Towards a Mathematical Theory of Cortical Micro-circuits
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{"title"=>"Towards a mathematical theory of cortical micro-circuits", "type"=>"journal", "authors"=>[{"first_name"=>"Dileep", "last_name"=>"George", "scopus_author_id"=>"8411588200"}, {"first_name"=>"Jeff", "last_name"=>"Hawkins", "scopus_author_id"=>"15022121900"}], "year"=>2009, "source"=>"PLoS Computational Biology", "identifiers"=>{"issn"=>"1553734X", "isbn"=>"1553-734X", "pmid"=>"19816557", "doi"=>"10.1371/journal.pcbi.1000532", "pui"=>"358060334", "scopus"=>"2-s2.0-73349116544", "sgr"=>"73349116544"}, "id"=>"03decfc9-3876-3f35-afc9-2f0665479d7c", "abstract"=>"The theoretical setting of hierarchical Bayesian inference is gaining acceptance as a framework for understanding cortical computation. In this paper, we describe how Bayesian belief propagation in a spatio-temporal hierarchical model, called Hierarchical Temporal Memory (HTM), can lead to a mathematical model for cortical circuits. An HTM node is abstracted using a coincidence detector and a mixture of Markov chains. Bayesian belief propagation equations for such an HTM node define a set of functional constraints for a neuronal implementation. Anatomical data provide a contrasting set of organizational constraints. The combination of these two constraints suggests a theoretically derived interpretation for many anatomical and physiological features and predicts several others. We describe the pattern recognition capabilities of HTM networks and demonstrate the application of the derived circuits for modeling the subjective contour effect. We also discuss how the theory and the circuit can be extended to explain cortical features that are not explained by the current model and describe testable predictions that can be derived from the model.", "link"=>"http://www.mendeley.com/research/towards-mathematical-theory-cortical-microcircuits", "reader_count"=>549, "reader_count_by_academic_status"=>{"Unspecified"=>2, "Professor > Associate Professor"=>38, "Librarian"=>1, "Researcher"=>139, "Student > Doctoral Student"=>10, "Student > Ph. D. Student"=>165, "Student > Postgraduate"=>15, "Student > Master"=>66, "Other"=>36, "Student > Bachelor"=>29, "Lecturer"=>10, "Lecturer > Senior Lecturer"=>3, "Professor"=>35}, "reader_count_by_user_role"=>{"Unspecified"=>2, "Professor > Associate Professor"=>38, "Librarian"=>1, "Researcher"=>139, "Student > Doctoral Student"=>10, "Student > Ph. D. Student"=>165, "Student > Postgraduate"=>15, "Student > Master"=>66, "Other"=>36, "Student > Bachelor"=>29, "Lecturer"=>10, "Lecturer > Senior Lecturer"=>3, "Professor"=>35}, "reader_count_by_subject_area"=>{"Unspecified"=>2, "Agricultural and Biological Sciences"=>141, "Arts and Humanities"=>4, "Philosophy"=>3, "Business, Management and Accounting"=>1, "Chemistry"=>2, "Computer Science"=>174, "Economics, Econometrics and Finance"=>2, "Engineering"=>71, "Materials Science"=>1, "Mathematics"=>17, "Medicine and Dentistry"=>25, "Neuroscience"=>34, "Design"=>1, "Physics and Astronomy"=>26, "Psychology"=>36, "Social Sciences"=>6, "Immunology and Microbiology"=>1, "Linguistics"=>2}, "reader_count_by_subdiscipline"=>{"Materials Science"=>{"Materials Science"=>1}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>25}, "Social Sciences"=>{"Social Sciences"=>6}, "Physics and Astronomy"=>{"Physics and Astronomy"=>26}, "Psychology"=>{"Psychology"=>36}, "Mathematics"=>{"Mathematics"=>17}, "Unspecified"=>{"Unspecified"=>2}, "Arts and Humanities"=>{"Arts and Humanities"=>4}, "Design"=>{"Design"=>1}, "Engineering"=>{"Engineering"=>71}, "Chemistry"=>{"Chemistry"=>2}, "Neuroscience"=>{"Neuroscience"=>34}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>2}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>141}, "Computer Science"=>{"Computer Science"=>174}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Linguistics"=>{"Linguistics"=>2}, "Philosophy"=>{"Philosophy"=>3}}, "reader_count_by_country"=>{"Republic of Singapore"=>2, "United States"=>38, "Portugal"=>4, "Russia"=>1, "Saudi Arabia"=>1, "Sweden"=>5, "Netherlands"=>2, "South Korea"=>2, "Austria"=>2, "Korea (South)"=>1, "Luxembourg"=>1, "China"=>2, "Ireland"=>2, "Brazil"=>1, "Poland"=>1, "Slovakia"=>2, "France"=>4, "Chile"=>1, "Argentina"=>1, "Japan"=>5, "United Kingdom"=>16, "Belarus"=>1, "Switzerland"=>4, "Spain"=>3, "India"=>1, "Canada"=>2, "Belgium"=>1, "Norway"=>2, "Finland"=>3, "Denmark"=>1, "Italy"=>5, "South Africa"=>1, "Australia"=>4, "Germany"=>12}, "group_count"=>37}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/436340", "https://ndownloader.figshare.com/files/436353", "https://ndownloader.figshare.com/files/436366", "https://ndownloader.figshare.com/files/436373", "https://ndownloader.figshare.com/files/436385", "https://ndownloader.figshare.com/files/436396", "https://ndownloader.figshare.com/files/436416"], "description"=>"<div><p>The theoretical setting of hierarchical Bayesian inference is gaining acceptance as a framework for understanding cortical computation. In