Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The neural network as a renormalizer of information

Author: Willard L. Miranker
Journal: Quart. Appl. Math. 66 (2008), 379-394
MSC (2000): Primary 91E30, 46N60
DOI: https://doi.org/10.1090/S0033-569X-08-01073-4
Published electronically: February 8, 2008
MathSciNet review: 2416779
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Abstract: We characterize the behavior of information in neural processing as the neuronal circuitry itself agglomerates into assemblies of increasing size and complexity. The basic synaptic stage of this processing is interpreted as the observer feature of a measurement process, a quality that extends up the assembly hierarchy. Renormalization techniques are employed, and they supply features of emergence to the information. Renormalization also supplies each observer feature with a measurable physical quantity called a token, the latter supplying quantitative aspects to the entire development. This development is used to frame an analytic theory of phenomenal consciousness, featuring emergent aspects. The tokens furnish the means for the various predictions and explanations of that theory to be subjected to measurement and experimental verification.

References [Enhancements On Off] (What's this?)

  • [1] Daniel J. Amit, Modeling brain function, Cambridge University Press, Cambridge, 1989. The world of attractor neural networks. MR 1025121
  • [2] Amit, D., Gutfreund, H., Sompolinsky, H. (1987), Statistical Mechanics of Neural Networks near Saturation, Annals of Physics 173, 30-67.
  • [3] Beckermann, M. (1997), Adaptive Cooperative Systems, Wiley, New York.
  • [4] Chalmers, D. (1996), The Conscious Mind: In Search of a Fundamental Theory, Oxford Univ. Press.
  • [5] Churchland, P. M. (1984), Matter and Consciousness, MIT Press, Cambridge.
  • [6] Damasio, A. (1994), Descartes Error, Grosset/Putnam, New York.
  • [7] Dennett, D. (1996), Kinds of Minds, Toward an Understanding of Consciousness, Basic Books, New York.
  • [8] Descartes, R. (1637), Discours sur la Méthode.
  • [9] Edelman, G., Tononi, G. (2001), A Universe of Consciousness: How Matter Becomes Imagination, Basic Books, New York.
  • [10] Einstein, A., Podolsky, B., Rosen, N. (1935), Can Quantum-Mechanical Description of Physical Reality be Considered Complete?, Phys. Rev. 47, 777-780.
  • [11] Fransen, E., Lansner, A. (1995), Low spiking rates in a population of mutually exciting pyramidal cells, Network 6, 271-288.
  • [12] -(1998), A model of cortical associative memory based on a horizontal network of connected columns, Network 9, 235-264.
  • [13] Freeman, A., Ed. (2001), The Emergence of Consciousness, J. Consc. Studies 8, 9-10.
  • [14] Goldenfeld, N. (1992), Lectures on Phase Transitions and the Renormalization Group, Addison-Wesley, Reading, MA.
  • [15] Hermann Haken, Synergetic computers and cognition, 2nd ed., Springer Series in Synergetics, vol. 50, Springer-Verlag, Berlin, 2004. A top-down approach to neural nets. MR 2081217
  • [16] Haykin, S. (1999), Neural Networks, A Comprehensive Foundation, Prentice Hall, Upper Saddle River, NJ.
  • [17] Hebb, D. (1939), Intelligence in man after large removals of cerebral tissue: Report of four left frontal lobe cases, J. Gen. Psychol., 73-87.
  • [18] -(1946), On the nature of fear, Physiol. Rev. 53, 259-276.
  • [19] -(1949), Organization of Behavior: A Neurophysiological Theory, Wiley, NY.
  • [20] -(1980a), The structure of thought, in The Nature of Thought, P.Jusczyk and R.Klein, Eds., Lawrence Erlbaum Associates, Hillsdale, NJ.
  • [21] -(1980b), Essay on Mind, Lawrence Erlbaum Associates, Hillsdale, NJ.
  • [22] John Hertz, Anders Krogh, and Richard G. Palmer, Introduction to the theory of neural computation, Santa Fe Institute Studies in the Sciences of Complexity. Lecture Notes, I, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1991. With forewords by Jack Cowan and Christof Koch. MR 1096298
