Chaos in random neural networks
Abstract
A continuous-time dynamic model of a network of $N$ nonlinear elements interacting via random asymmetric couplings is studied. A self-consistent mean-field theory, exact in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, predicts a transition from a stationary phase to a chaotic phase occurring at a critical value of the gain parameter. The autocorrelations of the chaotic flow as well as the maximal Lyapunov exponent are calculated.
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A recurrent neural network is difficult to train and control because it may exhibit chaotic behavior.
“A recurrent neural network is also known to be difficult to train and control because it may exhibit chaotic behavior (Sompolinsky et al., 1988; Sussillo and Abbott, 2009; Laje and Buonomano, 2013; Ben-Shushan and Tsodyks, 2017).”
From The Cerebro-Cerebellum as a Locus of Forward Model: A Review (2020) · cites this paper as Sompolinsky et al., 1988
Recurrent connections in a neural network provide computational flexibility to model a dynamical system but cause a chaotic instability due to dependence on previous activities and random noises.
“Recurrent connections in a neural network provide computational flexibility to model a dynamical system (Funahashi and Nakamura, 1993) but cause a chaotic instability due to dependence on previous activities and random noises (Sompolinsky et al., 1988).”
From The Cerebro-Cerebellum as a Locus of Forward Model: A Review (2020) · cites this paper as Sompolinsky et al., 1988
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- Authors
- Sompolinsky, H., Crisanti, A., & Sommers, H. J.
- Affiliations
- AT&T (United States) (US)
- University of Duisburg-Essen (DE)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1988-07-18
- Volume
- 61
- Issue
- 3
- Pages
- 259-262
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2027802883
- Cited by
- 1,061
- References
- 0
- Citations by year
- 2026: 65 · 2025: 97 · 2024: 74 · 2023: 65 · 2022: 67 · 2021: 53 · 2020: 75 · 2019: 59 · 2018: 51 · 2017: 38 · 2016: 42 · 2015: 34 · 2014: 22 · 2013: 27 · 2012: 16
- FWCI
- 12.26
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- IRIS Research product catalog (Sapienza University of Rome) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
- Keywords
- chaos, random neural networks, continuous-time dynamics, mean-field theory, autocorrelation, largest Lyapunov exponent
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