this paper, we describe how Bayesian belief propagation in a spatio-temporal hierarchical model, called Hierarchical Temporal Memory (HTM), can lead to a mathematical model for cortical circuits. An HTM node is abstracted using a coincidence detector and a mixture of Markov chains. Bayesian belief propagation equations for such an HTM node define a set of functional constraints for a neuronal implementation. Anatomical data provide a contrasting set of organizational constraints. The combination of these two constraints suggests a theoretically derived interpretation for many anatomical and physiological features and predicts several others. We describe the pattern recognition capabilities of HTM networks and demonstrate the application of the derived circuits for modeling the subjective contour effect. We also discuss how the theory and the circuit can be extended to explain cortical features that are not explained by the current model and describe testable predictions that can be derived from the model.</p></div>", "links"=>[], "tags"=>["mathematical", "cortical", "micro-circuits"], "article_id"=>146044, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.s001", "https://dx.doi.org/10.1371/journal.pcbi.1000532.s002", "https://dx.doi.org/10.1371/journal.pcbi.1000532.s003", "https://dx.doi.org/10.1371/journal.pcbi.1000532.s004", "https://dx.doi.org/10.1371/journal.pcbi.1000532.s005", "https://dx.doi.org/10.1371/journal.pcbi.1000532.s006", "https://dx.doi.org/10.1371/journal.pcbi.1000532.s007"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Towards_a_Mathematical_Theory_of_Cortical_Micro_circuits/146044", "title"=>"Towards a Mathematical Theory of Cortical Micro-circuits", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2009-10-09 01:40:44"}
  • {"files"=>["https://ndownloader.figshare.com/files/880335"], "description"=>"<p>Hierarchical Temporal Memory (HTM) is a model of neocortical function. HTMs can be specified using a generative model. Shown is a simple two-level three-node HTM-type generative model. Each node in the hierarchy contains a set of coincidence patterns (labeled with ) and a set of Markov chains (labeled with ) defined over the set of coincidence patterns. A coincidence pattern in a node represents a co-activation of particular Markov chains of its child nodes. HTM generative model is a spatio-temporal hierarchy in which higher levels remain stable for longer durations of time and can generate faster changing activations in lower levels.</p>", "links"=>[], "tags"=>["neuroscience/theoretical neuroscience", "neuroscience/natural and synthetic vision"], "article_id"=>550798, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Generative_model_for_HTM_/550798", "title"=>"Generative model for HTM.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:13:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/880461"], "description"=>"<p>(A) Structure of the reference node, with five coincidence patterns and two Markov chains. This is an HTM node that has finished its learning process. It is assumed that this is the first node at level 2 of a network and is therefore labeled as . Each coincidence pattern represents a co-occurrence of the Markov chains of the children. This node has 2 children. Child 1 has 3 Markov chains and child 2 has 4 Markov chains – hence there are seven elements in each coincidence pattern. The portions of the coincidence pattern coming from the first and second child are shown in different shades of gray. (B) Information flow in the reference node for the computation of the belief propagation equations shown in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000532#pcbi-1000532-t001\" target=\"_blank\">Table 1</a>. The rectangles inside the node are processing units for the equations in the rows corresponding to the number displayed in each rectangle. We will use ‘feed-forward’ or ‘bottom-up’ to qualify messages received from children and messages sent up to the parent of this node. We will use ‘feedback’ or ‘top-down’ to qualify messages received from the parent and messages sent to the child nodes of this node. The node shown in the figure has two bottom-up input messages coming from the two children and has two top-down outputs which are the messages sent to these children. The arrows show vectors of inputs, outputs, and intermediate computational results. The number of components of each vector is represented using an array of boxes placed on these arrows.</p>", "links"=>[], "tags"=>["htm"], "article_id"=>550925, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Structure_and_flow_of_a_reference_HTM_node_/550925", "title"=>"Structure and flow of a reference HTM node.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:15:25"}
