STDP Installs in Winner-Take-All Circuits an Online Approximation to Hidden Markov Model Learning
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{"title"=>"STDP Installs in Winner-Take-All Circuits an Online Approximation to Hidden Markov Model Learning", "type"=>"journal", "authors"=>[{"first_name"=>"David", "last_name"=>"Kappel", "scopus_author_id"=>"56094973100"}, {"first_name"=>"Bernhard", "last_name"=>"Nessler", "scopus_author_id"=>"36117883500"}, {"first_name"=>"Wolfgang", "last_name"=>"Maass", "scopus_author_id"=>"7005129380"}], "year"=>2014, "source"=>"PLoS Computational Biology", "identifiers"=>{"pui"=>"372738377", "issn"=>"15537358", "isbn"=>"10.1371/journal.pcbi.1003511", "doi"=>"10.1371/journal.pcbi.1003511", "scopus"=>"2-s2.0-84897460337", "pmid"=>"24675787", "sgr"=>"84897460337"}, "id"=>"28c126bd-c1f0-3d6c-a970-0f8864daa777", "abstract"=>"Author SummaryIt has recently been shown that STDP installs in ensembles of pyramidal cells with lateral inhibition networks for Bayesian inference that are theoretically optimal for the case of stationary spike input patterns. We show here that if the experimentally found lateral excitatory connections between pyramidal cells are taken into account, theoretically optimal probabilistic models for the prediction of time-varying spike input patterns emerge through STDP. Furthermore a rigorous theoretical framework is established that explains the emergence of computational properties of this important motif of cortical microcircuits through learning. We show that the application of an idealized form of STDP approximates in this network motif a generic process for adapting a computational model to data: expectation-maximization. The versatility of computations carried out by these ensembles of pyramidal cells and the speed of the emergence of their computational properties through STDP is demonstrated through a variety of computer simulations. We show the ability of these networks to learn multiple input sequences through STDP and to reproduce the statistics of these inputs after learning.", "link"=>"http://www.mendeley.com/research/stdp-installs-winnertakeall-circuits-online-approximation-hidden-markov-model-learning", "reader_count"=>119, "reader_count_by_academic_status"=>{"Unspecified"=>2, "Professor > Associate Professor"=>4, "Researcher"=>27, "Student > Doctoral Student"=>5, "Student > Ph. D. Student"=>40, "Student > Postgraduate"=>4, "Other"=>5, "Student > Master"=>14, "Student > Bachelor"=>11, "Professor"=>7}, "reader_count_by_user_role"=>{"Unspecified"=>2, "Professor > Associate Professor"=>4, "Researcher"=>27, "Student > Doctoral Student"=>5, "Student > Ph. D. Student"=>40, "Student > Postgraduate"=>4, "Other"=>5, "Student > Master"=>14, "Student > Bachelor"=>11, "Professor"=>7}, "reader_count_by_subject_area"=>{"Unspecified"=>4, "Agricultural and Biological Sciences"=>27, "Chemistry"=>1, "Computer Science"=>34, "Economics, Econometrics and Finance"=>1, "Engineering"=>10, "Environmental Science"=>1, "Nursing and Health Professions"=>1, "Mathematics"=>5, "Medicine and Dentistry"=>3, "Neuroscience"=>19, "Physics and Astronomy"=>12, "Psychology"=>1}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>3}, "Physics and Astronomy"=>{"Physics and Astronomy"=>12}, "Psychology"=>{"Psychology"=>1}, "Mathematics"=>{"Mathematics"=>5}, "Unspecified"=>{"Unspecified"=>4}, "Environmental Science"=>{"Environmental Science"=>1}, "Engineering"=>{"Engineering"=>10}, "Chemistry"=>{"Chemistry"=>1}, "Neuroscience"=>{"Neuroscience"=>19}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>27}, "Computer Science"=>{"Computer Science"=>34}, "Nursing and Health Professions"=>{"Nursing and Health Professions"=>1}}, "reader_count_by_country"=>{"New Zealand"=>1, "United States"=>6, "United Kingdom"=>6, "Australia"=>1, "France"=>1, "Belarus"=>1, "Switzerland"=>1, "Germany"=>5}, "group_count"=>3}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1438208"], "description"=>"<p>(A) The structure of the network. It consists of excitatory neurons (blue) that receive feedforward inputs (green synapses) and lateral excitatory all-to-all connections (blue synapses). Interneurons (red) install soft winner-take-all behavior by injecting a global inhibition to all neurons of the circuit in response to the network's spiking activity. (B) The Bayesian network representing the HMM over time steps. The prediction model (blue arrows) is implemented by the lateral synapses. It determines the evolution of the hidden states over time. The observation model (green arrows) is implemented by feedforward connections. The inference task for the HMM is to determine a sequence of hidden states (white), given the afferent activity (gray). (C) The STDP window that is used to update the excitatory synapses. The synaptic weight change is plotted against the time difference between pre- and postsynaptic spike events.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Circuit models", "neuroscience", "Neural homeostasis", "neural networks"], "article_id"=>976812, "categories"=>["Biological Sciences"], "users"=>["David Kappel", "Bernhard Nessler", "Wolfgang Maass"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003511.