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Cited by 404Neural dynamics and brain functionMemory and Neural MechanismsNeural Networks and Applications

The DOI matches its Crossref record; 79 of the 81 references it cites were found in a registry or an index; none of the 99 sources its claims cite is checked for support yet.

Towards a Mathematical Theory of Cortical Micro-circuits

Open access
George, Dileep, Hawkins, Jeff·2009·PLoS Computational Biology
DOI 10.1371/journal.pcbi.1000532PMC PMC2749218
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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.

Overview

AI snapshot

Written from the paper’s full text.

TL;DR

The paper formulates Hierarchical Temporal Memory (HTM) as a Bayesian belief-propagation model of cortical microcircuits and maps its abstract neuronal implementation onto laminar and columnar cortical anatomy. It also reports HTM vision experiments, including object recognition benchmarks and a feedback-based model of the subjective contour effect.

Key findings

  • The authors derive belief-propagation equations for an HTM node using coincidence patterns and Markov chains, then propose a cortical mapping: layer 4 stellate cells for coincidence likelihood, layer 2/3 pyramidal cells for sequence states and feed-forward/feedback computations, layer 5 cells for belief and timing, and layer 6 cells for feedback messages to child regions.
  • On the Pictures line-drawing dataset, an HTM with Markov-chain temporal pooling only at level 1 achieved 49% recognition accuracy; adding temporal pooling at higher levels increased accuracy to 72%, compared with 35% for a nearest-neighbor classifier using the same top-level training paradigm.
  • On Caltech-101, initial HTM experiments achieved 50% recognition with 15 training images and 62% with 30 training images; on a 4-category grayscale set with over 10,000 training images, the network gave 92% accuracy on a holdout set. Temporal inference improved frame-by-frame recognition by up to 30% over sliding-window averaging (window length = 4).
  • In a Kanizsa square test, the network classified the pattern as a rectangle despite not being trained on Kanizsa squares; a node with no feed-forward contour input showed nonzero feedback, modeling the subjective contour effect, and a corrupted Kanizsa figure produced a weaker response.

Methods

  • Theoretical/modeling study: starts from the HTM generative model, derives Bayesian belief-propagation equations for an HTM node, builds an abstract neuron-like circuit, and maps it onto cortical layers and columns by matching computational specifications with anatomical data.
  • Experiments used Numenta’s NuPIC HTM networks for visual object recognition on the Pictures dataset (48 categories of 32×32 line drawings), Caltech-101, a 4-category grayscale dataset, temporal inference on Pictures, top-down segmentation, and subjective contour/Kanizsa tests.
  • Analysis consisted of benchmark recognition-accuracy comparisons and qualitative inspection of node feed-forward and feedback states; no biological experiments are reported.

Limitations

  • The paper states the model is a starting point, the biological mapping is not unique, and it does not address learning, attention, motor action, asynchronous messages, detailed dendritic properties, inhibitory cells, cortical maps, or sparse distributed representations within a node; it also assumes singly connected non-loopy networks for simplicity.
  • The paper states the timing/duration mechanism is conjectural, the non-specific thalamic timing loop lacks direct evidence, no recordings from non-specific thalamic cells were found, and the subjective contour results are preliminary.
  • Evident from the text: the biological predictions are largely untested, the benchmark experiments are from Numenta/NuPIC and not independent, and no statistical tests or error bars are reported for the recognition results.