  • {"files"=>["https://ndownloader.figshare.com/files/880523"], "description"=>"<p>Circuit for calculating the bottom-up probability over coincidence patterns. Coincidence pattern neurons are represented by diamond shapes. The inputs to the circuit are the messages from the children, which are denoted by and . The output of the circuit is , as calculated by Equation 2 in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000532#pcbi-1000532-t001\" target=\"_blank\">Table 1</a>. The input connections to each neuron represent its coincidence pattern. For example, is the co-occurrence of Markov chain 3 from the left child and Markov chain 1 from the right child. The probabilities are calculated by multiplying the inputs to each neuron.</p>", "links"=>[], "tags"=>["neuroscience/theoretical neuroscience", "neuroscience/natural and synthetic vision"], "article_id"=>550988, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Coincidence_likelihood_circuit_/550988", "title"=>"Coincidence likelihood circuit.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:16:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/880566"], "description"=>"<p>The circuit for calculating the likelihoods of Markov chains based on a sequence of inputs. In this figure there are five possible bottom-up input patterns (c1–c5) and two Markov chains (g1, g2). The circle neurons represent a specific bottom-up coincidence within a learned Markov chain (two Markov chains are shown, one in blue and one in green). Each rectangular neuron represents the likelihood of an entire Markov chain to be passed to a parent node. This circuit implements the dynamic programming Equation 4 in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000532#pcbi-1000532-t001\" target=\"_blank\">Table 1</a>.</p>", "links"=>[], "tags"=>["neuroscience/theoretical neuroscience", "neuroscience/natural and synthetic vision"], "article_id"=>551033, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Markov_chain_likelihood_circuit_/551033", "title"=>"Markov chain likelihood circuit.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:17:13"}
  • {"files"=>["https://ndownloader.figshare.com/files/880633"], "description"=>"<p>Circuit for calculating the belief distribution over coincidence patterns by integrating the sequence of bottom-up inputs with the top-down inputs. The pentagon-shaped neurons are the belief neurons. These neurons pool over all the neurons representing the same coincidence in different Markov chains to calculate the belief value for each coincidence pattern. This circuit implements the Equation 6 in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000532#pcbi-1000532-t001\" target=\"_blank\">Table 1</a>.</p>", "links"=>[], "tags"=>["neuroscience/theoretical neuroscience", "neuroscience/natural and synthetic vision"], "article_id"=>551096, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Belief_circuit_/551096", "title"=>"Belief circuit.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:18:16"}
  • {"files"=>["https://ndownloader.figshare.com/files/880702"], "description"=>"<p>The circuit for computing the messages to be sent to children according to Equation 9. The two sets of hexagonal neurons correspond to the Markov chains of the two children of the reference node.</p>", "links"=>[], "tags"=>["neuroscience/theoretical neuroscience", "neuroscience/natural and synthetic vision"], "article_id"=>551168, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Feedback_message_circuit_/551168", "title"=>"Feedback message circuit.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:19:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/880764"], "description"=>"<p>The same circuit as shown in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000532#pcbi-1000532-g005\" target=\"_blank\">Figure 5</a> with the addition of circuitry for incorporating variable time delays between elements of the Markov chains. The pentagon neurons represent the belief at each node. The rounded rectangle neurons represent the belief at each node at the appropriate time delay. An external variable time delay mechanism provides time duration information to all the neurons involved in encoding sequences.</p>", "links"=>[], "tags"=>["neuroscience/theoretical neuroscience", "neuroscience/natural and synthetic vision"], "article_id"=>551222, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g007"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Timing_circuit_/551222", "title"=>"Timing circuit.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:20:22"}
  • {"files"=>["https://ndownloader.figshare.com/files/880872"], "description"=>"<p>(A) Schematic of neocortex inside the skull. The neocortex is a thin sheet of several layers of neurons. Different areas of the neocortical sheet process different information. Three successive areas of the visual hierarchy – V1, V2 and V4 – are marked on this sheet. The connections between the areas are reciprocal. The feed-forward connections are represented using green arrows and the feedback connections are represented using red arrows. (B) A slice of the neocortical sheet, showing its six layers and columnar organization. The cortical layers are numbered 1 to 6: layer 1 is closest to the skull, and layer 6 is the inner layer, closest to the white matter. (C) Areas in the neocortex are connected in a hierarchical manner. This diagram shows the logical hierarchical arrangement of the areas which are physically organized as shown in (A). (D) An HTM network that corresponds to the logical cortical hierarchy shown in (C). The number of nodes shown at each level in the HTM hierarchy is greatly reduced for clarity. Also, in real HTM networks the receptive fields of the nodes overlap. Here they are shown non-overlapping for clarity.