Rotation-invariant clustering of neuronal responses in primary visual cortex

Similar to a convolutional neural network (CNN), the mammalian retina encodes visual information into several dozen nonlinear feature maps, each formed by one ganglion cell type that tiles the visual space in an approximately shift-equivariant manner. Whether such organization into distinct cell types is maintained at the level of cortical image processing is an open question. Predictive models building upon convolutional features have been shown to provide state-of-the-art performance, and have recently been extended to include rotation equivariance in order to account for the orientation selectivity of V1 neurons. However, generally no direct correspondence between CNN feature maps and groups of individual neurons emerges in these models, thus rendering it an open question whether V1 neurons form distinct functional clusters. Here we build upon the rotation-equivariant representation of a CNN-based V1 model and propose a methodology for clustering the representations of neurons in this model to find functional cell types independent of preferred orientations of the neurons. We apply this method to a dataset of 6000 neurons and visualize the preferred stimuli of the resulting clusters. Our results highlight the range of non-linear computations in mouse V1.

[1]  Sridhar Mahadevan,et al.  Manifold alignment using Procrustes analysis , 2008, ICML '08.

[2]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[3]  Maneesh Sahani,et al.  Temporal alignment and latent Gaussian process factor inference in population spike trains , 2018, bioRxiv.

[4]  Gaël Varoquaux,et al.  Scikit-learn: Machine Learning in Python , 2011, J. Mach. Learn. Res..

[5]  J. Sanes,et al.  The types of retinal ganglion cells: current status and implications for neuronal classification. , 2015, Annual review of neuroscience.

[6]  Brendan J. Frey,et al.  Fast, Large-Scale Transformation-Invariant Clustering , 2001, NIPS.

[7]  Shiguang Shan,et al.  Generalized Unsupervised Manifold Alignment , 2014, NIPS.

[8]  Pascal Vincent,et al.  Visualizing Higher-Layer Features of a Deep Network , 2009 .

[9]  James A. Bednar,et al.  Model Constrained by Visual Hierarchy Improves Prediction of Neural Responses to Natural Scenes , 2016, PLoS Comput. Biol..

[10]  Matthias Bethge,et al.  The functional diversity of retinal ganglion cells in the mouse , 2015, Nature.

[11]  Wei Wu,et al.  Signal Estimation Under Random Time-Warpings and Nonlinear Signal Alignment , 2011, NIPS.

[12]  J. Gower Generalized procrustes analysis , 1975 .

[13]  Alexander S. Ecker,et al.  Neural system identification for large populations separating "what" and "where" , 2017, NIPS.

[14]  Surya Ganguli,et al.  Deep Learning Models of the Retinal Response to Natural Scenes , 2017, NIPS.

[15]  Santosh S. Vempala,et al.  Isotropic PCA and Affine-Invariant Clustering , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[16]  K. Mardia,et al.  Statistical Shape Analysis , 1998 .

[17]  Alexander S. Ecker,et al.  Inception in visual cortex: in vivo-silico loops reveal most exciting images , 2018 .

[18]  Fernando De la Torre,et al.  Generalized time warping for multi-modal alignment of human motion , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[19]  Elijah D. Christensen,et al.  Using deep learning to probe the neural code for images in primary visual cortex , 2019, Journal of vision.

[20]  Xu Ji,et al.  Invariant Information Clustering for Unsupervised Image Classification and Segmentation , 2019 .

[21]  Ieva Kazlauskaite,et al.  Gaussian Process Latent Variable Alignment Learning , 2018, AISTATS.

[22]  T. Tarpey Linear Transformations and the k-Means Clustering Algorithm , 2007, American Statistician.

[23]  Alexander S. Ecker,et al.  A rotation-equivariant convolutional neural network model of primary visual cortex , 2018, ICLR.