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustration_of_the_network_model_/976812", "title"=>"Illustration of the network model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-27 03:20:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1438209"], "description"=>"<p>(A) Illustration of the input encoding for sequence <i>AB-delay-ab</i>. The upper plot shows one example input spike train (blue dots) plotted on top of the mean firing rate (100 out of 200 afferent neurons shown). The lower panel shows the finite state grammar graph that represents the simple working memory task. The graph can be used to generate symbol sequences by following any path from <i>Start</i> to <i>Exit</i>. In the first state (<i>Start</i>) a random decision is made, which of the four paths to take. This decision determines all arcs that are passed throughout the sequence. On each arc that is passed the symbol next to the arc is emitted (and provided as input to the WTA circuit in the form of some 200-dimensional rate pattern). (B,C) Evoked activity of the WTA circuit for one example input sequence before learning (B) and for each of the four sequences after learning (C). The network activity is averaged and smoothed over 100 trial runs (gray traces), the blue dots show the spiking activity for one trial run. The input sequences are labeled by their pattern symbols on top of each plot. The neurons are sorted by the time of their highest average activity over all four sequences, after learning. For each sequence a different assembly of neurons becomes active in the WTA circuit. Dotted black lines indicate the boundaries between assemblies. Since the 4 assemblies that emerged have virtually no overlap, the WTA circuit has recovered the structure of the hidden states that underlie the task. (D) The lateral weights that emerged through STDP. The neurons are sorted using the same sorting algorithm as in (B,C). The black dotted lines correspond to assembly boundaries, neurons that fired on average less than one spike per sequence are not shown. Each neuron has learned to fire after a distinct set of predecessors, which reflects the sequential order of assembly firing. The stochastic switches between sequences are represented by enhanced weights between neurons active at the sequence onsets.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Circuit models", "neuroscience", "Neural homeostasis", "neural networks", "encoded", "neural", "assemblies", "hmm", "wta", "circuit"], "article_id"=>976813, "categories"=>["Biological Sciences"], "users"=>["David Kappel", "Bernhard Nessler", "Wolfgang Maass"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003511.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Emergence_of_working_memory_encoded_in_neural_assemblies_through_weak_HMM_learning_in_a_WTA_circuit_through_STDP_/976813", "title"=>"Emergence of working memory encoded in neural assemblies through weak HMM learning in a WTA circuit through STDP.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-27 03:20:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1438212"], "description"=>"<p>(A,B) The output behavior of a trained network for sequence <i>AB-delay-ab</i>. The network input is indicated by pattern symbols on top of the plot and pattern borders (gray vertical lines). (A) The average firing behavior of the network during evoked activity. The 30 circuit neurons that showed highest activity for this sequence are shown. The remaining neurons were almost perfectly silent. The network activity is averaged over 100 trial runs and neurons are sorted by the time of maximum average activity. Detailed spiking activities for three example neurons that became active after the delay pattern are shown. Each plot shows 20 example spike trains. (B) Spontaneous completion of sequence <i>AB-delay-free</i>. After presenting the cue sequence <i>AB</i> and the delay pattern for 150 ms the afferent input was turned off, letting the network run driven solely by lateral connections. During this spontaneous activity, the neurons are activated in the same sequential order as in the evoked trials. Detailed spiking activity is shown for the same three example neurons as in (A). (C) Histograms of the rank order correlation between the evoked and spontaneous network activity for all four sequences, computed over 100 trial runs. The sequential order of neural firing is reliably reproduced during the spontaneous activity and thus the structure of the hidden state is correctly completed.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Circuit models", "neuroscience", "Neural homeostasis", "neural networks", "replay"], "article_id"=>976816, "categories"=>["Biological Sciences"], "users"=>["David Kappel", "Bernhard Nessler", "Wolfgang Maass"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003511.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Spontaneous_replay_of_pattern_sequences_/976816", "title"=>"Spontaneous replay of pattern sequences.