</p>", "links"=>[], "tags"=>["neocortex", "hierarchy", "htm"], "article_id"=>551338, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g008"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mapping_between_neocortex_hierarchy_and_HTM_hierarchy_/551338", "title"=>"Mapping between neocortex hierarchy and HTM hierarchy.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:22:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/880981"], "description"=>"<p>The circuit shown here corresponds exactly to the instantiation of the reference HTM node shown in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000532#pcbi-1000532-g002\" target=\"_blank\">Figure 2</a>. The five vertical ‘columns’ in the circuit correspond to the 5 coincidence patterns stored in the reference node. Layers 1 to 6 are marked according to the standard practice in neuroscience. Emphasis is given to the functional connectivity between neurons and the placement of the cell bodies and dendrites. Detailed dendritic morphologies are not shown. Axons are shown using arrow-tipped lines. Feed-forward inputs and outputs are shown using green axons and feedback inputs and outputs are shown using red axons. Whether an axon is an input or output can be determined by looking at the direction of the arrows. The blue axons entering and exiting the region represent timing-duration signals. ‘T’ junctions represent the branching of axons. However, axonal crossings at ‘X’ junctions do not connect to each other. Inter-columnar connections exist mostly between neurons in layer 2/3, between layer 5 cells, and between layer 6 cells. The inter-columnar connections in layer 2/3 that represent sequence memories are represented using thicker lines.</p>", "links"=>[], "tags"=>["laminar", "instantiation", "bayesian", "propagation", "equations", "htm"], "article_id"=>551435, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g009"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_laminar_biological_instantiation_of_the_Bayesian_belief_propagation_equations_used_in_the_HTM_nodes_/551435", "title"=>"A laminar biological instantiation of the Bayesian belief propagation equations used in the HTM nodes.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:23:55"}
  • {"files"=>["https://ndownloader.figshare.com/files/881131"], "description"=>"<p>(A) A single idealized cortical column. This idealization could correspond to what is often referred to as a biological mini-column. It is analogous to one of the five columnar structures in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000532#pcbi-1000532-g009\" target=\"_blank\">Figure 9</a>. (B) A more dense arrangement of cells comprising several copies of the column (A). Although we typically show single cells performing computations, we assume there is always redundancy and that multiple cells within each layer are performing similar functions.</p>", "links"=>[], "tags"=>["neuroscience/theoretical neuroscience", "neuroscience/natural and synthetic vision"], "article_id"=>551601, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g010"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Columnar_organization_of_the_microcircuit_/551601", "title"=>"Columnar organization of the microcircuit.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:26:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/881236"], "description"=>"<p>Figures A and B show the effect of top-down propagation in HTM networks. The top half of each figure shows the original image submitted to the HTM, along with blue bars illustrating the recognition scores on the top five of the eight categories on which the network was trained. The bottom-left panel in each figure shows the input image after Gabor filtering. The bottom-right panel in each figure shows the image obtained after the feedback propagation of the winning category at the top of the HTM network. In these Gabor-space images, the colors illustrate different orientations, but the details of the color map are not pertinent. A). The input image has a car superposed on background clutter. The network recognizes the car. Top-down propagation segments out the car's contours from that of the background. B). The input image contains multiple objects superposed on a cluttered background and with some foreground occlusions. The network recognition result identifies teddy bear as the top category. Feedback propagation of this winning category correctly isolates the contours corresponding to the teddy bear.</p>", "links"=>[], "tags"=>["neuroscience/theoretical neuroscience", "neuroscience/natural and synthetic vision"], "article_id"=>551692, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g011"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Top_down_segmentation_/551692", "title"=>"Top-down segmentation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:28:12"}
