Symbolic functions from neural computation

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 370, Issue 1971, 2012, Pages 3543-3569

  Paul, Smolensky ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

Cognitive science; Connectionism; Language; Linguistics; Neural networks; Optimality theory

Indexed keywords

COGNITIVE SYSTEMS; FORMAL LANGUAGES; LINGUISTICS; NEURAL NETWORKS;

ACTIVATION VALUE; AXIOMATIC FRAMEWORK; COGNITIVE SCIENCE; COMPUTATIONAL SYSTEM; CONNECTIONISM; HUMAN LANGUAGE; LANGUAGE; MULTIPLE-SYMBOL; NEURAL COMPUTATIONS; NUMERICAL COMPUTATIONS; OPTIMALITY; RESEARCH PROGRAMS; REWRITE RULES; SUB-SYMBOLIC; SYMBOLIC FUNCTIONS;

RECURSIVE FUNCTIONS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; BIOMIMETICS; COGNITION; COMPUTER SIMULATION; HUMAN; LANGUAGE; METHODOLOGY; NERVE CELL; NERVE CELL NETWORK; PHYSIOLOGY; SYMBOLISM;

BIOMIMETICS; COGNITION; COMPUTER SIMULATION; HUMANS; LANGUAGE; MODELS, NEUROLOGICAL; NERVE NET; NEURAL NETWORKS (COMPUTER); NEURONS; SYMBOLISM;

EID: 84865296406     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2011.0334     Document Type: Review

References (57)

