Computing matrix inversion with optical networks

With this paper we bring about a discussion on the computing potential of complex optical networks and provide experimental demonstration that an optical fiber network can be used as an analog processor to calculate matrix inversion. A 3x3 matrix is inverted as a proof-of-concept demonstration using a fiber network containing three nodes and operating at telecomm wavelength. For an NxN matrix, the overall solving time (including setting time of the matrix elements and calculation time of inversion) scales as O(N^2), whereas matrix inversion by most advanced computer algorithms requires ~O(N^2.37) computational time. For well-conditioned matrices, the error of the inversion performed optically is found to be less than 3%, limited by the accuracy of measurement equipment.Comment: 5 page

All-Optical Reinforcement Learning in Solitonic X-Junctions

L'etologia ha dimostrato che gruppi di animali o colonie possono eseguire calcoli complessi distribuendo semplici processi decisionali ai membri del gruppo. Ad esempio, le colonie di formiche possono ottimizzare le traiettorie verso il cibo eseguendo sia un rinforzo (o una cancellazione) delle tracce di feromone sia spostarsi da una traiettoria ad un'altra con feromone più forte. Questa procedura delle formiche possono essere implementati in un hardware fotonico per riprodurre l'elaborazione del segnale stigmergico. Presentiamo qui innovative giunzioni a X completamente integrate realizzate utilizzando guide d'onda solitoniche in grado di fornire entrambi i processi decisionali delle formiche. Le giunzioni a X proposte possono passare da comportamenti simmetrici (50/50) ad asimmetrici (80/20) utilizzando feedback ottici, cancellando i canali di uscita inutilizzati o rinforzando quelli usati.Ethology has shown that animal groups or colonies can perform complex calculation distributing simple decision-making processes to the group members. For example ant colonies can optimize the trajectories towards the food by performing both a reinforcement (or a cancellation) of the pheromone traces and a switch from one path to another with stronger pheromone. Such ant's processes can be implemented in a photonic hardware to reproduce stigmergic signal processing. We present innovative, completely integrated X-junctions realized using solitonic waveguides which can provide both ant's decision-making processes. The proposed X-junctions can switch from symmetric (50/50) to asymmetric behaviors (80/20) using optical feedbacks, vanishing unused output channels or reinforcing the used ones