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Zuo Y, Ning N, Qiao GC, Wu JH, Bao JH, Zhang XY, Bai J, Wu FH, Liu Y, Yu Q, Hu SG. Floating-Point Approximation Enabling Cost-Effective and High-Precision Digital Implementation of FitzHugh-Nagumo Neural Networks. IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 2024; 18:347-360. [PMID: 37878421 DOI: 10.1109/tbcas.2023.3327496] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2023]
Abstract
The study of neuron interactions and hardware implementations are crucial research directions in neuroscience, particularly in developing large-scale biological neural networks. The FitzHugh-Nagumo (FHN) model is a popular neuron model with highly biological plausibility, but its complexity makes it difficult to apply at scale. This paper presents a cost-saving and improved precision approximation algorithm for the digital implementation of the FHN model. By converting the computational data into floating-point numbers, the original multiplication calculations are replaced by adding the floating-point exponent part and fitting the mantissa part with piecewise linear. In the hardware implementation, shifters and adders are used, greatly reducing resource overhead. Implementing FHN neurons by this approximation calculations on FPGA reduces the normalized root mean square error (RMSE) to 3.5% of the state-of-the-art (SOTA) while maintaining a performance overhead ratio improvement of 1.09 times. Compared to implementations based on approximate multipliers, the proposed method achieves a 20% reduction in error at the cost of a 2.8% increase in overhead.This model gained additional biological properties compared to LIF while reducing the deployment scale by only 9%. Furthermore, the hardware implementation of nine coupled circular networks with eight nodes and directional diffusion was carried out to demonstrate the algorithm's effectiveness on neural networks. The error decreased to 60% compared to the single neuron of the SOTA. This hardware-friendly algorithm allows for the low-cost implementation of high-precision hardware simulation, providing a novel perspective for studying large-scale, biologically plausible neural networks.
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Narisawa N, Chauvet N, Hasegawa M, Naruse M. Arm order recognition in multi-armed bandit problem with laser chaos time series. Sci Rep 2021; 11:4459. [PMID: 33627692 PMCID: PMC7904956 DOI: 10.1038/s41598-021-83726-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2020] [Accepted: 02/08/2021] [Indexed: 11/12/2022] Open
Abstract
By exploiting ultrafast and irregular time series generated by lasers with delayed feedback, we have previously demonstrated a scalable algorithm to solve multi-armed bandit (MAB) problems utilizing the time-division multiplexing of laser chaos time series. Although the algorithm detects the arm with the highest reward expectation, the correct recognition of the order of arms in terms of reward expectations is not achievable. Here, we present an algorithm where the degree of exploration is adaptively controlled based on confidence intervals that represent the estimation accuracy of reward expectations. We have demonstrated numerically that our approach did improve arm order recognition accuracy significantly, along with reduced dependence on reward environments, and the total reward is almost maintained compared with conventional MAB methods. This study applies to sectors where the order information is critical, such as efficient allocation of resources in information and communications technology.
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Affiliation(s)
- Naoki Narisawa
- Department of Mathematical Engineering and Information Physics, Faculty of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.
| | - Nicolas Chauvet
- Department of Mathematical Engineering and Information Physics, Faculty of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.,Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan
| | - Mikio Hasegawa
- Department of Electrical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo, 125-8585, Japan
| | - Makoto Naruse
- Department of Mathematical Engineering and Information Physics, Faculty of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan. .,Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.
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Seifikar M, Amann A, Peters FH. Dynamics of two identical mutually delay-coupled semiconductor lasers in photonic integrated circuits. APPLIED OPTICS 2018; 57:E37-E44. [PMID: 30117919 DOI: 10.1364/ao.57.000e37] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2018] [Accepted: 05/18/2018] [Indexed: 06/08/2023]
Abstract
We theoretically investigate a system of two mutually delay-coupled semiconductor lasers, in a face to face configuration for integration in a photonic integrated circuit. This system is described by single-mode rate equations, which are a system of delay differential equations with one fixed delay. Several bifurcation scenarios involving multistabilities are presented, followed by a comprehensive frequency analysis of the symmetric and symmetry-broken, one-color and two-color states.
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Jüngling T, Soriano MC, Oliver N, Porte X, Fischer I. Consistency properties of chaotic systems driven by time-delayed feedback. Phys Rev E 2018; 97:042202. [PMID: 29758606 DOI: 10.1103/physreve.97.042202] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2017] [Indexed: 06/08/2023]
Abstract
Consistency refers to the property of an externally driven dynamical system to respond in similar ways to similar inputs. In a delay system, the delayed feedback can be considered as an external drive to the undelayed subsystem. We analyze the degree of consistency in a generic chaotic system with delayed feedback by means of the auxiliary system approach. In this scheme an identical copy of the nonlinear node is driven by exactly the same signal as the original, allowing us to verify complete consistency via complete synchronization. In the past, the phenomenon of synchronization in delay-coupled chaotic systems has been widely studied using correlation functions. Here, we analytically derive relationships between characteristic signatures of the correlation functions in such systems and unequivocally relate them to the degree of consistency. The analytical framework is illustrated and supported by numerical calculations of the logistic map with delayed feedback for different replica configurations. We further apply the formalism to time series from an experiment based on a semiconductor laser with a double fiber-optical feedback loop. The experiment constitutes a high-quality replica scheme for studying consistency of the delay-driven laser and confirms the general theoretical results.
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Affiliation(s)
- T Jüngling
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
| | - M C Soriano
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
| | - N Oliver
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
| | - X Porte
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
| | - I Fischer
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
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Porte X, D'Huys O, Jüngling T, Brunner D, Soriano MC, Fischer I. Autocorrelation properties of chaotic delay dynamical systems: A study on semiconductor lasers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052911. [PMID: 25493862 DOI: 10.1103/physreve.90.052911] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2014] [Indexed: 06/04/2023]
Abstract
We present a detailed experimental characterization of the autocorrelation properties of a delayed feedback semiconductor laser for different dynamical regimes. We show that in many cases the autocorrelation function of laser intensity dynamics can be approximated by the analytically derived autocorrelation function obtained from a linear stochastic model with delay. We extract a set of dynamic parameters from the fit with the analytic solutions and discuss the limits of validity of our approximation. The linear model captures multiple fundamental properties of delay systems, such as the shift and asymmetric broadening of the different delay echoes. Thus, our analysis provides significant additional insight into the relevant physical and dynamical properties of delayed feedback lasers.
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Affiliation(s)
- Xavier Porte
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Otti D'Huys
- Institute of Theoretical Physics, University of Würzburg, 97074 Würzburg, Germany
| | - Thomas Jüngling
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Daniel Brunner
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Miguel C Soriano
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Ingo Fischer
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
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