Approximation of dynamical systems by continuous time recurrent neural networks
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We view selection as most closely related to the gating mechanism of traditional RNNs, which is a special case and also has a deeper history of connections to SSMs through variable discretization of Delta.
“Instead, we view it as most closely related to the gating mechanism of traditional RNNs, which is a special case (Theorem 1) and also has a deeper history of connections to SSMs through variable (input-dependent) discretization of Δ (Funahashi and Nakamura 1993; Gu, Dao, et al. 2020; Tallec and Ollivier 2018).”
From Mamba: Linear-Time Sequence Modeling with Selective State Spaces (2023) · cites this paper as Funahashi and Nakamura 1993
An artificial neural network model with recurrent connections can approximate any dynamical systems.
“An artificial neural network model with recurrent connections is known to be able to approximate any dynamical systems (Funahashi and Nakamura, 1993), so it is appropriate to model a neural process that evolves over a period such as a production of a motor sequence.”
From The Cerebro-Cerebellum as a Locus of Forward Model: A Review (2020) · cites this paper as Funahashi and Nakamura, 1993
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 Funahashi and Nakamura, 1993
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- Authors
- Funahashi, K.-I., & Nakamura, Y.
- Affiliations
- Toyohashi University of Technology (JP)
- Corresponding author
- Funahashi, Ken-ichi
- ORCID
- Nakamura, Yuichi
- Venue
- Neural Networks
- Publisher
- Elsevier BV
- Published
- 1993-01
- Volume
- 6
- Issue
- 6
- Pages
- 801-806
- ISSN
- 0893-6080 (ISSN-L)
- OpenAlex
- W2058580716
- Cited by
- 980
- References
- 0
- Citations by year
- 2026: 31 · 2025: 57 · 2024: 54 · 2023: 58 · 2022: 60 · 2021: 78 · 2020: 67 · 2019: 55 · 2018: 52 · 2017: 49 · 2016: 42 · 2015: 28 · 2014: 23 · 2013: 19 · 2012: 24
- FWCI
- 8.86
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Neural Networks (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Computer Networks and Communications › Neural Networks Stability and Synchronization
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Reservoir Computing
- Keywords
- continuous-time recurrent neural networks, dynamical systems, trajectory approximation, continuous curves, initial conditions
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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