarios are then derived using the symmetry and fundamental consistency conditions of the Keldysh formalism. As an example, I apply this framework to study the critical Ising model in both one and two spatial dimensions. Our results demonstrate that non-unitary dynamics of open systems can be systematically studied based on simple symmetry constraints

    Gurus and Media: Sound, image, machine, text and the digital

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    Gurus and Media is the first book dedicated to media and mediation in domains of public guruship and devotion. Illuminating the mediatisation of guruship and the guru-isation of media, it bridges the gap between scholarship on gurus and the disciplines of media and visual culture studies. It investigates guru iconographies in and across various time periods and also the distinctive ways in which diverse gurus engage with and inhabit different forms of media: statuary, games, print publications, photographs, portraiture, films, machines, social media, bodies, words, graffiti, dolls, sound, verse, tombs and more. The book’s interdisciplinary chapters advance, both conceptually and ethnographically, our understanding of the function of media in the dramatic production of guruship, and reflect on the corporate branding of gurus and on mediated guruship as a series of aesthetic traps for the captivation of devotees and others. They show how different media can further enliven the complex plurality of guruship, for instance in instantiating notions of ‘absent-present’ guruship and demonstrating the mutual mediation of gurus, caste and Hindutva. Throughout, the book foregrounds contested visions of the guru in the development of devotional publics and pluriform guruship across time and space. Thinking through the guru’s many media entanglements in a single place, the book contributes new insights to the study of South Asian religions and to the study of mediation more broadly

    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
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