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arXiv 2022年

作者： Burns, Thomas F. Irwansyah Neural Coding and Brain Computing Unit OIST Graduate University Okinawa Japan Department of Mathematics University of Mataram West Nusa Tenggara Indonesia

Artificial and biological neural networks (ANNs and BNNs) can encode inputs in the form of combinations of individual neurons' activities. These combinatorial neural codes present a computational challenge for direct and efficient analysis due to their high dimensionality and often large volumes of data. Here we improve the computational complexity - from factorial to quadratic time - of direct algebraic methods previously applied to small examples and apply them to large neural codes generated by experiments. These methods provide a novel and efficient way of probing algebraic, geometric, and topological characteristics of combinatorial neural codes and provide insights into how such characteristics are related to learning and experience in neural networks. We introduce a procedure to perform hypothesis testing on the intrinsic features of neural codes using information geometry. We then apply these methods to neural activities from an ANN for image classification and a BNN for 2D navigation to, without observing any inputs or outputs, estimate the structure and dimensionality of the stimulus or task space. Additionally, we demonstrate how an ANN varies its internal representations across network depth and during *** Codes 92B20 (Primary) 12Y05, 92B05 (Secondary) © 2022, CC BY-NC-SA.

关键词： neural networks

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Detecting danger in gridworlds using Gromov's Link Condition

arXiv

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arXiv 2022年

作者： Burns, Thomas F. Tang, Robert Neural Coding and Brain Computing Unit OIST Graduate University 1919-1 Tancha Onna-son Kunigami-gun Okinawa 904-0495 Japan Department of Pure Mathematics Xi'an Jiaotong Liverpool University 111 Ren'ai Road Suzhou Industrial Park Suzhou Jiangsu Province 215123 China

Gridworlds have been long-utilised in AI research, particularly in reinforcement learning, as they provide simple yet scalable models for many real-world applications such as robot navigation, emergent behaviour, and operations research. We initiate a study of gridworlds using the mathematical framework of reconfigurable systems and state complexes due to Abrams, Ghrist & Peterson. State complexes represent all possible configurations of a system as a single geometric space, thus making them conducive to study using geometric, topological, or combinatorial methods. The main contribution of this work is a modification to the original Abrams, Ghrist & Peterson setup which we introduce to capture agent braiding and thereby more naturally represent the topology of gridworlds. With this modification, the state complexes may exhibit geometric defects (failure of Gromov's Link Condition). Serendipitously, we discover these failures occur exactly where undesirable or dangerous states appear in the gridworld. Our results therefore provide a novel method for seeking guaranteed safety limitations in discrete task environments with single or multiple agents, and offer useful safety information (in geometric and topological forms) for incorporation in or analysis of machine learning systems. More broadly, our work introduces tools from geometric group theory and combinatorics to the AI community and demonstrates a proof-of-concept for this geometric viewpoint of the task domain through the example of simple gridworld *** Codes 57Z25 (Primary) 68R01, 51F99 (Secondary) © 2022, CC BY.

关键词： Geometry

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26th Annual Computational Neuroscience Meeting (CNS*2017) of the Organization for Computational Neuroscience Antwerp, Belgium, July 15-20, 2017

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BMC NEUROSCIENCE 2017年第SUPPL 1期18卷 59-59页

作者： [Anonymous] Indiana University Purdue University Indianapolis Indianapolis IN 46032 USA Stark Neurosciences Research Institute Indiana University School of Medicine Indianapolis IN 46032 USA Department of Mathematics East Carolina University Greenville NC 27858 USA Jülich Supercomputing Centre Forschungszentrum Jülich 52425 Jülich Germany Future Systems Swiss National Supercomputing Centre 8092 Zurich Switzerland User Engagement and Support Swiss National Supercomputing Centre 6900 Lugano Switzerland Institut de Neurosciences des Systèmes Aix Marseille Univ 13005 Marseille France Simulation Lab Neuroscience Forschungszentrum Jülich Jülich Germany Department of Experimental Psychology Ghent University 9000 Ghent Belgium Donders Center for Cognitive Neuroimaging Radboud University 6525HR Nijmegen The Netherlands Department of Electrical Computer and Energy Engineering University of Colorado Boulder CO 80309 USA Department of Neurosurgery Johns Hopkins School of Medicine Baltimore MD 21287 USA Department of Neurology Johns Hopkins School of Medicine Baltimore MD 21287 USA Department of Otolaryngology Johns Hopkins School of Medicine Baltimore MD 21287 USA INSERM U968 Paris France Sorbonne Universités UPMC University Paris 06 UMR_S 968 Institut de la Vision Paris France CNRS UMR_7210 Paris France Department of Computer Architecture and Technology University of Granada (CITIC) Granada Spain Sorbonne Universités UPMC Univ Paris 06 INSERM CNRS Institut de la Vision Paris France Department of Adaptive Machine Systems Osaka University Osaka Japan Department of Computer Science University of Cergy-Pontoise Cergy-Pontoise France Department of Physics and Astronomy College of Charleston Charleston SC 29424 USA School of Physics Faculty of Science University of Sydney Sydney NSW 2006 Australia Center of Excellence for Integrative Brain Function Australian Research Council Sydney Australia Max Planck Institute for Human Cognitive and Brain Sciences Saxony Lei

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