Slowness and Sparseness Have Diverging Effects on Complex Cell Learning
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{"title"=>"Slowness and Sparseness Have Diverging Effects on Complex Cell Learning", "type"=>"journal", "authors"=>[{"first_name"=>"Jörn Philipp", "last_name"=>"Lies", "scopus_author_id"=>"56095278600"}, {"first_name"=>"Ralf M.", "last_name"=>"Häfner", "scopus_author_id"=>"56094911100"}, {"first_name"=>"Matthias", "last_name"=>"Bethge", "scopus_author_id"=>"6603439763"}], "year"=>2014, "source"=>"PLoS Computational Biology", "identifiers"=>{"scopus"=>"2-s2.0-84897405997", "pui"=>"372738405", "doi"=>"10.1371/journal.pcbi.1003468", "issn"=>"15537358", "pmid"=>"24603197", "sgr"=>"84897405997"}, "id"=>"1d6bc399-e646-3c72-96bc-453d2f8a13d4", "abstract"=>"Author SummaryA key question in visual neuroscience is how neural representations achieve invariance against appearance changes of objects. In particular, the invariance of complex cell responses in primary visual cortex against small translations is commonly interpreted as a signature of an invariant coding strategy possibly originating from an unsupervised learning principle. Various models have been proposed to explain the response properties of complex cells using a sparsity or a slowness criterion and it has been concluded that physiologically plausible receptive field properties can be derived from either criterion. Here, we show that the effect of the two objectives on the resulting receptive field properties is in fact very different. We conclude that slowness alone cannot explain the filter shapes of complex cells and discuss what kind of experimental measurements could help us to better asses the role of slowness and sparsity for complex cell representations.", "link"=>"http://www.mendeley.com/research/slowness-sparseness-diverging-effects-complex-cell-learning", "reader_count"=>35, "reader_count_by_academic_status"=>{"Unspecified"=>2, "Professor > Associate Professor"=>2, "Researcher"=>6, "Student > Ph. D. Student"=>19, "Other"=>1, "Student > Master"=>3, "Student > Bachelor"=>2}, "reader_count_by_user_role"=>{"Unspecified"=>2, "Professor > Associate Professor"=>2, "Researcher"=>6, "Student > Ph. D. Student"=>19, "Other"=>1, "Student > Master"=>3, "Student > Bachelor"=>2}, "reader_count_by_subject_area"=>{"Engineering"=>3, "Unspecified"=>2, "Biochemistry, Genetics and Molecular Biology"=>1, "Agricultural and Biological Sciences"=>8, "Neuroscience"=>2, "Physics and Astronomy"=>4, "Psychology"=>1, "Computer Science"=>13, "Economics, Econometrics and Finance"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>3}, "Neuroscience"=>{"Neuroscience"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>4}, "Psychology"=>{"Psychology"=>1}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>8}, "Computer Science"=>{"Computer Science"=>13}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}, "Unspecified"=>{"Unspecified"=>2}}, "reader_count_by_country"=>{"United States"=>4, "France"=>2, "Germany"=>1}, "group_count"=>0}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1409863"], "description"=>"<p>The complete set of filters learned from translated images with open and cyclic boundary conditions are shown in (A) and (C), respectively. Each row shows the filters of 6 subspaces with 2 dimensions. The subspaces are ordered according to their slowness, with the slowest filter in the upper left corner and decreasing slowness from left to right and top to bottom. The <i>inverse</i> slowness for the individual subspaces after learning (black dots) and for the initial random filters (gray squares) is shown in (B) and (D), respectively. For open boundary conditions (B), the inverse slowness does not converge to 0, hence perfect invariance is not achieved. For cyclic shifts, however, the inverse slowness approaches 0 with arbitrary precision (D), indicating convergence to perfect invariance.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "neuroscience", "Sensory systems", "Visual system", "translations", "cyclic"], "article_id"=>953794, "categories"=>["Biological Sciences"], "users"=>["Jörn-Philipp Lies", "Ralf M. Häfner", "Matthias Bethge"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003468.g002", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_SSA_on_translations_with_open_and_cyclic_boundary_conditions_/953794", "title"=>"SSA on translations with open and cyclic boundary conditions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-06 03:34:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1409868"], "description"=>"<p>Here, we started the optimization with the Fourier basis () as initial condition. We used 3 different data sets sampled from the van Hateren image database using 2D translations with a shift amplitude of maximally 1, 2, or 3 pixels. The optimized filters , where is the maximal shift amplitude, do not deviate dramatically from the initial condition. The amplitude spectra of all filters are shown in the <i>upper panel</i> with the DC component being at the center. The amplitude spectra of the optimized filters blur out towards the lower frequencies except for the lowest frequencies, which blur out towards the higher frequencies. Only the highest frequencies show additional sensitivity at the lowest spatial frequencies which cannot be explained by spatial localization. The slowness of the individual components is shown in the <i>lower panel</i>. The black lines indicate the performance of the Fourier basis applied to test data with shift amplitudes of up to 1 (solid), 2 (long dashes), or 3 (short dashes) pixels. The gray lines show the performance of the optimal filters. SSA sacrifices slowness on the slower filters to gain a comparatively larger amount of slowness on the faster filters. In this way, overall SSA achieves better slowness.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "neuroscience", "Sensory systems", "Visual system", "fourier", "translations"], "article_id"=>953799, "categories"=>["Biological Sciences"], "users"=>["Jörn-Philipp Lies", "Ralf M. Häfner", "Matthias Bethge"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003468.g003", "stats"=>{"downloads"=>0, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Deviations_from_the_Fourier_basis_for_translations_with_open_boundary_conditions_/953799", "title"=>"Deviations from the Fourier basis for translations with open boundary conditions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-06 03:34:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1409870"], "description"=>"<p>Illustration of the filters obtained from patch-centered rotation sequences (A,B) and patch-centered scaling sequences (C) with the slowness of the individual filter subspaces before (<i>random</i>) and after the optimization (<i>learned</i>). The filters are ordered in ascending inverse slowness (row-wise) with the slowest feature in the upper left and the fastest feature in the lower right corner. The data in (A) and (C) consist of square patches from the van Hateren data set while the data for (B) consist of 121-dimensional round patches which are, for visualization, embedded in a 14×14 square patch. The rotation filters match those found in steerable filter theory <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003468#pcbi.1003468-Bethge1\" target=\"_blank\">[28]</a>. The filters of the patch-centered anisotropic scaling exhibit localized edge filters centered towards the patch boundaries.