Derivatives and inverse of cascaded linear + nonlinear neural models

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• dc.contributor.author Martínez García, Marina
• dc.contributor.author Cyriac, Praveen
• dc.contributor.author Batard, Thomas
• dc.contributor.author Bertalmío, Marcelo
• dc.contributor.author Malo, Jesús
• dc.date.accessioned 2019-05-22T13:22:04Z
• dc.date.available 2019-05-22T13:22:04Z
• dc.date.issued 2018
• dc.description.abstract In vision science, cascades of Linear+Nonlinear transforms are very successful in modeling a number of perceptual experiences. However, the conventional literature is usually too focused on only describing the forward input-output transform. Instead, in this work we present the mathematics of such cascades beyond the forward transform, namely the Jacobian matrices and the inverse. The fundamental reason for this analytical treatment is that it offers useful analytical insight into the psychophysics, the physiology, and the function of the visual system. For instance, we show how the trends of the sensitivity (volume of the discrimination regions) and the adaptation of the receptive fields can be identified in the expression of the Jacobian w.r.t. the stimulus. This matrix also tells us which regions of the stimulus space are encoded more efficiently in multi-information terms. The Jacobian w.r.t. the parameters shows which aspects of the model have bigger impact in the response, and hence their relative relevance. The analytic inverse implies conditions for the response and model parameters to ensure appropriate decoding. From the experimental and applied perspective, (a) the Jacobian w.r.t. the stimulus is necessary in new experimental methods based on the synthesis of visual stimuli with interesting geometrical properties, (b) the Jacobian matrices w.r.t. the parameters are convenient to learn the model from classical experiments or alternative goal optimization, and (c) the inverse is a promising model-based alternative to blind machine-learning methods for neural decoding that do not include meaningful biological information. The theory is checked by building and testing a vision model that actually follows a modular Linear+Nonlinear program. Our illustrative derivable and invertible model consists of a cascade of modules that account for brightness, contrast, energy masking, and wavelet masking. To stress the generality of this modular setting we show examples where some of the canonical Divisive Normalization modules are substituted by equivalent modules such as the Wilson-Cowan interaction model (at the V1 cortex) or a tone-mapping model (at the retina).en
• dc.description.sponsorship This work was partially funded by the Spanish Ministerio de Economia y Competitividad projects CICYT TEC2013-50520-EXP and CICYT BFU2014-59776-R, by the European Research Council, Starting Grant ref. 306337, by the Spanish government and FEDER Fund, grant ref. TIN2015- 71537-P(MINECO/FEDER,UE), 1021, and by the ICREA Academia Award.
• dc.format.mimetype application/pdf
• dc.identifier.citation Martinez-Garcia M, Cyriac P, Batard T, Bertalmío B, Malo J. Derivatives and inverse of cascaded linear + nonlinear neural models. PLoS ONE. 2018 Oct 15;13(10):e0201326. DOI: 10.1371/journal.pone.0201326
• dc.identifier.doi http://dx.doi.org/10.1371/journal.pone.0201326
• dc.identifier.issn 1932-6203
• dc.identifier.uri http://hdl.handle.net/10230/37265
• dc.language.iso eng
• dc.publisher Public Library of Science (PLoS)
• dc.relation.ispartof PLoS ONE. 2018 Oct 15;13(10):e0201326.
• dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/306337
• dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/TIN2015-71537-P
• dc.rights © 2018 Martinez-Garciaet al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Luminanceen
• dc.subject.keyword Psychophysicsen
• dc.subject.keyword Visionen
• dc.subject.keyword Signal decodersen
• dc.subject.keyword Eigenvectorsen
• dc.subject.keyword Sensory perceptionen
• dc.subject.keyword Sensory systemsen
• dc.subject.keyword Bioassays and physiological analysisen
• dc.title Derivatives and inverse of cascaded linear + nonlinear neural models
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion