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 |
2018 |
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.citation |
1932-6203 |
dc.identifier.citation |
https://dx.doi.org/10.1371/journal.pone.0201326 |
dc.identifier.uri |
http://hdl.handle.net/10230/37265 |
dc.format |
application/pdf |
dc.language.iso |
eng |
dc.publisher |
Public Library of Science (PLoS) |
dc.relation |
PLoS ONE. 2018 Oct 15;13(10):e0201326. |
dc.relation |
info:eu-repo/grantAgreement/EC/FP7/306337 |
dc.relation |
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 |
info:eu-repo/semantics/openAccess |
dc.rights |
http://creativecommons.org/licenses/by/4.0/ |
dc.subject |
Luminance |
dc.subject |
Psychophysics |
dc.subject |
Vision |
dc.subject |
Signal decoders |
dc.subject |
Eigenvectors |
dc.subject |
Sensory perception |
dc.subject |
Sensory systems |
dc.subject |
Bioassays and physiological analysis |
dc.title |
Derivatives and inverse of cascaded linear + nonlinear neural models |
dc.type |
info:eu-repo/semantics/article |
dc.type |
info:eu-repo/semantics/publishedVersion |
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). |
dc.description.abstract |
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. |