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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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Reduced subjective contour effect.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 Figure 15(C). 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.
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pcbi-1000532-g016: Reduced subjective contour effect.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 Figure 15(C). 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.

Mentions: We did an additional experiment where we presented a corrupted Kanizsa square identical to one of the control experiments used in [64]. As shown in Figure 16, the corrupted rectangle produces a subjective contour response similar to, but substantially weaker than, the one produced by an intact Kanizsa figure. This is consistent with the results that Nguyen and Lee saw in monkeys. In our experiment the corrupted figure was recognized as a rectangle at the top of the network, albeit with a lower level of certainty. This lower level of certainty is reflected in the lower activation level of the subjective contour. Had we put a threshold on the strength of recognition at the top level to filter out input images that were not close to any category, we could have reduced the subjective contour response to close to zero.


Towards a mathematical theory of cortical micro-circuits.

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

Reduced subjective contour effect.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 Figure 15(C). 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.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000532-g016: Reduced subjective contour effect.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 Figure 15(C). 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.
Mentions: We did an additional experiment where we presented a corrupted Kanizsa square identical to one of the control experiments used in [64]. As shown in Figure 16, the corrupted rectangle produces a subjective contour response similar to, but substantially weaker than, the one produced by an intact Kanizsa figure. This is consistent with the results that Nguyen and Lee saw in monkeys. In our experiment the corrupted figure was recognized as a rectangle at the top of the network, albeit with a lower level of certainty. This lower level of certainty is reflected in the lower activation level of the subjective contour. Had we put a threshold on the strength of recognition at the top level to filter out input images that were not close to any category, we could have reduced the subjective contour response to close to zero.

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