IDEAS home Printed from https://ideas.repec.org/a/plo/pcbi00/1000532.html
   My bibliography  Save this article

Towards a Mathematical Theory of Cortical Micro-circuits

Author

Listed:
  • Dileep George
  • Jeff Hawkins

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.Author Summary: Understanding the computational and information processing roles of cortical circuitry is one of the outstanding problems in neuroscience. In this paper, we work from a theory of neocortex that models it as a spatio-temporal hierarchical system to derive a biological cortical circuit. This is achieved by combining the computational constraints provided by the inference equations for this spatio-temporal hierarchy with anatomical data. The result is a mathematically consistent biological circuit that can be mapped to the cortical laminae and matches many prominent features of the mammalian neocortex. The mathematical model can serve as a starting point for the construction of machines that work like the brain. The resultant biological circuit can be used for modeling physiological phenomena and for deriving testable predictions about the brain.

Suggested Citation

  • Dileep George & Jeff Hawkins, 2009. "Towards a Mathematical Theory of Cortical Micro-circuits," PLOS Computational Biology, Public Library of Science, vol. 5(10), pages 1-26, October.
    • Handle: RePEc:plo:pcbi00:1000532
    DOI: 10.1371/journal.pcbi.1000532
    as

    Download full text from publisher

    File URL: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1000532
    Download Restriction: no
    File URL: https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1000532&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pcbi.1000532?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Karl Friston, 2008. "Hierarchical Models in the Brain," PLOS Computational Biology, Public Library of Science, vol. 4(11), pages 1-24, November.
    2. Nicolas Pinto & David D Cox & James J DiCarlo, 2008. "Why is Real-World Visual Object Recognition Hard?," PLOS Computational Biology, Public Library of Science, vol. 4(1), pages 1-6, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Adam Safron, 2019. "Multilevel evolutionary developmental optimization (MEDO): A theoretical framework for understanding preferences and selection dynamics," Papers 1910.13443, arXiv.org, revised Nov 2019.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Micha Heilbron & Florent Meyniel, 2019. "Confidence resets reveal hierarchical adaptive learning in humans," PLOS Computational Biology, Public Library of Science, vol. 15(4), pages 1-24, April.
    2. John C. Boik, 2020. "Science-Driven Societal Transformation, Part I: Worldview," Sustainability, MDPI, vol. 12(17), pages 1-28, August.
    3. Mateus Joffily & Giorgio Coricelli, 2013. "Emotional Valence and the Free-Energy Principle," Post-Print halshs-00834063, HAL.
    4. Falk Lieder & Klaas E Stephan & Jean Daunizeau & Marta I Garrido & Karl J Friston, 2013. "A Neurocomputational Model of the Mismatch Negativity," PLOS Computational Biology, Public Library of Science, vol. 9(11), pages 1-14, November.
    5. Pavel Škrabánek & Alexandra Zahradníková jr., 2019. "Automatic assessment of the cardiomyocyte development stages from confocal microscopy images using deep convolutional networks," PLOS ONE, Public Library of Science, vol. 14(5), pages 1-18, May.
    6. Jaroslav Vítků & Petr Dluhoš & Joseph Davidson & Matěj Nikl & Simon Andersson & Přemysl Paška & Jan Šinkora & Petr Hlubuček & Martin Stránský & Martin Hyben & Martin Poliak & Jan Feyereisl & Marek Ros, 2020. "ToyArchitecture: Unsupervised learning of interpretable models of the environment," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-50, May.
    7. Ünsal Özdilek, 2021. "Sensing Happiness in Senseless Information," Applied Research in Quality of Life, Springer;International Society for Quality-of-Life Studies, vol. 16(5), pages 2059-2084, October.
    8. Xiaofu He & Zhiyong Yang & Joe Z Tsien, 2011. "A Hierarchical Probabilistic Model for Rapid Object Categorization in Natural Scenes," PLOS ONE, Public Library of Science, vol. 6(5), pages 1-15, May.
    9. Yuri Vankov & Aleksey Rumyantsev & Shamil Ziganshin & Tatyana Politova & Rinat Minyazev & Ayrat Zagretdinov, 2020. "Assessment of the Condition of Pipelines Using Convolutional Neural Networks," Energies, MDPI, vol. 13(3), pages 1-12, February.
    10. Adeeti Aggarwal & Connor Brennan & Jennifer Luo & Helen Chung & Diego Contreras & Max B. Kelz & Alex Proekt, 2022. "Visual evoked feedforward–feedback traveling waves organize neural activity across the cortical hierarchy in mice," Nature Communications, Nature, vol. 13(1), pages 1-16, December.
    11. David Balduzzi & Giulio Tononi, 2009. "Qualia: The Geometry of Integrated Information," PLOS Computational Biology, Public Library of Science, vol. 5(8), pages 1-24, August.
    12. Qianli Yang & Edgar Walker & R. James Cotton & Andreas S. Tolias & Xaq Pitkow, 2021. "Revealing nonlinear neural decoding by analyzing choices," Nature Communications, Nature, vol. 12(1), pages 1-13, December.
    13. Sebastian Bach & Alexander Binder & Grégoire Montavon & Frederick Klauschen & Klaus-Robert Müller & Wojciech Samek, 2015. "On Pixel-Wise Explanations for Non-Linear Classifier Decisions by Layer-Wise Relevance Propagation," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-46, July.
    14. Pedro Malaca & Luis F. Rocha & D. Gomes & João Silva & Germano Veiga, 2019. "Online inspection system based on machine learning techniques: real case study of fabric textures classification for the automotive industry," Journal of Intelligent Manufacturing, Springer, vol. 30(1), pages 351-361, January.
    15. Boris Vladimirskiy & Robert Urbanczik & Walter Senn, 2015. "Hierarchical Novelty-Familiarity Representation in the Visual System by Modular Predictive Coding," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-19, December.
    16. Alexander Ororbia & Daniel Kifer, 2022. "The neural coding framework for learning generative models," Nature Communications, Nature, vol. 13(1), pages 1-14, December.
    17. Adam Safron, 2019. "Multilevel evolutionary developmental optimization (MEDO): A theoretical framework for understanding preferences and selection dynamics," Papers 1910.13443, arXiv.org, revised Nov 2019.
    18. Biswa Sengupta & Arturo Tozzi & Gerald K Cooray & Pamela K Douglas & Karl J Friston, 2016. "Towards a Neuronal Gauge Theory," PLOS Biology, Public Library of Science, vol. 14(3), pages 1-12, March.
    19. Hailay Hagos Entahabu & Amare Sewnet Minale & Emiru Birhane, 2023. "Modeling and Predicting Land Use/Land Cover Change Using the Land Change Modeler in the Suluh River Basin, Northern Highlands of Ethiopia," Sustainability, MDPI, vol. 15(10), pages 1-15, May.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pcbi00:1000532. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ploscompbiol (email available below). General contact details of provider: https://journals.plos.org/ploscompbiol/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.