Abstract
In the paper we address the problem of computation in recurrent neural networks (RNN). In the first part we provide a formal analysis of the dynamical behavior of a RNN with a single self-recurrent unit in the hidden layer, show how such a RNN may be designed to perform an (unrestricted) counting task and describe a generalization of the counter network that performs binary stack operations.
In the second part of the paper we focus on the analysis of RNNs. We show how a layered RNN can be mapped to a corresponding iterated function system (IFS) and formulate conditions under which the behavior of the IFS and therefore the behavior of the corresponding RNN can be characterized as the performance of stack operations. This result enables us to analyze any layered RNN in terms of classical computation and, hence, improves our understanding of computation within a broad class of RNNs.
Moreover, we show how to use this knowledge as a design principle for RNNs which implement computational tasks that require stack operations. This principle is exemplified by presenting the design of particular RNNs for the recognition of words within the class of Dyck languages.
The author acknowledges support from the German Academic Exchange Service (DAAD) under grant no. D/97/29570.
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References
M. Barnsley: Fractals Everywhere. CA: Academic Press, San Diego, 1988.
M. Casey. The dynamics of discrete-time computation, with application to recurrent neural networks and finite state machine extraction. Neural Computation, 8(6):1135–1178, 1996.
J.L. Elman: Finding Structure in Time. Cognitive Science, 14, pp. 179–211, 1990.
J. Wiles and J. Elman: Learning to Count without a Counter: A Case Study of Dynamics and Activation Landscapes in Recurrent Networks. Proceedings of the Seventeenth Annual Conference of the Cognitive Science Society, Cambridge, MA, MIT Press, 1995.
C.W. Omlin and C.L. Giles. Constructing deterministic finite-state automata in recurrent neural networks. Journal of the ACM, 45(6):p. 937, 1996.
P. Grünwald and M. Steijvers: A Recurrent Network that performs a context-sensitive prediction task. Proceedings of the Eighteenth Annual Conference of the Cognitive Science Society, Morgan Kauffman, 1996.
S. Hölldobler and Y. Kalinke and H. Lehmann: Designing a Counter: Another Case Study of Dynamics and Activation Landscapes in Recurrent Networks. LNAI 1303, Proceedings of the KI97: Advances in Artificial Intelligence, Springer, pp. 313–324, 1997.
M.I. Jordan: Attractor Dynamics and Parallelism in a Connectionist Sequential Machine. Proceedings of the Annual Conference of the Cognitive Science Society, pp. 531–546, 1986.
J.F. Kolen: Exploring the Computational Capabilities of Recurrent Neural Networks. PhD Thesis, Ohio State University, 1994.
H. Nakahara and K. Doya: Dynamics of Attention as Near Saddle-Node Bifurcation Behavior. In: D.S. Touretzky and M.C. Mozer and M.E. Hasselmo (eds.): Advances in Neural Information Processing Systems, Volume 8, Neural Information Processing Systems 1995, MIT Press, 1996.
J.B. Pollack: Recursive Distributed Representations. Artificial Intelligence, 46, pp. 77–105, 1990.
P. Rodriguez and J. Wiles: Recurrent Neural Networks can Learn to Implement Symbol-Sensitive Counting. Proceedings of the 11th Conference on Neural Information Processing Systems, Denver CA, USA, 1998 (to appear).
H. Siegelmann and E.D. Sontag: Turing Computability with Neural Nets. Applied Mathematics Letters, 4(6), pp. 77–80, 1991.
A. Stolcke and D. Wu: Tree Matching with Recursive Distributed Representations. International Computer Science Institute, Berkeley, Technical Report TR-92-025, 1992.
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© 1998 Springer-Verlag Berlin Heidelberg
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Kalinke, Y., Lehmann, H. (1998). Computation in recurrent neural networks: From counters to iterated function systems. In: Antoniou, G., Slaney, J. (eds) Advanced Topics in Artificial Intelligence. AI 1998. Lecture Notes in Computer Science, vol 1502. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0095051
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DOI: https://doi.org/10.1007/BFb0095051
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