Abstract
The work relates to the categorical approach to general theory of systems, different from well-known Goguen category direction in Computer Science. Developed by the author generalized polycategories (convolution polycategories and categorical splices) are used. The composition of arrows in generalized polycategories is replaced by convolutions. Models for artificial neural networks of various architectures, including those for quantum neuron networks, are found in the categorical approach to the theory of systems. Neural networks are modeled by associative composite convolutional polycategories of the corona type. Previously unknown nature of branching connections of individual neurons with many others is revealed within this model. Categorical splices, as a separate categorical formation, simulate dynamic systems, including classical and quantum mechanics. It is shown how functor and splices, modeling system-forming P.K. Anokhin’s factor, collect an integral system from individual classical or quantum particles. Categorical splices as well simulate simplicial connections in R. Atkin’s q-analysis, which are used for physiological and mental traffic in a cognitom by K.V. Anokhin. As a result, the neuro-graph model of “brain-mind” is detailed in relation to simplicial connections in neural network as a model of “brain-mind”, and in possible models of artificial neural networks.
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Tolokonnikov, G.K. (2020). Convolution Polycategories and Categorical Splices for Modeling Neural Networks. In: Hu, Z., Petoukhov, S., Dychka, I., He, M. (eds) Advances in Computer Science for Engineering and Education II. ICCSEEA 2019. Advances in Intelligent Systems and Computing, vol 938. Springer, Cham. https://doi.org/10.1007/978-3-030-16621-2_24
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