Abstract
We describe a sparse coding model of visual cortex that encodes image transformations in an equivariant and hierarchical manner. The model consists of a group-equivariant convolutional layer with internal recurrent connections that implement sparse coding through neural population attractor dynamics, consistent with the architecture of visual cortex. The layers can be stacked hierarchically by introducing recurrent connections between them. The hierarchical structure enables rich bottom-up and top-down information flows, hypothesized to underlie the visual system’s ability for perceptual inference. The model’s equivariant representations are demonstrated on time-varying visual scenes.
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References
Bekkers, E.J., Lafarge, M.W., Veta, M., Eppenhof, K.A.J., Pluim, J.P.W., Duits, R.: Roto-translation covariant convolutional networks for medical image analysis. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11070, pp. 440–448. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00928-1_50
Boutin, V., Franciosini, A., Ruffier, F., Perrinet, L.: Effect of top-down connections in hierarchical sparse coding. Neural Computation 32(11), 2279–2309 (Nov 2020). https://doi.org/10.1162/neco_a_01325
Bronstein, M.M., Bruna, J., Cohen, T., Veličković, P.: Geometric deep learning: Grids, groups, graphs, geodesics, and gauges. arXiv preprint arXiv:2104.13478 (2021)
Cohen, T., Welling, M.: Group equivariant convolutional networks. In: International Conference on Machine Learning, pp. 2990–2999. PMLR (2016)
Hall, B.C.: Lie groups, lie algebras, and representations. In: Quantum Theory for Mathematicians, pp. 333–366. Springer (2013). https://doi.org/10.1007/978-3-319-13467-3
Hyvärinen, A., Hurri, J., Väyrynen, J.: Bubbles: a unifying framework for low-level statistical properties of natural image sequences. JOSA 20(7), 1237–1252 (2003). https://doi.org/10.1364/josaa.20.001237
Olshausen, B.A., Field, D.J.: Sparse coding with an overcomplete basis set: A strategy employed by v1? Vision. Res. 37(23), 3311–3325 (1997)
Paiton, D.M., Shepard, S., Chan, K.H.R., Olshausen, B.A.: Subspace locally competitive algorithms. In: Proceedings of the Neuro-inspired Computational Elements Workshop, pp. 1–8 (2020)
Rozell, C.J., Johnson, D.H., Baraniuk, R.G., Olshausen, B.A.: Sparse coding via thresholding and local competition in neural circuits. Neural Comput. 20(10), 2526–2563 (2008)
Zhang, K.: Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: A theory. J. Neurosci. 16(6), 2112–2126 (1996)
Acknowledgements
The authors thank their helpful colleagues at the Redwood Center and Bioshape Lab. CS acknowledges support from the NIH NEI Training Grant T32EY007043.
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Shewmake, C., Miolane, N., Olshausen, B. (2023). Group Equivariant Sparse Coding. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14071. Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_10
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DOI: https://doi.org/10.1007/978-3-031-38271-0_10
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