Post on 27-Jul-2020
Contact information: Amir Khosrowshahi, Redwood Center for Theoretical Neuroscience, University of California, 132Barker, MC #3190, Berkeley CA 94720-3190 – Email:amirk@berkeley.edu; Web:http://redwood.berkeley.edu/
Results SummaryValidation ρ for STA from natural scenes vs m-sequences
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Validation ρ for STC from natural scenes vs m-sequences
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Validation ρ for natural scene STA vs STC
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Conclusions• Computing informative spatiotemporal STA and STC kernels using full-field natural movie stimuli is feasible.
• Second order kernels computed from natural movies displayed additional structure when m-sequences did not.
• Natural movie kernels resulted in improved prediction overmsequence kernels in many of the validation tests.
• Overall, however, the predictive capabilities of this model are poor in most cases.
References
1. Paninski, L., Convergence properties of three spike-triggered analysis techniques. Network: Comput. Neural Syst.14, 437–464 (2003).
2. Touryan, J. and Felsen, G. and Dan, Y. Spatial structure of complex cell receptive fields measured with natural images.Neuron 45, 781–791(2005).
3. Rust, N.C., Schwartz, O., Movshon, J.A. and Simoncelli, E. Spatiotemporal elements of macaque V1 receptive fields.Neuron 46, 945–956 (2005).
4. David, S.V. and Gallant, J.L., Predicting neuronal responses during natural vision.Network 16, 239–260 (2005).5. Yen, S-C., Baker, J. and Gray, C.M. Heterogeneity in the responses of adjacent neurons to natural stimuli in cat striate cortex. J Neurophys 97,
1326–1341 (2007).
Acknowledgments
This work was supported by NIH grant EY07043, NGA grant MCA 015894-UCB, NSF grant IIS-06-25223, and a Kopriva Fellowshipto J.B.
Example CellsSimple CellSTA validation for kernels from msequence and two natural movies. Note the temporal differences in RF structure.Predictedfiringrates are in red,actualin blue.
Simple/Complex CellA cell with STA and STC structure using m-sequences and two long movies. Note additional natural movie STC structure aidsvalidtion.
Complex CellNatural movie STC structure captures pronounced peaks in firing rate.
ModelSpatiotemporal frames and correcting for correlationsAn ensemble of spike-triggered vectors was constructed from the 8 movie frames displayed at 35ms intervalsbefore each spike. RF spatial bounds were determined from m-sequence-derived 1st-order kernel structureor by hand mapping when no structure was evident. Extracted movie patches were downsampled to thesame spatial resolution as m-sequences. To correct for intrinsic 2nd-order correlations in natural stimuli, thespike-triggered ensemble was projected onto a subspace consisting of the most significant eigenvectors of awhitening transform. Axes were rescaled to equate variancealong each dimension (see Touryanet al. [2]).
Calculation of whitening trans-form:
E[xxT] = UDV T (SVD)
W = D−1
2UT
vw = Wv
with x the whole movie ensem-ble, W the whitening transform,vw the projected vector. Eigen-vectors are columns ofU and aredisplayed to the right for a sam-ple cell and movie.
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Kernel and non-linearity estimation1st and 2nd order spatiotemporal kernelsK0 (STA) andKi (STC) are respectively the mean and the eigen-vectors of the covariance matrix of the spike-triggered ensemble. Separate kernels were derived for eachm-sequence and long movie session. An output non-linearitywas fit to firing rates calculated from the shortmovie repeats with parameters varied to reduce the mean-squared error between actual and predicted fir-ing rates. Predictions arebest-case correlations given a fixed kernel and the functional form of the staticnon-linearity. The form of the STC component was motivated by Rustet al. [3].
r(t) = r0 + α(|K0It + θ|+)p +∑
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Image
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Receptive Field Nonlinearity Response
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Firing rates as a function of movies projected onto kernelsInset histograms are frequency of spiking given a projection of movie onto kernel. Corresponding inset plotsare of firing rate per frame as a function of the projection.
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IntroductionResponse properties of visual cortical neurons have been typically characterized by the conditional probabilitydistribution that a neuron spikes given the presentation ofa particular stimulus. We studied to what extent onefunctional class for this distribution, the linear-nonlinear Poisson (LNP) cascade receptive field (RF) model,can account for the variance of responses to natural movies when fit using different training stimuli1−4.
MethodsSingle cell recordings were made from striate cortex of anesthetized cats viewing the followingfull-fieldstimuli5:
• 2-D binary m-sequences (44min)
• Long duration natural movies with few repeats (44min)
• Short 30s natural movie segments with 100 repeats
Kernels were computed from m-sequence and long movie sessions. Non-linearities were fit to either long orshort movie sessions.
Extracellular recordings using silicon tetrode probes
Full-field natural movies
Heterogeneity in response to 30s natural movie5
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R E D W O O D C E N T E R
f o r T h e o r e t i c a l N e u r o s c i e n c eAmir Khosrowshahi1 , Jonathan Baker2, Shih-Cheng Yen3, Charles M. Gray2, and Bruno A. Olshausen1
1Redwood Center for Theoretical Neuroscience, University of California, Berkeley, 2Center for Computational Biology, Montana State University, Bozeman, 3Department of Electrical and Computer Engineering, National University of Singapore.
Predicting responses of V1 neurons to natural movies