1. Turing, A. M. 1950 Computing machinery and intelligence. Mind 59, 433-460. (doi:10.1093/mind/LIX.236.433)
2. Floridi, L. 2010 Information-a very short introduction. Oxford, UK: Oxford University Press.
3. Floridi, L. 2011 The philosophy of information. Oxford, UK: Oxford University Press.
4. Floridi, L., Taddeo, M. & Turilli, M. 2009 Turing's imitation game: still a challenge for any machine and some judges. Minds Mach. 19, 145-150. (doi:10.1007/s11023-008-9130-6)
5. Moor, J. 2003 The Turing test: the elusive standard of artificial intelligence. Dordrecht, The Netherlands: Kluwer Academic Publishers.
6. Floridi, L. 2008 The method of levels of abstraction. Minds Mach 18, 303-329. (doi:10.1007/s11023-008-9113-7)
7. Floridi, L. In press. Turing test and the method of levels of abstraction. In Alan Turing-his work and impact (eds S. B. Cooper & J. van Leeuwen). Amsterdam, The Netherlands: Elsevier.
8. Floridi, L. 2010 Information ethics. In The Cambridge handbook of information and computer ethics (ed. L. Floridi), ch. 5. Cambridge, UK: Cambridge University Press.
9. Freud, S. 1917 A difficulty in the path of psycho-analysis. In The complete psychological works of Sigmund Freud, the Standard Edition, vol. XVII (ed. J. Strachey), pp. 135-144. London, UK: Hogarth Press.
10. Weinert, F. 2009 Copernicus, Darwin, and Freud: revolutions in the history and philosophy of science. Oxford, UK: Blackwell.
11. Turing, A. M. 2004 The essential Turing: seminal writings in computing, logic, philosophy, artificial intelligence and artificial life, plus the secrets of enigma. Oxford, UK: Clarendon Press.
12. Luenberger, D. G. 2006 Information science. Princeton, NJ: Princeton University Press.
13. Turing, A. M. 1936 On computable numbers, with an application to the Entscheidungsproblem. Proc. Lond. Math. Soc. 42, 230-265.
14. Pylyshyn, Z. W. 1984 Computation and cognition: toward a foundation for cognitive science. Cambridge, MA: MIT Press.
15. Smolensky, P. 1988 On the proper treatment of connectionism. Behav. Brain Sci. 11, 1-74. (doi:10.1017/S0140525X00052432)
16. Copeland, B. J. & Proudfoot, D. 1996 On Alan Turing's anticipation of connectionism. Synthese 108, 361-377. (Pubitemid 126788298)
17. Hofstadter, D. R. 1985 Waking up from the Boolean dream, or, subcognition as computation. In Metamagical themas, pp. 631-665. New York, NY: Basic Books.
18. Cummins, R. & Schwarz, G. 1991 Connectionism, computation, and cognition. In Connectionism and the philosophy of mind (eds T. E. Horgan & J. Tienson), pp. 60-73. Dordrecht, The Netherlands: Kluwer.
19. Smolensky, P. 2006 Computational levels and integrated connectionist/symbolic explanation. In The harmonic mind: from neural computation to optimality-theoretic grammar, vol. 2, pp. 503-592. Cambridge, MA: MIT Press.
20. McClelland, J. L. 2010 Letting structure emerge: connectionist and dynamical systems approaches to cognition. Trends Cogn. Sci. 14, 348-356. (doi:10.1016/j.tics.2010.06.002)
21. Smolensky, P. & Legendre, G. 2006 The harmonic mind: from neural computation to optimality-theoretic grammar, vol. 1: Cognitive architecture, vol. 2: Linguistic and philosophical implications. Cambridge, MA: MIT Press.
22. Grossberg, S. 1982 Studies of mind and brain: neural principles of learning, perception, development, cognition, and motor control. Boston, MA: Reidel.
23. Kohonen, T. 1977 Associative memory: a system-theoretical approach. New York, NY: Springer.
24. Smolensky, P. 1986 Neural and conceptual interpretations of parallel distributed processing models. In Parallel distributed processing: explorations in the microstructure of cognition, vol. 2 (eds J. L. McClelland, D. E. Rumelhart & the PDP Research Group), pp. 390-431. Cambridge, MA: MIT Press.
25. Smolensky, P. 1996 Dynamical perspectives on neural networks. In Mathematical perspectives on neural networks (eds P. Smolensky, M. C. Mozer & D. E. Rumelhart), pp. 245-270. Mahwah, NJ: Erlbaum Associates.
26. Fodor, J. A. 1975 The language of thought. Cambridge, MA: Harvard University Press.
27. Smolensky, P. 1990 Tensor product variable binding and the representation of symbolic structures in connectionist networks. Artif. Intell. 46, 159-216.
28. Abelson, H., Sussman, G. J. & Sussman, J. 1985 Structure and interpretation of computer programs. Cambridge, MA: MIT Press.
29. Smolensky, P. 2006 Formalizing the principles I: representation and processing in the mind/brain. In The harmonic mind: from neural computation to optimality-theoretic grammar, vol. 1, pp. 147-205. Cambridge, MA: MIT Press.