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Registry

Crossref · 10.1371/journal.pcbi.1000532

Cites

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Statistics

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Figures

Figure 1 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.
Figure 1 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.CC BY · PubMed Central
Figure 2 Structure and flow of a reference HTM node. (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 Table 1. 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.
Figure 2 Structure and flow of a reference HTM node. (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 Table 1. 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.CC BY · PubMed Central
Figure 3 Coincidence likelihood circuit. 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 Table 1. 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.
Figure 3 Coincidence likelihood circuit. 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 Table 1. 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.CC BY · PubMed Central
Figure 4 Markov chain likelihood circuit. 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 Table 1.
Figure 4 Markov chain likelihood circuit. 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 Table 1.CC BY · PubMed Central
Figure 5 Belief circuit. 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 Table 1.
Figure 5 Belief circuit. 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 Table 1.CC BY · PubMed Central
Figure 6 Feedback message circuit. 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.
Figure 6 Feedback message circuit. 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.CC BY · PubMed Central
Figure 7 Timing circuit. The same circuit as shown in Figure 5 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.
Figure 7 Timing circuit. The same circuit as shown in Figure 5 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.CC BY · PubMed Central
Figure 8 Mapping between neocortex hierarchy and HTM hierarchy. (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.
Figure 8 Mapping between neocortex hierarchy and HTM hierarchy. (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.CC BY · PubMed Central
Figure 9 A laminar biological instantiation of the Bayesian belief propagation equations used in the HTM nodes. The circuit shown here corresponds exactly to the instantiation of the reference HTM node shown in Figure 2. 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.
Figure 9 A laminar biological instantiation of the Bayesian belief propagation equations used in the HTM nodes. The circuit shown here corresponds exactly to the instantiation of the reference HTM node shown in Figure 2. 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.CC BY · PubMed Central
Figure 10 Columnar organization of the microcircuit. (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 Figure 9. (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.
Figure 10 Columnar organization of the microcircuit. (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 Figure 9. (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.CC BY · PubMed Central
Figure 11 Top-down segmentation. 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.
Figure 11 Top-down segmentation. 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.CC BY · PubMed Central
Figure 12 Kanizsa diagrams. A Kanizsa square (left) and a Kanizsa triangle (right) are shown.
Figure 12 Kanizsa diagrams. A Kanizsa square (left) and a Kanizsa triangle (right) are shown.CC BY · PubMed Central
Figure 13 Examples of training and testing images for an HTM network trained for visual object recognition. 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.
Figure 13 Examples of training and testing images for an HTM network trained for visual object recognition. 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.CC BY · PubMed Central
Figure 14 Recognition of the Kanizsa square by an HTM network. The network was not shown Kanizsa squares during training. The bar graph displays the order of recognition certainty of the HTM.
Figure 14 Recognition of the Kanizsa square by an HTM network. The network was not shown Kanizsa squares during training. The bar graph displays the order of recognition certainty of the HTM.CC BY · PubMed Central
Figure 15 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.
Figure 15 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.CC BY · PubMed Central
Figure 16 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.
Figure 16 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.CC BY · PubMed Central

Verification

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163 Own interpretation · 79 Not checked yet · 21 Own result · 21 No basis given

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  • Probably not a substantial claim. 106
  • It may state two separate claims as one. 55
  • The quote only partly states this claim. 1
139 of 139

  • The authors state this as an assumption.

    The equation for the output of a circle neuron assumes a simple step-wise notion of time.

    “(Again, the above equation assumes a simple step-wise notion of time which is insufficient for encoding duration and for non-discrete time problems.”

  • The authors state this as an assumption.

    The cortical circuits implement the HTM belief propagation equations described in Table 1.

    “Our working hypothesis can be stated simply: The cortical circuits implement the HTM belief propagation equations described in Table 1.”
    “Under the assumption that the cortical circuits are implementing these equations, what remains to be explained is how the abstract neuronal implementation of the previous section is physically organized in the layers and columns of actual cortical anatomy.”

  • The authors state this as an assumption.

    A timing signal is available at layer 1.

    “In addition, the availability of a timing signal at layer 1 is assumed.”

  • The authors state this as an assumption.

    Durations are signaled to a node by an external timing unit that determines the rate of change of the signals using some system-level measurements.

    “Instead, we assume that durations are signaled to a node by an external timing unit that determines the rate of change of the signals using some system-level measurements.”

  • The authors state this as an assumption.

    In real brains the basic computational column will consist of many redundant cells bound together using common input and short-range intra-laminar connections.

    “Therefore, we assume that in real brains the basic computational column will consist of many redundant cells bound together using common input and short-range intra-laminar connections resulting in a column as shown in Figure 10(B) [41].”

  • The authors state this as an assumption.

    The green neurons and the yellow neurons in Figure 9 encode states within sequences.

    “The green neurons and the yellow neurons in Figure 9 correspond to this description and are assumed to encode states within sequences.”

  • The paper relies on this without support.

    The number of non-exclusive patterns that needs to be maintained decreases as you ascend in the hierarchy.

    “Typically, the number of non-exclusive patterns that needs to be maintained decreases as you ascend in the hierarchy.”

  • The paper relies on this without support.

    The model requires that sequences at higher levels of the hierarchy represent longer durations of time.

    “Our model requires that sequences at higher levels of the hierarchy represent longer durations of time.”

  • The authors state this as an assumption.

    Cortical circuits store duration of individual elements within sequences and the mechanism used to store duration must be present in many if not all cortical areas.

    “Our model makes the assumption that cortical circuits store duration of individual elements within sequences and that the mechanism used to store duration must be present in many if not all cortical areas.”

  • The paper relies on this without support.

    A human can store specific durations, such as duration of notes in music, that last up to about a second.

    “Further, a human can store specific durations, such as duration of notes in music, that last up to about a second.”

  • The paper relies on this without support.

    Humans have the ability to speed up and slow down memorized sequences during recall.

    “Humans also have the ability to speed up and slow down memorized sequences during recall, which suggests a partially centralized mechanism that can influence the rate of recall over multiple elements in a sequence.”

  • The paper relies on this without support.

    Duration information must be available over broad areas of cortex so that duration information can be associated between any subsequent elements in a Markov chain.

    “Duration information must also be available over broad areas of cortex so that duration information can be associated between any subsequent elements in a Markov chain.”

  • The authors state this as an assumption.

    The timing signal is broadly available in layer 1.

    “The timing signal, assumed to be broadly available in layer 1, is shown as blue colored axons.”