  • {"files"=>["https://ndownloader.figshare.com/files/881334"], "description"=>"<p>A Kanizsa square (left) and a Kanizsa triangle (right) are shown.</p>", "links"=>[], "tags"=>["neuroscience/theoretical neuroscience", "neuroscience/natural and synthetic vision"], "article_id"=>551793, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g012"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Kanizsa_diagrams_/551793", "title"=>"Kanizsa diagrams.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:29:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/881389"], "description"=>"<p>The top two rows are examples of training images. The bottom three rows are examples of correctly recognized test images. The last row shows test images that incorporated distracter backgrounds.</p>", "links"=>[], "tags"=>["images", "htm", "trained"], "article_id"=>551854, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g013"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Examples_of_training_and_testing_images_for_an_HTM_network_trained_for_visual_object_recognition_/551854", "title"=>"Examples of training and testing images for an HTM network trained for visual object recognition.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:30:54"}
  • {"files"=>["https://ndownloader.figshare.com/files/881491"], "description"=>"<p>The network was not shown Kanizsa squares during training. The bar graph displays the order of recognition certainty of the HTM.</p>", "links"=>[], "tags"=>["kanizsa", "htm"], "article_id"=>551956, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g014"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Recognition_of_the_Kanizsa_square_by_an_HTM_network_/551956", "title"=>"Recognition of the Kanizsa square by an HTM network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:32:36"}
  • {"files"=>["https://ndownloader.figshare.com/files/881577"], "description"=>"<p>. Feed-forward and feedback inputs of 4 different nodes at level 1 of the HTM network for the Kanizsa rectangle stimulus. Four figures, (a) to (d), are shown corresponding to 4 different nodes from which the responses are recorded. In each figure, the left top panel is the input stimulus and the left bottom panel is the input stimulus as seen by the network after Gabor filtering. In these panels, the receptive field of the HTM node is indicated using a small blue square. In each figure, the top-right panel shows the feed-forward input to the node and the bottom-right panel shows the feedback input to the node. The feed-forward inputs correspond to the activity on thalamo-cortical projections. The feedback inputs correspond to the activations of the layer 6 cells that project backward from the higher level in the hierarchy. (a) The receptive field of this node does not contain any edges. There is no feed-forward input and no feedback input. (b) The receptive field of this node has a real contour in its input field. The node has both feed-forward and feedback inputs. (c) The subjective contour node. The receptive field of this node has no real contours. Therefore, the feed-forward input is zero. However, the feedback input is not zero because the network expects the edges of a rectangle. This is the subjective contour effect. (d) The opposite of the subjective contour effect. In this case, a real contour is present in the receptive field of this node but it does not contribute to the high-level perception of the rectangle. Hence the feedback input to this node is zero even though the feed-forward response is non-zero.</p>", "links"=>[], "tags"=>["contour"], "article_id"=>552041, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g015"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Subjective_contour_effect_in_HTM_/552041", "title"=>"Subjective contour effect in HTM", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:34:01"}
  • {"files"=>["https://ndownloader.figshare.com/files/881641"], "description"=>"<p>When presented with a corrupted version of a Kanizsa rectangle, the HTM still recognizes a rectangle but with reduced certainty. Shown are the feed-forward and feedback inputs to a node analogous to <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000532#pcbi-1000532-g015\" target=\"_blank\">Figure 15(C)</a>. The node is receiving feedback indicating the network expects an edge at this location, but the strength of this expectation is substantially reduced compared to a non-corrupted rectangle.</p>", "links"=>[], "tags"=>["subjective", "contour"], "article_id"=>552103, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.g016"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Reduced_subjective_contour_effect_/552103", "title"=>"Reduced subjective contour effect.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-10-09 00:35:03"}
