Random Projection in the Brain and Computation with Assemblies of Neurons

Authors Christos H. Papadimitriou, Santosh S. Vempala

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Christos H. Papadimitriou
  • Columbia University, USA
Santosh S. Vempala
  • Georgia Tech, USA

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Christos H. Papadimitriou and Santosh S. Vempala. Random Projection in the Brain and Computation with Assemblies of Neurons. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 57:1-57:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


It has been recently shown via simulations [Dasgupta et al., 2017] that random projection followed by a cap operation (setting to one the k largest elements of a vector and everything else to zero), a map believed to be an important part of the insect olfactory system, has strong locality sensitivity properties. We calculate the asymptotic law whereby the overlap in the input vectors is conserved, verifying mathematically this empirical finding. We then focus on the far more complex homologous operation in the mammalian brain, the creation through successive projections and caps of an assembly (roughly, a set of excitatory neurons representing a memory or concept) in the presence of recurrent synapses and plasticity. After providing a careful definition of assemblies, we prove that the operation of assembly projection converges with high probability, over the randomness of synaptic connectivity, even if plasticity is relatively small (previous proofs relied on high plasticity). We also show that assembly projection has itself some locality preservation properties. Finally, we propose a large repertoire of assembly operations, including associate, merge, reciprocal project, and append, each of them both biologically plausible and consistent with what we know from experiments, and show that this computational system is capable of simulating, again with high probability, arbitrary computation in a quite natural way. We hope that this novel way of looking at brain computation, open-ended and based on reasonably mainstream ideas in neuroscience, may prove an attractive entry point for computer scientists to work on understanding the brain.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Theory of computation → Randomness, geometry and discrete structures
  • Brain computation
  • random projection
  • assemblies
  • plasticity
  • memory
  • association


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  1. Rosa I. Arriaga, David Rutter, Maya Cakmak, and Santosh S. Vempala. Visual Categorization with Random Projection. Neural Computation, 27(10):2132-2147, 2015. URL: http://dx.doi.org/10.1162/NECO_a_00769.
  2. Rosa I. Arriaga and Santosh Vempala. An algorithmic theory of learning: Robust concepts and random projection. Machine Learning, 63(2):161-182, 2006. URL: http://dx.doi.org/10.1007/s10994-006-6265-7.
  3. M.F. Balcan, A. Blum, and S. Vempala. Kernels as Features: On Kernels, Margins, and Low-dimensional Mappings. Machine Learning, 65(1):79-94, 2006. Google Scholar
  4. Robert C Berwick and Noam Chomsky. Why only us: Language and evolution. MIT Press, 2016. Google Scholar
  5. G Buzsaki. Neural syntax: cell assemblies, synapsembles, and readers. Neuron, 68(3), 2010. Google Scholar
  6. Sophie JC Caron, Vanessa Ruta, LF Abbott, and Richard Axel. Random convergence of olfactory inputs in the drosophila mushroom body. Nature, 497(7447):113, 2013. Google Scholar
  7. S. DasGupta. Learning mixtures of Gaussians. In Proc. of FOCS, 1999. Google Scholar
  8. Sanjoy Dasgupta, Charles F. Stevens, and Saket Navlakha. A neural algorithm for a fundamental computing problem. Science, 358(6364):793-796, 2017. URL: http://dx.doi.org/10.1126/science.aam9868.
  9. Emanuela De Falco, Matias J Ison, Itzhak Fried, and Rodrigo Quian Quiroga. Long-term coding of personal and universal associations underlying the memory web in the human brain. Nature Communications, 7:13408, 2016. Google Scholar
  10. Nai Ding, Lucia Melloni, Hang Zhang, Xing Tian, and David Poeppel. Cortical tracking of hierarchical linguistic structures in connected speech. Nature neuroscience, 19(1):158, 2016. Google Scholar
  11. S. M. Frankland and J. D. Greene. An architecture for encoding sentence meaning in left mid-superior temporal cortex. Proceedings of the National Academy of Sciences, 112(37):11732-11737, 2015. Google Scholar
  12. Kevin M Franks, Marco J Russo, Dara L Sosulski, Abigail A Mulligan, Steven A Siegelbaum, and Richard Axel. Recurrent circuitry dynamically shapes the activation of piriform cortex. Neuron, 72(1):49-56, 2011. Google Scholar
  13. Kenneth D Harris. Neural signatures of cell assembly organization. Nature Reviews Neuroscience, 6(5):399, 2005. Google Scholar
  14. Kenneth D Harris, Jozsef Csicsvari, Hajime Hirase, George Dragoi, and György Buzsáki. Organization of cell assemblies in the hippocampus. Nature, 424(6948):552, 2003. Google Scholar
  15. Matias J Ison, Rodrigo Quian Quiroga, and Itzhak Fried. Rapid encoding of new memories by individual neurons in the human brain. Neuron, 87(1):220-230, 2015. Google Scholar
  16. Sheena A Josselyn, Stefan Köhler, and Paul W Frankland. Finding the engram. Nature Reviews Neuroscience, 16(9):521, 2015. Google Scholar
  17. R. Legenstein, W. Maass, C. H. Papadimitriou, and S. S. Vempala. Long-term Memory and the Densest k-subgraph Problem. In Proc. of 9th Innovations in Theoretical Computer Science (ITCS) conference, Cambridge, USA, Jan 11-14. 2018, 2018. Google Scholar
  18. Robert Legenstein, Christos H Papadimitriou, Santosh Vempala, and Wolfgang Maass. Assembly pointers for variable binding in networks of spiking neurons. arXiv preprint, 2016. URL: http://arxiv.org/abs/1611.03698.
  19. Eva Pastalkova, Vladimir Itskov, Asohan Amarasingham, and György Buzsáki. Internally generated cell assembly sequences in the rat hippocampus. Science, 321(5894):1322-1327, 2008. Google Scholar
  20. C. Pokorny, M. J. Ison, A. Rao, R. Legenstein, C. Papadimitriou, and W. Maass. Associations between memory traces emerge in a generic neural circuit model through STDP. bioRxiv:188938, 2017. Google Scholar
  21. Leslie G. Valiant. Circuits of the mind. Oxford University Press, 1994. Google Scholar
  22. Leslie G. Valiant. A neuroidal architecture for cognitive computation. J. ACM, 47(5):854-882, 2000. URL: http://dx.doi.org/10.1145/355483.355486.
  23. Santosh Srinivas Vempala. The Random Projection Method, volume 65 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science. DIMACS/AMS, 2004. URL: http://dimacs.rutgers.edu/Volumes/Vol65.html.
  24. Emiliano Zaccarella and Angela D. Friederici. Merge in the Human Brain: A Sub-Region Based Functional Investigation in the Left Pars Opercularis. Frontiers in Psychology, 6:1818, 2015. URL: http://dx.doi.org/10.3389/fpsyg.2015.01818.
  25. Emiliano Zaccarella, Lars Meyer, Michiru Makuuchi, and Angela D Friederici. Building by syntax: the neural basis of minimal linguistic structures. Cerebral Cortex, 27(1):411-421, 2017. Google Scholar
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