際際滷shows by User: PierreBaudot / http://www.slideshare.net/images/logo.gif 際際滷shows by User: PierreBaudot / Fri, 20 Mar 2020 20:09:09 GMT 際際滷Share feed for 際際滷shows by User: PierreBaudot Information topology, Deep Network generalization and Consciousness quantification- Fields institute /slideshow/information-topology-deep-network-generalization-and-consciousness-quantification-fields-institute/230606221 ydvg0j2frqguin1add8h-signature-556ff40d632a2a3a12af9d5964e7bed6022346f995e4d461aaf9c9290b23e7e5-poli-200320200909
Presentation - 12 march 2020 - Fields Institute, Toronto, Canada ]]>
Presentation - 12 march 2020 - Fields Institute, Toronto, Canada ]]> Fri, 20 Mar 2020 20:09:09 GMT /slideshow/information-topology-deep-network-generalization-and-consciousness-quantification-fields-institute/230606221 PierreBaudot@slideshare.net(PierreBaudot) Information topology, Deep Network generalization and Consciousness quantification- Fields institute PierreBaudot Presentation - 12 march 2020 - Fields Institute, Toronto, Canada <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/ydvg0j2frqguin1add8h-signature-556ff40d632a2a3a12af9d5964e7bed6022346f995e4d461aaf9c9290b23e7e5-poli-200320200909-thumbnail.jpg?width=120&amp;height=120&amp;fit=bounds" /><br> Presentation - 12 march 2020 - Fields Institute, Toronto, Canada
Information topology, Deep Network generalization and Consciousness quantification- Fields institute from Pierre BAUDOT
]]> 41 0 https://cdn.slidesharecdn.com/ss_thumbnails/ydvg0j2frqguin1add8h-signature-556ff40d632a2a3a12af9d5964e7bed6022346f995e4d461aaf9c9290b23e7e5-poli-200320200909-thumbnail.jpg?width=120&height=120&fit=bounds presentation Black http://activitystrea.ms/schema/1.0/post http://activitystrea.ms/schema/1.0/posted 0 Topological and Informational Methods for AI /slideshow/topological-and-informational-methods-for-ai/196033155 presentationaisummitnov2019compressedforwebdifusion-191121140721
As a domain that formalizes the classification and recognition of patterns-structures in mathematics, Topological Data Analysis has progressively gathered the interest of the data science community. On the side of neural networks following Hinton, Amari, information geometric approaches have provided well defined metric and gradient descent methods. This presentation will focus on an original approach of algebraic topology intrinsically based on probability/statistics and information, developed notably with D. Bennequin since 2006. Information topology characterizes uniquely usual information functions, unraveling that two theories, cohomology and information theory, are of the same nature. These probabilistic tools describe the statistical forms or patterns present in databases and make them correspond to discrete symmetries. The set of statistical interactions-dependencies between k elementary variables is quantified by the multivariate mutual information between these k components. It provides a generalized and metric-free decomposition of free energy that is used in machine learning and artificial intelligence, with brand new computationally expensive algorithm for unsupervised and supervised learning, where simplicial complexes provide topologically constrained Deep Neural Networks architectures. Its application to gene expression under open source software makes it possible to detect functional modules of covariant variables (collective dynamics) as well as clusters (corresponding to condensation phenomena and negative synergistic interactions) in high dimension, and thus to analyze the structure and to quantify diversity in data or arbitrary complex systems.]]>
As a domain that formalizes the classification and recognition of patterns-structures in mathematics, Topological Data Analysis has progressively gathered the interest of the data science community. On the side of neural networks following Hinton, Amari, information geometric approaches have provided well defined metric and gradient descent methods. This presentation will focus on an original approach of algebraic topology intrinsically based on probability/statistics and information, developed notably with D. Bennequin since 2006. Information topology characterizes uniquely usual information functions, unraveling that two theories, cohomology and information theory, are of the same nature. These probabilistic tools describe the statistical forms or patterns present in databases and make them correspond to discrete symmetries. The set of statistical interactions-dependencies between k elementary variables is quantified by the multivariate mutual information between these k components. It provides a generalized and metric-free decomposition of free energy that is used in machine learning and artificial intelligence, with brand new computationally expensive algorithm for unsupervised and supervised learning, where simplicial complexes provide topologically constrained Deep Neural Networks architectures. Its application to gene expression under open source software makes it possible to detect functional modules of covariant variables (collective dynamics) as well as clusters (corresponding to condensation phenomena and negative synergistic interactions) in high dimension, and thus to analyze the structure and to quantify diversity in data or arbitrary complex systems.]]