  • [23] J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci. U.S.A. 79 (1982), no. 8, 2554–2558. MR 652033
  • [24] Johnston, V. (1999), Why We Feel, The Science of Human Emotion, Perseus, Cambridge, MA.
  • [25] Kadanoff, L. (1966), Scaling laws for Ising models near $ Tc$, Physics, vol. 2, pp. 263-272.
  • [26] Kandel, E.R., Schwartz, J.H., Jessel, T.M. (2000), Principles of Neural Science, 4th ed., McGraw-Hill/Appleton & Lange, New York.
  • [27] Libet, B. (2003), Neurophysiology of Consciousness: Selected Papers and New Essays by Benjamin Libet, Birkhäuser, Boston.
  • [28] Llinas, R. (2001), i of the Vortex, MIT Press, Cambridge.
  • [29] Henry Margenau, The Nature of Physical Reality. A Philosophy of Modern Physics, McGraw-Hill Book Co., Inc., New York, N. Y., 1950. MR 0035258
  • [30] -(1978), Physics and Philosophy: Selected Essays , Dordrecht, Boston. MR 0529767 (80c:01020)
  • [31] Warren S. McCulloch and Walter Pitts, A logical calculus of the ideas immanent in nervous activity, Bull. Math. Biophys. 5 (1943), 115–133. MR 0010388
  • [32] McDermott, D. (2001), Mind and Mechanism, MIT Press, Cambridge.
  • [33] Marc Mézard, Giorgio Parisi, and Miguel Angel Virasoro, Spin glass theory and beyond, World Scientific Lecture Notes in Physics, vol. 9, World Scientific Publishing Co., Inc., Teaneck, NJ, 1987. MR 1026102
  • [34] Milner, P. (1957), The cell assembly: Mark II, Psychol. Rev. 64, 242-252.
  • [35] Miranker, W.L. (2000), Consciousness is an information state, J. Neural Parallel and Scientific Computation 8, 83-104.
  • [36] -(2001), The Renormalization of Information, Yale Univ. DCS/TR-1215.
  • [37] -(2005), Consciousness, A Darwinian Process, Yale Univ. DCS/TR-1344.
  • [38] O'Donnell, P., Greene, J., Pabello, N., Lewis, B., Grace, A. (1999), Modulation of cell firing in the nucleus accumbens, Annals of the NY Academy of Sciences 877, 157-175.
  • [39] Roger Penrose, Shadows of the mind, Oxford University Press, Oxford, 1994. A search for the missing science of consciousness. MR 1865778
  • [40] Mitja Peruš, Multi-level synergetic computation in brain, Nonlinear Phenom. Complex Syst. 4 (2001), no. 2, 157–193. MR 1886860
  • [41] Rakovi, D., Dugi, M. (2005), Quantum-holographic classical Hopfield-like associative nets: Implications for modeling two cognitive modes of consciousness, Opticheski J. 75, 13-18 (Special issue on Topical Meeting on Optoinformatics `Optics Meets --' Saint Petersburg (2004); also www.iasc-bg.org.yu.
  • [42] Rolls, E., Treves, A. (1999), Neural Networks and Brain Function, Oxford Univ. Press, Oxford.
  • [43] Searle, J. (1994), The Rediscovery of the Mind, MIT Press, Cambridge.
  • [44] Sheets-Johnstone, M. (1998), Consciousness; a natural history, J. Consc. Studies 3, 260-294.
  • [45] Stapp, H. (1998), The Hard problem: a quantum approach, J. Consc. Studies 3, 194-210.
  • [46] Thompson, M., Varela, F. (2001), Radical embodiments: neural dynamics and consciousness experiences, Trends in Cognitive Sciences 5, 418-425.
  • [47] Velmans, M. (2000), Understanding Consciousness, Routledge, London.
  • [48] Wilson, K. (1971), Renormalization group and critical phenomena I & II, Phys. Rev. B4, 3174-3183 and 3184-3205.

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Additional Information

Willard L. Miranker
Affiliation: Department of Computer Science, Yale University, New Haven, CT

DOI: https://doi.org/10.1090/S0033-569X-08-01073-4
Keywords: Consciousness, dualist construct, emergence, Hebbian dynamics, measurement, neural networks, phase change, renormalization
Received by editor(s): January 4, 2007
Published electronically: February 8, 2008
Article copyright: © Copyright 2008 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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