On the computational power of neural nets
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Recurrent NNs have a remarkable capacity for algorithmic learning and are Turing-complete.
“recent work has shown a remarkable capacity for algorithmic learning with recurrent NNs [14] that are known to be Turing-complete [15].”
From An Introduction to Deep Learning for the Physical Layer (2017) · cites this paper as [15]
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Research works printed but not linked: 16
- J. Berstel, C. Reutenauer, Rational Series and Their Languages, Springer-Verlag, Berlin, 1988.
- L, Blum, M. Shub, and S. Smale, "On a theory of computation and complexity over the real numbers: NP completeness, recursive functions, and univer- sal machines," Buii. A.M.S. 21(1989): 1-46:
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- J.E. Hopcroft, and J .D. Unman, ntro uction to Automata Theory, Languages, and Computation, Addison-Wesley, 1979.
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- w. . cCulloch, W. Pitts, "A logical calculus of the ideas immanent in nervous activity," Bull. Math. Biophys. 5(1943): 115-133.
- M.L. Minsky, Computation: Finite and Infinite Machines, Prentice Hall, Engelwood Cliffs, 1967.
- J.B. Pollack, On Connectionist Models of Natu- ral Language Processing, Ph.D. Dissertation, Com- puter Science Dept, Univ. of Illinois, Urbana, 1987.
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- G.Z. Sun, H.H. Chen, Y.C. Lee, and C.L. Giles, "Turin~equivalence of neural networks with second order ~on~ection weights," Nets, Seattle, 1991:11,357-. in Int .Jt. Conf.Neural
Cited by
Sorted by citations
An Introduction to Deep Learning for the Physical Layer
O'Shea, T., & Hoydis, J. (2017) · IEEE Transactions on Cognitive Communications and Networking · doi:10.1109/tccn.2017.2758370 · Cited by 2,980 · see citing works
Transformers learn to implement preconditioned gradient descent for in-context learning
Ahn, K., Cheng, X., Daneshmand, H., & Sra, S. (2023) · arXiv · doi:10.48550/arxiv.2306.00297 · Cited by 11 · see citing works
“The seminal work by Siegelmann and Sontag (1992) investigate the Turing completeness of recurrent neural networks.”
BackgroundDissociating Artificial Intelligence from Artificial Consciousness
Findlay, G., Marshall, W., Albantakis, L., David, I., Mayner, W. G., Koch, C., & Tononi, G. (2024) · arXiv · doi:10.48550/arxiv.2412.04571 · Cited by 6 · see citing works
“Turing completeness can be achieved using radically different substrates [72–75], whether simple [46, 76] or complex, feedfor-ward [77] or recurrent [78, 79].”
Implicit Language Models are RNNs: Balancing Parallelization and Expressivity
Schöne, M., Rahmani, B., Kremer, H., Falck, F., Ballani, H., & Gladrow, J. (2025) · arXiv · doi:10.48550/arxiv.2502.07827
“On the theoretical side, The pio-neering work of Siegelmann & Sontag (1992) shows that iterated RNNs are Turing complete at infinite numerical precision.”
- Authors
- Siegelmann, H. T., & Sontag, E. D.
- Affiliations
- Department of Computer Science, Rutgers University, New Brunswick, NJ
- Department of Mathematics, Rutgers University, New Brunswick, NJ
- Venue
- Proceedings of the fifth annual workshop on Computational learning theory
- Publisher
- ACM
- Published
- 1992-07
- Pages
- 440-449
- Cited by
- 139
- References
- 0
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