30. Messiah, A. 1961 Quantum mechanics. Amsterdam, The Netherlands: Elsevier Science.
31. Smolensky, P. 2006 Tensor product representations: formal foundations. In The harmonic mind: from neural computation to optimality-theoretic grammar, vol. 1, pp. 271-344. Cambridge, MA: MIT Press.
32. Hinton, G. E., McClelland, J. L. & Rumelhart, D. E. 1986 Distributed representation. In Parallel distributed processing: explorations in the microstructure of cognition, vol. 1 (eds D. E. Rumelhart, J. L. McClelland & the PDP Research Group), pp. 77-109. Cambridge, MA: MIT Press.
33. Churchland, P. S. & Sejnowski, T. J. 1992 The computational brain. Cambridge, MA: MIT Press.
34. Abbott, L. & Sejnowski, T. J. (eds) 1999 Neural codes and distributed representations. Cambridge, MA: MIT Press.
35. Fischer-Baum, S. 2010 Position representation: general principles or domain-specificity? Doctoral dissertation. Johns Hopkins University, Baltimore, MD.
36. Legendre, G., Miyata, Y. & Smolensky, P. 1990 Harmonic grammar-a formal multi-level connectionist theory of linguistic well-formedness: theoretical foundations. In Proc. Cognitive Science Society, pp. 388-395. Cambridge, MA: Erlbaum.
37. Hale, J. & Smolensky, P. 2006 Harmonic grammars and harmonic parsers for formal languages. In The harmonic mind: from neural computation to optimality-theoretic grammar, vol. 1, pp. 393-415. Cambridge, MA: MIT Press.
38. Prince, A. & Smolensky, P. 1993/2004 Optimality theory: constraint interaction in generative grammar. Technical Report, Rutgers University and University of Colorado at Boulder, 1993. ROA 537, 2002. Revised version published by Blackwell, 2004.
39. Prince, A. & Smolensky, P. 1997 Optimality: from neural networks to universal grammar. Science 275, 1604-1610. (Pubitemid 27125906)
40. Grimshaw, J. & Samek-Lodovici, V. 1998 Optimal subjects and subject universals. In Is the best good enough? Optimality and competition in syntax (eds P. Barbosa, D. Fox, P. Hagstrom, M. McGinnis & D. Pesetsky), pp. 193-219. Cambridge, MA: MIT Press.
41. Kager, R. 1999 Optimality theory. Cambridge, UK: Cambridge University Press.
42. McCarthy, J. J. (ed.) 2004 Optimality theory in phonology: a reader. Malden, MA: Blackwell.
43. Legendre, G., Grimshaw, J. & Vikner, S. (eds) 2001 Optimality-theoretic syntax. Cambridge, MA: MIT Press.
44. Blutner, R., De Hoop, H. & Hendriks, P. 2006 Optimal communication. Stanford, CA: CSLI Publications.
45. Prince, A. 2002 Anything goes. In A new century of phonology and phonological theory (eds T. Honma, M. Okazaki, T. Tabata & S. Tanaka), pp. 66-90. Tokyo, Japan: Kaitakusha.
46. Soderstrom, M., Mathis, D. W. & Smolensky, P. 2006 Abstract genomic encoding of universal grammar in optimality theory. In The harmonic mind: from neural computation to optimalitytheoretic grammar, vol. 2, pp. 403-471. Cambridge, MA: MIT Press.
47. Cohen, M. A. & Grossberg, S. 1983 Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 13, 815-825.
48. Hopfield, J. J. 1984 Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl Acad. Sci. USA 81, 3088-3092. (Pubitemid 14109528)
49. Golden, R. M. 1986 The 'brain-state-in-a-box' neural model is a gradient descent algorithm. Math. Psychol. 30-31, 73-80. (doi:10.1016/0022-2496 (86) 90043-X)
50. Kirkpatrick, S., Gelatt Jr, C. D. & Vecchi, M. P. 1983 Optimization by simulated annealing. Science 220, 671-680. (doi:10.1126/science.220.4598.671)
51. Ackley, D. H., Hinton, G. E. & Sejnowski, T. J. 1985 A learning algorithm for Boltzmann machines. Cogn. Sci. 9, 147-169.
52. Smolensky, P. 1986 Information processing in dynamical systems: foundations of harmony theory. In Parallel distributed processing: explorations in the microstructure of cognition, vol. 1 (eds D. E. Rumelhart, J. L. McClelland & the PDP Research Group), pp. 194-281. Cambridge, MA: MIT Press.
53. Movellan, J. R. 1998 A learning theorem for networks at detailed stochastic equilibrium. Neural Comput. 10, 1157-1178. (Pubitemid 128463667)
54. Movellan, J. R. & McClelland, J. L. 1993 Learning continuous probability distributions with symmetric diffusion networks. Cogn. Sci. 17, 463-496.
55. Geman, S. & Geman, D. 1984 Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6, 721-741. (Pubitemid 15453722)
56. Baird, B. & Eeckman, F. 1993 A normal form projection algorithm for associative memory. In Associative neural memories (ed. M. H. Hassoun), pp. 135-166. New York, NY: Oxford University Press.
57. Smolensky, P., Goldrick, M. & Mathis, D. W. In press. Optimization and quantization in gradient symbol systems: a framework for integrating the continuous and the discrete in cognition. Cogn. Sci.