title: Slowness and sparseness have diverging effects on complex cell learning.
abstract: Following earlier studies which showed that a sparse coding principle may explain the receptive field properties of complex cells in primary visual cortex, it has been concluded that the same properties may be equally derived from a slowness principle. In contrast to this claim, we here show that slowness and sparsity drive the representations towards substantially different receptive field properties. To do so, we present complete sets of basis functions learned with slow subspace analysis (SSA) in case of natural movies as well as translations, rotations, and scalings of natural images. SSA directly parallels independent subspace analysis (ISA) with the only difference that SSA maximizes slowness instead of sparsity. We find a large discrepancy between the filter shapes learned with SSA and ISA. We argue that SSA can be understood as a generalization of the Fourier transform where the power spectrum corresponds to the maximally slow subspace energies in SSA. Finally, we investigate the trade-off between slowness and sparseness when combined in one objective function.
authors.affiliation: Werner Reichardt Centre for Integrative Neuroscience, University of Tübingen, Tübingen, Germany.
authors.forename: Jörn-Philipp
authors.initials: JP
authors.lastname: Lies
authors.affiliation: Swartz Center for Theoretical Neurobiology, Brandeis University, Waltham, Massachusetts, United States of America.
authors.forename: Ralf M
authors.initials: RM
authors.lastname: Häfner
authors.affiliation: Werner Reichardt Centre for Integrative Neuroscience, University of Tübingen, Tübingen, Germany; Bernstein Center for Computational Neuroscience, Tübingen, Germany; Max Planck Institute for Biological Cybernetics, Tübingen, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Bethge
mesh_terms: D000465:Algorithms; D000818:Animals; D019295:Computational Biology / Q000379:methods*; D005583:Fourier Analysis; D006801:Humans; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology; D016011:Normal Distribution; D014785:Vision, Ocular; D014793:Visual Cortex / Q000502:physiology*