  • {"files"=>["https://ndownloader.figshare.com/files/881725"], "description"=>"<p>Belief propagation equations for an HTM node.</p>", "links"=>[], "tags"=>["propagation", "equations", "htm"], "article_id"=>552189, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.t001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Belief_propagation_equations_for_an_HTM_node_/552189", "title"=>"Belief propagation equations for an HTM node.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2009-10-09 00:36:29"}
  • {"files"=>["https://ndownloader.figshare.com/files/881749"], "description"=>"<p>See <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000532#pcbi.1000532-Thomson1\" target=\"_blank\">[42]</a> for details on the anatomical features summarized in this table.</p>", "links"=>[], "tags"=>["anatomical", "computational"], "article_id"=>552210, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.t003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Summary_of_anatomical_features_and_their_proposed_computational_functions_/552210", "title"=>"Summary of anatomical features and their proposed computational functions.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2009-10-09 00:36:50"}
  • {"files"=>["https://ndownloader.figshare.com/files/881774"], "description"=>"<p>Summary of notation used for belief propagation in HTM nodes.</p>", "links"=>[], "tags"=>["notation", "propagation", "htm"], "article_id"=>552238, "categories"=>["Neuroscience"], "users"=>["Dileep George", "Jeff Hawkins"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000532.t002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Summary_of_notation_used_for_belief_propagation_in_HTM_nodes_/552238", "title"=>"Summary of notation used for belief propagation in HTM nodes.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2009-10-09 00:37:18"}

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  • {"month"=>"3", "scanned-page-browse"=>"0", "cited-by"=>"0", "abstract"=>"0", "full-text"=>"26", "year"=>"2012", "pdf"=>"2", "unique-ip"=>"23", "figure"=>"0", "scanned-summary"=>"0", "supp-data"=>"0"}
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  • {"month"=>"5", "scanned-page-browse"=>"0", "cited-by"=>"0", "abstract"=>"1", "full-text"=>"25", "year"=>"2012", "pdf"=>"9", "unique-ip"=>"22", "figure"=>"1", "scanned-summary"=>"0", "supp-data"=>"0"}
  • {"scanned-page-browse"=>"0", "month"=>"10", "cited-by"=>"0", "abstract"=>"1", "full-text"=>"5", "unique-ip"=>"7", "pdf"=>"4", "year"=>"2009", "figure"=>"0", "scanned-summary"=>"0", "supp-data"=>"0"}
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  • {"month"=>"6", "scanned-page-browse"=>"0", "cited-by"=>"1", "abstract"=>"0", "full-text"=>"21", "year"=>"2012", "pdf"=>"6", "unique-ip"=>"18", "figure"=>"1", "scanned-summary"=>"0", "supp-data"=>"0"}
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  • {"unique-ip"=>"19", "full-text"=>"16", "pdf"=>"5", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"16", "supp-data"=>"6", "cited-by"=>"0", "year"=>"2012", "month"=>"9"}
  • {"unique-ip"=>"25", "full-text"=>"44", "pdf"=>"4", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"3", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2012", "month"=>"10"}
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  • {"unique-ip"=>"25", "full-text"=>"26", "pdf"=>"5", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"3", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2013", "month"=>"7"}
  • {"unique-ip"=>"26", "full-text"=>"31", "pdf"=>"1", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2013", "month"=>"8"}
  • {"unique-ip"=>"17", "full-text"=>"17", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2013", "month"=>"9"}
  • {"unique-ip"=>"22", "full-text"=>"25", "pdf"=>"5", "abstract"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2013", "month"=>"10"}
  • {"unique-ip"=>"18", "full-text"=>"36", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2013", "month"=>"11"}
  • {"unique-ip"=>"16", "full-text"=>"22", "pdf"=>"5", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"5", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2013", "month"=>"12"}
  • {"unique-ip"=>"61", "full-text"=>"134", "pdf"=>"6", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"2", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2014", "month"=>"1"}
  • {"unique-ip"=>"32", "full-text"=>"32", "pdf"=>"14", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"2", "cited-by"=>"0", "year"=>"2014", "month"=>"2"}
  • {"unique-ip"=>"22", "full-text"=>"19", "pdf"=>"8", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"8", "supp-data"=>"6", "cited-by"=>"0", "year"=>"2014", "month"=>"3"}
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  • {"unique-ip"=>"25", "full-text"=>"33", "pdf"=>"10", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"16", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2014", "month"=>"4"}
  • {"unique-ip"=>"31", "full-text"=>"13", "pdf"=>"10", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"6", "cited-by"=>"2", "year"=>"2014", "month"=>"7"}