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "neuroscience", "Sensory systems", "Visual system", "filters", "rotation"], "article_id"=>953801, "categories"=>["Biological Sciences"], "users"=>["Jörn-Philipp Lies", "Ralf M. Häfner", "Matthias Bethge"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003468.g004", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_SSA_filters_for_local_rotation_and_scaling_/953801", "title"=>"SSA filters for local rotation and scaling.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-06 03:34:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1409873"], "description"=>"<p>The lower panel shows the performance with respect to both the slowness objective (blue) and the sparsity objective (red) and the upper panel displays four sets of filters as obtained for different values for the trade-off parameter : The leftmost case () is equivalent to SSA and the rightmost case () is equivalent to ISA. There is a large difference between the two that can easily be grasped by eye. The example for reflects the crossing point in performance (see lower panel) meaning that the representation performs slightly better than 80% of its maximal performance with respect to both objectives simultaneously. The case was hand-picked to represent the point where the filters perceptually look similarly close to ISA and SSA.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "neuroscience", "Sensory systems", "Visual system", "learned"], "article_id"=>953804, "categories"=>["Biological Sciences"], "users"=>["Jörn-Philipp Lies", "Ralf M. Häfner", "Matthias Bethge"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003468.g005", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Filters_of_slowness_independence_and_mixture_objective_learned_on_movies_/953804", "title"=>"Filters of slowness, independence and mixture objective learned on movies.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-06 03:34:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1409879"], "description"=>"<p>When optimizing the filter set for a weighted superposition of the slowness and sparsity objectives the performance with respect to decreases monotonically with (<i>upper left</i>). The steepness of decay indicates the impact of the trade-off. The different colors correspond to different datasets (see legend). While the performance with respect to for the rotation data falls off quickly (green), the differences between scaling, translation and movie data (cyan, blue, red) are not significant. The concave shapes of the curves indicate a rather gentle trade-off. The dashed diagonal line indicates an intermediate point for this trade-off. We chose it such that both objectives are reduced by the same factor relative to their optimal performance in the units used here. The corresponding filters are shown in the adjacent panels: The ISA filters are shown in (A) which are independent of the temporal statistics. The ISSA filters at the break even point are shown in (B) for movies, in (C) for translations, in (D) for rotations, and in (E) for scalings. The last row shows the SSA filters in the same order: (F) for movies, in (G) for translations, in (H) for rotations, and in (I) for scalings.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "neuroscience", "Sensory systems", "Visual system", "slowness"], "article_id"=>953810, "categories"=>["Biological Sciences"], "users"=>["Jörn-Philipp Lies", "Ralf M. Häfner", "Matthias Bethge"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003468.g006", "stats"=>{"downloads"=>0, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Trade_off_in_the_performance_with_respect_to_slowness_and_sparsity_/953810", "title"=>"Trade-off in the performance with respect to slowness and sparsity.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-06 03:34:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1409880"], "description"=>"<p>Objective on training and test set for optimized filters and Fourier basis.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "neuroscience", "Sensory systems", "Visual system"], "article_id"=>953811, "categories"=>["Biological Sciences"], "users"=>["Jörn-Philipp Lies", "Ralf M. Häfner", "Matthias Bethge"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003468.t001", "stats"=>{"downloads"=>3, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Control_for_overfitting_/953811", "title"=>"Control for overfitting.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-03-06 03:34:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1409881"], "description"=>"<div><p>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 <i>slow subspace analysis</i> (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.</p></div>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "neuroscience", "Sensory systems", "Visual system", "sparseness", "diverging"], "article_id"=>953812, "categories"=>["Biological Sciences"], "users"=>["Jörn-Philipp Lies", "Ralf M. Häfner", "Matthias Bethge"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003468", "stats"=>{"downloads"=>6, "page_views"=>22, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Slowness_and_Sparseness_Have_Diverging_Effects_on_Complex_Cell_Learning_/953812", "title"=>"Slowness and Sparseness Have Diverging Effects on Complex Cell Learning", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-03-06 03:34:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1409852"], "description"=>"<p>The input signal, e.g. a movie sequence, is applied to several filters. Two filters form a subspace. The output of each filter is passed through a quadratic nonlinearity and summed within each subspace. The output corresponds to the radial component of the 2D subspace. The responses then form the multidimensional output signal . If the filters are the discrete Fourier transform basis where each subspace consists of the two filters which only differ in phase, then the output is the power spectrum of the input signal .</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "neuroscience", "Sensory systems", "Visual system", "subspace"], "article_id"=>953784, "categories"=>["Biological Sciences"], "users"=>["Jörn-Philipp Lies", "Ralf M. Häfner", "Matthias Bethge"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003468.g001", "stats"=>{"downloads"=>6, "page_views"=>53, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_structure_for_both_independent_subspace_analysis_ISA_and_slow_subspace_analysis_SSA_/953784", "title"=>"Model structure for both independent subspace analysis (ISA) and slow subspace analysis (SSA).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-06 03:34:35"}

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