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-27 03:20:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1438213"], "description"=>"<p>(A,B) Mean firing rate of the circuit neurons for evoked activity during pattern <i>a</i> in sequence <i>AB-delay-ab</i> (A) and <i>BA-delay-ba</i> (B). A threshold of 10 Hz (dashed line) was used to distinguish between neurons that were active or inactive during the pattern. Firing rates of neurons that were not context selective are shown in green, that of neurons selective for starting sequences <i>AB</i> and <i>BA</i> are shown in red and blue, respectively. Neurons that did not fall in one of these groups are not shown. Spike trains of one context selective (C) and one non-selective (D) neuron are presented for spontaneous completion of sequence <i>AB-delay-ab</i> (upper) and <i>BA-delay-ba</i> (lower) (cue phase is not shown). Spike raster plots over 20 trial runs and corresponding averaged neural activity (PETH) are shown. The two neurons encode the input on different levels of abstraction. The neuron in panel (D) shows context cell behavior, since it encodes pattern <i>a</i> only if it occurs in the context of sequence <i>ab</i>. During <i>ba</i> it remains (almost) perfectly silent. The neuron in (C) is not context selective, but nevertheless fires reliably during the time slot of pattern <i>a</i> during the free run by integrating information from other (context selective) neurons. It belongs to a WTA circuit with 15 neurons, for which the network state projection is shown in panel (E). (E,F) Linear projection of the network activity during the delay phase to the first two components of the jPCA, for a single WTA circuit with 15 neurons (E) and for the whole network (F). 10 trajectories are plotted for each sequence (<i>AB-delay-ab</i> red, <i>BA-delay-ba</i> green, <i>CD-delay-cd</i> blue, <i>DC-delay-dc</i> yellow). The dots at the beginning of each line, indicate the onsets of the delay state, i.e. the beginning of the trajectories. The plots have arbitrary scale. The projection of the WTA circuit in (E) does not allow a linear separation between all four sequences, whereas the activity of the whole network (F) clusters into four sequence-specific regions. The network neurons use this state representation to modulate their behavior during spontaneous activity.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Circuit models", "neuroscience", "Neural homeostasis", "neural networks", "selectivity", "networks", "interconnected", "wta"], "article_id"=>976817, "categories"=>["Biological Sciences"], "users"=>["David Kappel", "Bernhard Nessler", "Wolfgang Maass"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003511.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mixed_selectivity_in_networks_of_multiple_interconnected_WTA_circuits_/976817", "title"=>"Mixed selectivity in networks of multiple interconnected WTA circuits.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-27 03:20:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1438224"], "description"=>"<p>(A) A network was trained with an extended delay phase of 500 ms. Input spike trains of a single run for sequence <i>A-delay</i> (25 out of 100 afferent neurons). Throughout the delay phase the afferent neurons fire with fixed stationary Poisson rates. (B) The output behavior for sequence <i>A-delay</i> averaged over 100 trial runs. The circuit neurons are sorted according to their mean firing time within the sequences (120 out of 704 neurons are shown). (C) Histograms of the rank order correlation between the evoked and spontaneous network activity. The sequential order of neural firing is preserved during spontaneous activity. (D,E) Homeostatic plasticity enhances the formation of this sequential structure. The output behavior of the network trained with STDP and the homeostatic plasticity mechanism is shown. Approximately 50% of the neurons encode each of the two sequence. The neurons learn to fire at a specific point in time within the delay patterns, building up stable trajectories.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Circuit models", "neuroscience", "Neural homeostasis", "neural networks", "trajectories", "stationary"], "article_id"=>976819, "categories"=>["Biological Sciences"], "users"=>["David Kappel", "Bernhard Nessler", "Wolfgang Maass"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003511.g005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Neural_trajectories_emerge_for_stationary_input_patterns_/976819", "title"=>"Neural trajectories emerge for stationary input patterns.