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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.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1371/journal.pcbi.1000532

Cites

79 of 79 references verified0 citation errors · 0 not checkable

Statistics

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Claims the paper makes

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Show all 145 claims

  • 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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  • Hardware-implementation citation points to an object-categorization paper

    Minor

    The text cites reference 19 for hardware implementations and parallel architectures, but reference 19 is titled as an object-categorization paper. The reconfigurable-logic implementation is listed as reference 17.

  • Object-categorization citation points to a hardware paper

    Minor

    The text cites reference 17 for object categorization, but reference 17 is titled as a reconfigurable-logic implementation. The object-categorization paper is listed as reference 19.

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Citations

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2 of the 81 references couldn’t be matched to a known paper.

Research works printed but not linked: 1

  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
2026: 7 · 2025: 17 · 2024: 13 · 2023: 15 · 2022: 13 · 2021: 24 · 2020: 29 · 2019: 25 · 2018: 28 · 2017: 28 · 2016: 31 · 2015: 24 · 2014: 35 · 2013: 22 · 2012: 34
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

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