ADAPTATION OF COMPUTER OPTICS METHODS FOR SIMULATING SEMANTIC DYNAMICS OF TEXT BASED ON GEOMETRIZATION IN MINKOWSKI SPACE
V.V. Antonov1, A.Kh. Sultanov1, L.E. Rodionova1, E.V. Palchevsky2, V.A. Suvorova1
1Ufa University of Science and Technology, Ufa, Russia
2MIREA - Russian Technological University (RTU MIREA), Moscow, Russia
Keywords: wave optics, computer optics, finite difference time domain (FDTD) method, phase reconstruction, semantic analysis, Minkowski space, coherence, multidimensional signal processing
Abstract
The work solves the problem of quantitative modeling of the semantic structure of text, which is formulated as the inverse problem of wave optics. Based on the established operational analogy between semantic dynamics and the propagation of coherent radiation in an inhomogeneous environment, geometrization of text in Minkowski space is proposed. Within this analogy, the concept of "semantic refractive index" is introduced, and the text is considered as a field of complex amplitude. The key result is to demonstrate the applicability of numerical methods of computer optics - the Finite-Difference Time-Domain (FDTD) method for direct modeling of the propagation of the semantic front and iterative phase recovery algorithms (Gershberg-Saxton) for reconstructing the latent thematic structure by the distribution of the "intensity" of embeddings. Experimental testing on a scientific text confirmed that the proposed approach makes it possible to visualize thematic clusters as a mode structure of a waveguide beam and quantify the coherence of discourse through a coefficient similar to the degree of spatial coherence. The work expands the scope of computer optics methods to the problems of analyzing complex semantic systems.
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