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-27 03:20:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1438225"], "description"=>"<p>(A) The artificial grammar from <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003511#pcbi.1003511-Conway1\" target=\"_blank\">[27]</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003511#pcbi.1003511-Gomez1\" target=\"_blank\">[74]</a> represented as a finite state grammar graph. Grammatical sequences are generated by following a path from <i>Start</i> to <i>Exit</i>. If a node has more than one outgoing arc one is chosen at random with equal probability to continue the path. (B) Convergence of the network performance on that task. The blue curve shows the evolution of the mean classification performance against the number of training samples, when forward sampling was used. The blue shaded area indicates the standard deviation over 20 trial runs. After 80 training samples the network exceeds human performance reported in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003511#pcbi.1003511-Conway1\" target=\"_blank\">[27]</a>. Using rejection sampling with 10 samples on average (red curve) does not significantly outperform forward sampling on this task.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Circuit models", "neuroscience", "Neural homeostasis", "neural networks"], "article_id"=>976820, "categories"=>["Biological Sciences"], "users"=>["David Kappel", "Bernhard Nessler", "Wolfgang Maass"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003511.g006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Fast_learning_of_an_artificial_grammar_/976820", "title"=>"Fast learning of an artificial grammar.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-27 03:20:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1438229"], "description"=>"<p>(A) The grammar graph used for this task. A three letter sequence composed of <i>A</i>s and <i>B</i>s identifies the last symbol, <i>C</i> or <i>D</i>. Therefore, the most salient information is provided at the end of the sequence. (B) The classification rate on this task is plotted for forward (green) and rejection sampling (red). The error bars indicate the standard deviation over 10 trial runs. Rejection sampling significantly increases the classification performance on this task. (C,D) Comparison of the time courses of the instantaneous input log likelihood for a legal input sequence <i>BBAC</i> (C) and an illegal sequence <i>BBAD</i> (D). Input patterns are indicated by the pattern symbols on top of the plots. The upper plot shows the output spike trains of the network, the lower plot shows the traces of the instantaneous input likelihood plotted in the log domain, which indicates the ability of the network to predict the continuation of the afferent spike train. The trace in (D) shows a strong negative peak at the illegal transition at 150 ms. The prediction model that emerged through STDP augmented with rejection sampling, enables the network to detect illegal sequences.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Circuit models", "neuroscience", "Neural homeostasis", "neural networks", "sampling", "classification"], "article_id"=>976824, "categories"=>["Biological Sciences"], "users"=>["David Kappel", "Bernhard Nessler", "Wolfgang Maass"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003511.g007"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Rejection_sampling_enhances_the_classification_performance_of_the_network_/976824", "title"=>"Rejection sampling enhances the classification performance of the network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-27 03:20:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1438234"], "description"=>"<p>Comparison of the sampling approximations to standard HMM learning. The performance is assessed by the log likelihood averaged over 50 trial runs. The plots show average convergence properties of: forward sampling (solid blue), importance sampling over 10 (dashed yellow) and 100 trials on average (solid yellow), rejection sampling over 10 (dashed red) and 100 trials (solid red), rejection sampling with the simple linear tracking of over 10 (dashed green) and 100 trials on average (solid green), and the Baum-Welch algorithm (solid black). With increased number of samples the performance of the algorithm converges towards the solution of the standard EM algorithm. There was no significant performance difference between rejection and importance sampling. The simple tracking mechanism for the rejection sampler is outperformed by the exact algorithm, but still a significant performance gain with increased number of samples can be observed.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Circuit models", "neuroscience", "Neural homeostasis", "neural networks", "convergence", "sampling"], "article_id"=>976829, "categories"=>["Biological Sciences"], "users"=>["David Kappel", "Bernhard Nessler", "Wolfgang Maass"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003511.g008"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_the_convergence_speed_and_learning_performance_of_different_sampling_methods_/976829", "title"=>"Comparison of the convergence speed and learning performance of different sampling methods.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-27 03:20:35"}

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Relative Metric

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