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Towards a mathematical theory of cortical micro-circuits.

George D, Hawkins J - PLoS Comput. Biol. (2009)

Bottom Line: 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 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.

View Article: PubMed Central - PubMed

Affiliation: Numenta Inc., Redwood City, California, United States of America. dgeorge@numenta.com

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.

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Generative model for HTM.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.
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pcbi-1000532-g001: Generative model for HTM.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.

Mentions: HTMs can be specified mathematically using a generative model. A simplified two-level generative model is shown in Figure 1. Each node in the hierarchy contains a set of coincidence patterns and a set of Markov chains where each Markov chain is defined over a subset of the set coincidence patterns in that node. A coincidence pattern in a node represents a co-activation of the Markov chains of its child nodes. A coincidence pattern that is generated by sampling a Markov chain in a higher level node concurrently activates its constituent Markov chains in the lower level nodes. For a particular coincidence pattern and Markov chain that is ‘active’ at a higher-level node, sequences of coincidence patterns are generated concurrently by sampling from the activated Markov chains of the child nodes.


Towards a mathematical theory of cortical micro-circuits.

George D, Hawkins J - PLoS Comput. Biol. (2009)

Generative model for HTM.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.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2749218&req=5

pcbi-1000532-g001: Generative model for HTM.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.
Mentions: HTMs can be specified mathematically using a generative model. A simplified two-level generative model is shown in Figure 1. Each node in the hierarchy contains a set of coincidence patterns and a set of Markov chains where each Markov chain is defined over a subset of the set coincidence patterns in that node. A coincidence pattern in a node represents a co-activation of the Markov chains of its child nodes. A coincidence pattern that is generated by sampling a Markov chain in a higher level node concurrently activates its constituent Markov chains in the lower level nodes. For a particular coincidence pattern and Markov chain that is ‘active’ at a higher-level node, sequences of coincidence patterns are generated concurrently by sampling from the activated Markov chains of the child nodes.

Bottom Line: 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 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.

View Article: PubMed Central - PubMed

Affiliation: Numenta Inc., Redwood City, California, United States of America. dgeorge@numenta.com

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.

Show MeSH
Related in: MedlinePlus