УДК: 535.417

Models of the advancement of hypotheses in a Fourier-holography layout

Bekyasheva, Z.S., Vasiliev, V.N., Pavlov, A.V.

Publication in Journal of Optical Technology

For Russian citation (Opticheskii Zhurnal):

Бекяшева З.С., Васильев В.Н., Павлов А.В. Модели выдвижения гипотез в схеме голографии Фурье // Оптический журнал. 2013. Т. 80. № 3. С. 37–46.

Bekyasheva Z.S., Vasiliev V.N., Pavlov A.V. Models of the advancement of hypotheses in a Fourier-holography layout [in Russian] // Opticheskii Zhurnal. 2013. V. 80. № 3. P. 37–46.

For citation (Journal of Optical Technology):

Z. S. Bekyasheva, V. N. Vasil’ev, and A. V. Pavlov, "Models of the advancement of hypotheses in a Fourier-holography layout," Journal of Optical Technology. 80(3), 154-161 (2013). https://doi.org/10.1364/JOT.80.000154

Abstract:

As applied to the description of a Fourier-holography layout with phase conjugation in the correlation plane as the implementation of a two-layer neural network, this paper discusses two models of the advancement of hypotheses: linear regression of the conditions of a problem from knowledge, and inductive inference. The factors that influence the adequacy of the hypotheses generated for the conditions of a problem are determined and numerically investigated. It is shown that the adequacy of the hypotheses increases as the number of spatial degrees of freedom of the patterns that represent the conditions of the problem (the generalized frequency) increases; moreover, because of internal correlation (as an attribute of the information), increasing the size of the pattern influences the adequacy more effectively than does high-frequency filtering.

Keywords:

holography, artificial intelligence, visual thinking, advancement of hypotheses, random process

Acknowledgements:

This work was carried out with the financial support of the Russian Foundation for Basic Research (Grant 12-01-00418-a) and of a program of the Ministry of Education and Science of the Russian Federation (Project Reg. No. 01201253217).

OCIS codes: 090.6186, 070.6110, 100.2960, 070.4790

References:

1. P. A. Belov, V. G. Bespalov, V. N. Vasil’ev, S. A. Kozlov, A. V. Pavlov, K. R. Simovskiĭ, and Yu. A. Shpolyanskiĭ, “Optical processors: achievements and new ideas,” in Problems in Coherent and Nonlinear Optics, I. P. Gurov and S. A. Kozlov ed. (SPbGU ITMO, St. Petersburg, 2006).
2. D. Gabor, “Associative holographical memories,” IBM J. Res. Dev. 13, 156 (1969).
3. Yu. N. Denisyuk, “Some problems and prospects of holography in three-dimensional media,” in Handbook of Optical Holography, H. J. Caulfield ed. (Academic Press, New York, 1979; Mir, Moscow, 1982), vol. 2, pp. 691–729.
4. K. Pribram, “Nonlocalization and localization: a holographic hypothesis concerning the functioning of the brain in the process of perception and memory,” in Synergetics and Psychology, chap. 1, Methodological Questions (MGSU Soyuz, Moscow, 1997).
5. S. B. Gurevich, B. S. Gurevich, and A. Peckus, “The problems of holographic information recording and storage: modern state,” Proc. SPIE 7142, 71420X (2008).
6. A. V. Pavlov, “Fourier holography as a modern paradigm of artificial intelligence,” Opt. Zh. 70, No. 5, 44 (2003) [J. Opt. Technol. 70, 340 (2003)].
7. A. M. Alekseev and A. V. Pavlov, “Implementation of fuzzy logic with exclusions by the Fourier-holography method,” Opt. Zh. 75, No. 4, 41 (2008) [J. Opt. Technol. 75, 242 (2008)].
8. A. V. Pavlov, “The algebra of Fourier-dual operations: logic with exclusion,” Iskusst. Intell. Prin. Resh. No. 3, 26 (2012).
9. T. Gergeĭ, “Cognitive systems,” in Transactions of the Ninth National Conference on Artificial Intelligence (Fizmatlit, Moscow, 2004), vol. 1, p. 3.
10. R. Moller and Kh.-M. Gross, “The detection of coincidences and the generation of hypotheses—an elementary function of the cerebral cortex,” in Synergetics and Psychology, chap. 3, Cognitive Processes (Kogito-Tsentr, Moscow, 2004), pp. 210–217.
11. I. B. Fominykh, “On the technology of the solution of creative problems,” in Transactions of the Eighth National Conference on Artificial Intelligence, KII-2002 (Fizmatlit, Moscow, 2002), vol. 1, pp. 519–526.

