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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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Subjective contour effect in HTM. 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.
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pcbi-1000532-g015: Subjective contour effect in HTM. 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.

Mentions: We then tested the network on a Kanizsa square test pattern. Figure 14 shows the response of the network to the Kanizsa square test pattern. The network classifies this pattern as a rectangle, even though this type of pattern was not seen during training. We examined the network for the presence of illusory contour responses. Illusory contour responses are characterized by top-down activations with no bottom-up activation. We used the capability of Numenta's software to inspect the node states of a network to probe for illusory contour responses. Figure 15 shows the feed-forward and feedback inputs to nodes at 4 different locations. The subjective contour effect can be seen in Figure 15(C). There are no actual contours in the receptive field of this node. Therefore, the feed-forward input of this node is zero. However, the feedback input is nonzero because the network expects the edges of a rectangle. This is the subjective contour effect.


Towards a mathematical theory of cortical micro-circuits.

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

Subjective contour effect in HTM. 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.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2749218&req=5

pcbi-1000532-g015: Subjective contour effect in HTM. 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.
Mentions: We then tested the network on a Kanizsa square test pattern. Figure 14 shows the response of the network to the Kanizsa square test pattern. The network classifies this pattern as a rectangle, even though this type of pattern was not seen during training. We examined the network for the presence of illusory contour responses. Illusory contour responses are characterized by top-down activations with no bottom-up activation. We used the capability of Numenta's software to inspect the node states of a network to probe for illusory contour responses. Figure 15 shows the feed-forward and feedback inputs to nodes at 4 different locations. The subjective contour effect can be seen in Figure 15(C). There are no actual contours in the receptive field of this node. Therefore, the feed-forward input of this node is zero. However, the feedback input is nonzero because the network expects the edges of a rectangle. This is the subjective contour effect.

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