  • {"unique-ip"=>"17", "full-text"=>"12", "pdf"=>"5", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"13", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2014", "month"=>"8"}
  • {"unique-ip"=>"21", "full-text"=>"16", "pdf"=>"4", "abstract"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"2", "supp-data"=>"12", "cited-by"=>"0", "year"=>"2014", "month"=>"9"}
  • {"unique-ip"=>"31", "full-text"=>"27", "pdf"=>"5", "abstract"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"6", "supp-data"=>"2", "cited-by"=>"0", "year"=>"2014", "month"=>"10"}
  • {"unique-ip"=>"23", "full-text"=>"24", "pdf"=>"3", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"5", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2014", "month"=>"11"}
  • {"unique-ip"=>"20", "full-text"=>"23", "pdf"=>"4", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"3", "cited-by"=>"0", "year"=>"2014", "month"=>"12"}
  • {"unique-ip"=>"21", "full-text"=>"21", "pdf"=>"6", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2015", "month"=>"1"}
  • {"unique-ip"=>"17", "full-text"=>"17", "pdf"=>"6", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "month"=>"2"}
  • {"unique-ip"=>"19", "full-text"=>"23", "pdf"=>"5", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "month"=>"3"}
  • {"unique-ip"=>"16", "full-text"=>"14", "pdf"=>"8", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"5", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "month"=>"4"}
  • {"unique-ip"=>"15", "full-text"=>"18", "pdf"=>"3", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"4", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "month"=>"5"}
  • {"unique-ip"=>"22", "full-text"=>"21", "pdf"=>"10", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"2", "supp-data"=>"12", "cited-by"=>"0", "year"=>"2015", "month"=>"6"}
  • {"unique-ip"=>"13", "full-text"=>"16", "pdf"=>"5", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"10", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "month"=>"7"}
  • {"unique-ip"=>"19", "full-text"=>"16", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"5", "supp-data"=>"4", "cited-by"=>"0", "year"=>"2015", "month"=>"8"}
  • {"unique-ip"=>"27", "full-text"=>"38", "pdf"=>"12", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "month"=>"9"}
  • {"unique-ip"=>"22", "full-text"=>"20", "pdf"=>"5", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"2", "supp-data"=>"0", "cited-by"=>"1", "year"=>"2015", "month"=>"10"}
  • {"unique-ip"=>"33", "full-text"=>"34", "pdf"=>"12", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"2", "supp-data"=>"0", "cited-by"=>"2", "year"=>"2015", "month"=>"11"}
  • {"unique-ip"=>"23", "full-text"=>"22", "pdf"=>"5", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"15", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2015", "month"=>"12"}
  • {"unique-ip"=>"21", "full-text"=>"26", "pdf"=>"8", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"1"}
  • {"unique-ip"=>"19", "full-text"=>"18", "pdf"=>"6", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2016", "month"=>"2"}
  • {"unique-ip"=>"24", "full-text"=>"33", "pdf"=>"3", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"1", "year"=>"2016", "month"=>"3"}
  • {"unique-ip"=>"16", "full-text"=>"16", "pdf"=>"4", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"5", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"4"}
  • {"unique-ip"=>"17", "full-text"=>"19", "pdf"=>"5", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"5"}
  • {"unique-ip"=>"24", "full-text"=>"28", "pdf"=>"6", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"9", "supp-data"=>"2", "cited-by"=>"2", "year"=>"2016", "month"=>"6"}
  • {"unique-ip"=>"20", "full-text"=>"22", "pdf"=>"5", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"8", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2016", "month"=>"7"}
  • {"unique-ip"=>"13", "full-text"=>"23", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"1", "year"=>"2016", "month"=>"8"}
  • {"unique-ip"=>"7", "full-text"=>"5", "pdf"=>"3", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2016", "month"=>"9"}
  • {"unique-ip"=>"19", "full-text"=>"20", "pdf"=>"5", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"4", "cited-by"=>"0", "year"=>"2016", "month"=>"10"}
  • {"unique-ip"=>"25", "full-text"=>"29", "pdf"=>"4", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"13", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2016", "month"=>"11"}
  • {"unique-ip"=>"14", "full-text"=>"18", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"5", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"12"}
  • {"unique-ip"=>"18", "full-text"=>"17", "pdf"=>"4", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"2", "cited-by"=>"0", "year"=>"2017", "month"=>"1"}
  • {"unique-ip"=>"18", "full-text"=>"18", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"2"}
  • {"unique-ip"=>"21", "full-text"=>"23", "pdf"=>"5", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"3"}

Relative Metric

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