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Derivatives and Inverse of Cascaded Linear+Nonlinear Neural Models
- Source :
- Recercat. Dipósit de la Recerca de Catalunya, instname, PLoS ONE, PLoS ONE, Vol 13, Iss 10, p e0201326 (2018)
- Publication Year :
- 2017
-
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).<br />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.
- Subjects :
- 0301 basic medicine
Light
Computer science
Vision
Sensory systems
lcsh:Medicine
Inverse
Social Sciences
Sensory perception
law.invention
Machine Learning
Matrix (mathematics)
0302 clinical medicine
Wavelet
law
Signal Decoders
Psychology
lcsh:Science
Bioassays and physiological analysis
Visual Cortex
Multidisciplinary
Physics
Electromagnetic Radiation
Linear model
Sensory Systems
Invertible matrix
Bioassays and Physiological Analysis
Jacobian matrix and determinant
Physical Sciences
symbols
Engineering and Technology
Neurons and Cognition (q-bio.NC)
Sensory Perception
Algorithm
Algorithms
Neural decoding
Research Article
Normalization (statistics)
Visible Light
Models, Neurological
Research and Analysis Methods
03 medical and health sciences
symbols.namesake
Signal decoders
Psychophysics
Humans
Vision, Ocular
lcsh:R
Neurosciences
Biology and Life Sciences
Nonlinear system
030104 developmental biology
Algebra
Luminance
Linear Algebra
Nonlinear Dynamics
FOS: Biological sciences
Quantitative Biology - Neurons and Cognition
Linear Models
lcsh:Q
Electronics
Eigenvectors
030217 neurology & neurosurgery
Mathematics
Neuroscience
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Recercat. Dipósit de la Recerca de Catalunya, instname, PLoS ONE, PLoS ONE, Vol 13, Iss 10, p e0201326 (2018)
- Accession number :
- edsair.doi.dedup.....daa023df6549aed0327699575efecb58