> Thu, 21 Nov 2019 14:07:21 GMT /slideshow/topological-and-informational-methods-for-ai/196033155 PierreBaudot@slideshare.net(PierreBaudot) Topological and Informational Methods for AI PierreBaudot As a domain that formalizes the classification and recognition of patterns-structures in mathematics, Topological Data Analysis has progressively gathered the interest of the data science community. On the side of neural networks following Hinton, Amari, information geometric approaches have provided well defined metric and gradient descent methods. This presentation will focus on an original approach of algebraic topology intrinsically based on probability/statistics and information, developed notably with D. Bennequin since 2006. Information topology characterizes uniquely usual information functions, unraveling that two theories, cohomology and information theory, are of the same nature. These probabilistic tools describe the statistical forms or patterns present in databases and make them correspond to discrete symmetries. The set of statistical interactions-dependencies between k elementary variables is quantified by the multivariate mutual information between these k components. It provides a generalized and metric-free decomposition of free energy that is used in machine learning and artificial intelligence, with brand new computationally expensive algorithm for unsupervised and supervised learning, where simplicial complexes provide topologically constrained Deep Neural Networks architectures. Its application to gene expression under open source software makes it possible to detect functional modules of covariant variables (collective dynamics) as well as clusters (corresponding to condensation phenomena and negative synergistic interactions) in high dimension, and thus to analyze the structure and to quantify diversity in data or arbitrary complex systems. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/presentationaisummitnov2019compressedforwebdifusion-191121140721-thumbnail.jpg?width=120&amp;height=120&amp;fit=bounds" /><br> As a domain that formalizes the classification and recognition of patterns-structures in mathematics, Topological Data Analysis has progressively gathered the interest of the data science community. On the side of neural networks following Hinton, Amari, information geometric approaches have provided well defined metric and gradient descent methods. This presentation will focus on an original approach of algebraic topology intrinsically based on probability/statistics and information, developed notably with D. Bennequin since 2006. Information topology characterizes uniquely usual information functions, unraveling that two theories, cohomology and information theory, are of the same nature. These probabilistic tools describe the statistical forms or patterns present in databases and make them correspond to discrete symmetries. The set of statistical interactions-dependencies between k elementary variables is quantified by the multivariate mutual information between these k components. It provides a generalized and metric-free decomposition of free energy that is used in machine learning and artificial intelligence, with brand new computationally expensive algorithm for unsupervised and supervised learning, where simplicial complexes provide topologically constrained Deep Neural Networks architectures. Its application to gene expression under open source software makes it possible to detect functional modules of covariant variables (collective dynamics) as well as clusters (corresponding to condensation phenomena and negative synergistic interactions) in high dimension, and thus to analyze the structure and to quantify diversity in data or arbitrary complex systems.
Topological and Informational Methods for AI from Pierre BAUDOT
]]> 90 0 https://cdn.slidesharecdn.com/ss_thumbnails/presentationaisummitnov2019compressedforwebdifusion-191121140721-thumbnail.jpg?width=120&height=120&fit=bounds presentation Black http://activitystrea.ms/schema/1.0/post http://activitystrea.ms/schema/1.0/posted 0 https://public.slidesharecdn.com/v2/images/profile-picture.png https://cdn.slidesharecdn.com/ss_thumbnails/ydvg0j2frqguin1add8h-signature-556ff40d632a2a3a12af9d5964e7bed6022346f995e4d461aaf9c9290b23e7e5-poli-200320200909-thumbnail.jpg?width=320&height=320&fit=bounds slideshow/information-topology-deep-network-generalization-and-consciousness-quantification-fields-institute/230606221 Information topology, ... https://cdn.slidesharecdn.com/ss_thumbnails/presentationaisummitnov2019compressedforwebdifusion-191121140721-thumbnail.jpg?width=320&height=320&fit=bounds slideshow/topological-and-informational-methods-for-ai/196033155 Topological and Inform...