12. V. N. Vagin, E. Yu. Golovina, A. A. Zagoryanskaya, and M. V. Fomina, A Reliable and Probable Conclusion in Intelligent Systems (Fizmatlit, Moscow, 2008).
13. A. V. Pavlov, “On the possibility of using Fourier holography in the problem of modeling creative thought: requirements on the transfer characteristics of reversible holographic media,” Opt. Zh. 75, No. 10, 42 (2008) [J. Opt. Technol. 75, 643 (2008)].
14. A. V. Pavlov, “The possibility of implementing plausible reasoning by means of Fourier holography,” Opt. Zh. 77, No. 5, 24 (2010) [J. Opt. Technol. 77, 316 (2010)].
15. N. B. Tushkanov and O. N. Tushkanova, “On the construction of multisensor systems: the operating principles of the neocortex of the brain when recognizing objects of the external world,” in Transactions of the Congress on Intelligent Systems and Information Technologies IS-IT’12 (Fizmatlit, Moscow, 2012), vol. 1, pp. 373–378.
16. G. A. Sergeev and D. A. Yanutsh, Statistical Methods of Investigating Natural Objects (Gidrometeoizdat, Leningrad, 1973).
17. Yu. S. Tolchel’nikov, Optical Properties of the Landscape (Nauka, Leningrad, 1974).
18. Z. S. Bekyasheva and A. V. Pavlov, “The effect of high-frequency filtering on the characteristics of a random process as applied to the implementation of the linear-predictor model by the method of Fourier holography,” Opt. Zh. 77, No. 2, 44 (2010) [J. Opt. Technol. 77, 113 (2010)].
19. Z. S. Bekyasheva and A. V. Pavlov, “How filtering affects the statistical characteristics of images when a linear-predictor model is implemented by Fourier holography,” Opt. Zh. 78, No. 11, 36 (2011) [J. Opt. Technol. 78, 718 (2011)].
20. Z. S. Bekyasheva, V. N. Vasil’ev, A. A. Vostrikov, and A. V. Pavlov, “The effect of the characteristics of the pattern of a problem on the adequacy of hypotheses generated by a neural network with couplings according to the scheme of Fourier holography,” Nauchnotekhn. Vestnik SPb GU ITMO 74, No. 4, 20 (2011).
21. A. V. Pavlov, “On the possibility of modelling creative thought by Fourier holography,” in Transactions of the Eleventh National Conference on Artificial Intelligence (URSS, Moscow, 2008), vol. 1, pp. 384–392.
22. A. M. Kuleshov, E. I. Shubnikov, and S. A. Smaeva, “Concerning the optimal nature of a holographic matched filter,” Opt. Spektrosk. 60, 1273 (1986) [Opt. Spectrosc. 60, 791 (1986)].
23. S. A. Aleksandrina and A. M. Kuleshov, “How the rejection of the lower spatial frequencies of a spectrum affects the signal parameters in a holographic correlator,” Opt. Spektrosk. 68, 652 (1990) [Opt. Spectrosc. 68, 381 (1990)].
24. A. M. Alekseev and A. V. Pavlov, “Approximation of transfer function of the 4f scheme of Fourier holography upon fuzzy-valued logics implementation,” Opt. Spektrosk. 108, 137 (2010) [Opt. Spectrosc. 108, 137 (2010)].
25. A. D. Wentzel, A Course in the Theory of Stochastic Processes (McGraw-Hill, New York, 1981; Nauka, Moscow, 1975).
26. A. V. Pavlov, “Implementing a linear predictor model by Fourier holography,” Opt. Zh. 72, No. 2, 43 (2005) [J. Opt. Technol. 72, 199 (2005)].
27. S. B. Gurevich, V. B. Konstantinov, V. K. Sokolov, and D. F. Chernykh, Information Transmission and Processing by Holographic Methods (Sov. Radio, Moscow, 1978).
28. E. N. Knyazeva and S. P. Kurdyumov, “Intuition as self-completion,” Voprosy Fil. No. 2, 110 (1994).
29. A. M. Yaglom, Correlation Theory of Stationary Random Functions (Gidrometeoizdat, Leningrad, 1981).
30. S. B. Gurevich and B. S. Gurevich, “Possibilities of using the concept of optical degrees of freedom to evaluate the informational properties of optical systems,” Opt. Zh. 77, No. 2, 15 (2010) [J. Opt. Technol. 77, 88 (2010)].
31. S. B. Gurevich and B. S. Gurevich, “Features of representing the information content of holograms in terms of optical degrees of freedom,” Pis’ma Zh. Tekh. Fiz. 38, No. 11, 14 (2012) [Tech. Phys. Lett. 38, 503 (2012)].
32. A. V. Pavlov, “On the dependence of the characteristics of understanding when it is inductively formed on neural networks with bonds according to a Fourier-holography setup,” in The Seventh International Scientific–Practical Conference on Integrated Models and Soft Computations in Artificial Intelligence, Kolomna, 16–19 May 2011: Collection of Scientific Works (Fizmatlit, Moscow, 2011), vol. 1, pp. 349–359.