Slowness and sparseness have diverging effects on complex cell learning


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.

Matthias Bethge
Matthias Bethge
Professor for Computational Neuroscience and Machine Learning & Director of the Tübingen AI Center

Matthias Bethge is Professor for Computational Neuroscience and Machine Learning at the University of Tübingen and director of the Tübingen AI Center, a joint center between Tübingen University and MPI for Intelligent Systems that is part of the German AI strategy.