  • The authors state this as an assumption.

    Belief-timing neurons project to non-specific thalamic regions (the thalamic matrix) which implement a variable delay mechanism that projects back to layer 1 to complete a timing loop.

    “It is assumed that the belief-timing neurons project to non-specific thalamic regions (the thalamic matrix) [54] which implement a variable delay mechanism that projects back to layer 1 to complete a timing loop, as shown in Figure 7.”

  • The paper relies on this without support.

    There is a need for a neuron representing a belief in a coincidence pattern that does not incorporate precise timing information.

    “Introspection leads us to believe that there is indeed the need for such a neuron.”

  • The paper relies on this without support.

    Layer 3 pyramidal cells that connect to layer 5 cells have their apical dendrites in layer 1.

    “It is also known that layer 3 pyramidal cells that connect to layer 5 cells have their apical dendrites in layer 1.”

  • The paper relies on this without support.

    There are primarily two kinds of pyramidal neurons in layer 5 of the cortex: regular-spiking (RS) neurons and intrinsically bursting (IB) neurons.

    “There are primarily two kinds of pyramidal neurons in layer 5 of the cortex. The first type are called 'regular-spiking' (RS) neurons and the second type are called 'intrinsically bursting' (IB) neurons.”

  • The paper relies on this without support.

    IB cells are larger, extend apical dendrites into layer 1, and exhibit a burst of action potentials when they become active.

    “The IB cells are larger, they extend apical dendrites into layer 1, and as their name suggests they exhibit a burst of action potentials when they become active.”

  • The paper relies on this without support.

    RS cells are smaller, their apical dendrites are mostly in superficial layer 4, and they exhibit a stream of action potentials when active.

    “The RS cells are smaller, their apical dendrites are mostly in superficial layer 4, and they exhibit a stream of action potentials when active.”

  • The paper relies on this without support.

    IB neurons of layer 5 also project to sub-cortical areas and to motor areas.

    “The IB neurons of layer 5 also project to sub-cortical areas and to motor areas.”

  • The paper relies on this without support.

    The cerebellum is known to encode specific timing and its connectivity to the thalamus suggests it could play a role in encoding duration.

    “For example, the cerebellum is known to encode specific timing and its connectivity to the thalamus suggests it could play this role.”

  • The paper relies on this without support.

    Caltech-101 images have low intra-category variation, and most images are centered and approximately of the same size.

    “Caltech-101 images have low intra-category variation. Most of the images are centered and approximately of the same size.”

  • The authors state this as an assumption.

    Excitatory neurons provide the prominent information-processing pathway and inhibitory neurons largely play a supporting role in implementing the learning algorithms.

    “we have adopted the common assumption that excitatory neurons provide the prominent information-processing pathway and that inhibitory neurons largely play a supporting role in implementing the learning algorithms.”

  • The authors state this as an assumption.

    Child-node states change synchronously.

    “The belief propagation messages in this paper were derived under the simplifying assumption that child-node states change synchronously.”

  • The authors state this as an assumption.

    A node represents a set of mutually exclusive hypotheses.

    “relaxing the assumption that a node represents a set of mutually exclusive hypotheses.”

  • The authors state this as an assumption.

    The HTM model assumes a hierarchy of nodes where each node learns spatial coincidences and then learns a mixture of Markov models over the set of coincidences.

    “The model, called Hierarchical Temporal Memory (HTM), is a type of Bayesian network which assumes a hierarchy of nodes where each node learns spatial coincidences and then learns a mixture of Markov models over the set of coincidences.”
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  1. RPN Rao, 2005, Hierarchical Bayesian Inference in Networks of Spiking Neurons, MIT Press., 1113

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Metadata

Authors
George, D., & Hawkins, J.
ORCID
Hawkins, Jeff
Venue
PLoS Computational Biology
Publisher
Public Library of Science (PLoS)
Published
2009-10-09
Volume
5
Issue
10
Pages
e1000532
ISSN
  • 1553-734X (ISSN-L)
  • 1553-7358
DOI
10.1371/journal.pcbi.1000532
PMC
PMC2749218
OpenAlex
W2010124835
Semantic Scholar
2f53caf8443a28ea47f7dafe422c06d132b253de
Cited by
404
References
81
Citations by year
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FWCI
14.68
Type
journal article
Language
en
Open access
Licence
Locations
  • PLoS Computational Biology (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • Figshare (submittedVersion, cc-by)
Topics
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Memory and Neural Mechanisms
  • Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
Keywords
hierarchical temporal memory, hierarchical Bayesian inference, coincidence detectors, cortical anatomy, pattern recognition, cortical computation
MeSH terms
Artificial Intelligence, Bayes Theorem, Cerebral Cortex, Feedback, Markov Chains, Memory, Models, Neurological, Pattern Recognition, Automated, Pyramidal Cells

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

A language model drew the claims from the paper on 2026-10-09, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).

A second model labelled each claim on 2026-10-09 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

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