Abstract
The possibility to represent and to process structures in a neural network greatly increases the computational capability of neural networks. This new capability, besides to provide a new tool for the classification of structures, can also be exploited to integrate neural networks and symbolic systems in a hybrid system. In fact, structures generated by a symbolic module can be evaluated by this type of networks and their evaluation can be used to modify the behavior of the symbolic module. An instance of this integration scheme is given, for example, by learning heuristics for automated deduction systems. Goller reported very successful results in using a Back-propagation Through Structure network within the SETHEO theorem prover [8]. On the other side, it is not difficult to figure out, in analogy with finite state automata extraction from recurrent networks, how to extract tree automata from a neural network for structures. This would allow the above scheme to work on the other side around, with a neural module which is driven by a symbolic subsystem.
The computational results presented in this tutorial, however, need to be extended to DOAGs in order to fully characterize the kind of symbolic computations which can be performed by recursive neural network. Nevertheless it must be pointed out that, due to its numerical nature, recursive neural networks perform a kind of computation which is not possible to easily reproduce by a symbolic system. The impact of this new style of computation should find very useful application in domains where structure and numerical values are both important aspects of the computational problem, such as in the prediction of the biological activity of drugs in Chemistry.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
N. Alon, A. K. Dewdney, and T. J. Ott. Efficient simulation of finite automata byneural nets. Journal of the Association for Computing Machinery, 38(2):495–514, 1991.
L. Atlas and al. A performance comparison of trained multilayer perceptrons and trained classification trees. Proceedings of the IEEE, 78:1614–1619, 1992.
Y. Bengio, P. Frasconi, and P. Simard. Learning long-term dependencies with gradient descent is difficult. IEEE Transactions on Neural Networks, 5(5):157–166, March 1994. Special Issue on Recurrent Neural Networks.
L. Breiman, J. Friedman, R. Olshen, and C. Stone. Classification and Regression Trees. Wadsworth International Group, 1984.
S. E. Fahlman. The recurrent cascade-correlation architecture. Technical Report CMU-CS-91-100, Carnegie Mellon, 1991.
S. E. Fahlman and C. Lebiere. The cascade-correlation learning architecture. In D. S. Touretzky, editor, Advances in Neural Information Processing Systems 2, pages 524–532. San Mateo, CA: Morgan Kaufmann, 1990.
CL. Giles, D. Chen, G.Z. Sun, H.H. Chen, Y.C. Lee, and M.W. Goudreau. Constructive learning of recurrent neural networks: Limitations of recurrent casade correlation and a simple solution. IEEE Transactions on Neural Networks, 6(4):829–836, 1995.
C. Goller. A Connectionist Approach for Learning Search-Control Heuristics for Automated Deduction Systems. PhD thesis, Technical University Munich, Computer Science, 1997.
C. Goller and A. Küchler. Learning task-dependent distributed structure-representations by backpropagation through structure. In IEEE International Conference on Neural Networks, pages 347–352, 1996.
R. C. Gonzalez and M. G. Thomason. Syntactical Pattern Recognition. Addison-Wesley, 1978.
M.W. Goudreau, C.L. Giles, S.T. Chakradhar, and D. Chen. First-order vs. second-order single layer recurrent neural networks. IEEE Transactions on Neural Networks, 5(3):511–513, 1994.
L. H. Hall and L. B. Kier. Reviews in Computational Chemistry, chapter 9, The Molecular Connectivity Chi Indexes and Kappa Shape Indexes in Structure-Property Modeling, pages 367–422. VCH Publishers, Inc.: New York, 1991.
B. Hammer and V. Sperschneider. Neural networks can approximate mappings on structured objects. In Proceedings of the 2nd International Conference on Computational Intelligence and Neuroscience, 1997. Research Triangle Park, USA.
B. G. Horne and D. R. Hush. Bounds on the complexity of recurrent neural network implementations of finite state machines. Neural Networks, 9(2):243–252, 1996.
S. C. Kremer. Comments on “constructive learning of recurrent neural networks: ...”, cascading the proof describing limitations of recurrent cascade correlation. IEEE Transactions on Neural Networks, 1995. In press.
S.C. Kremer. Finite state automata that recurrent cascade-correlation cannot represent. In D. Touretzky, M. Mozer, and M. Hasselno, editors, Advances in Neural Information Processing Systems 8. MIT Press, 1996. 612–618.
A. Küchler and C. Goller. Inductive Learning in Symbolic Domains Using Structure-Driven Recurrent Neural Networks. In Günther Görz and Steffen Hölldobler, editors, KI-96: Advances in Artificial Intelligence, Lecture Notes in Computer Science (LNCS 1137), pages 183–197, Berlin, 1996. Springer.
T. Li, L. Fang, and A. Jennings. Structurally adaptive self-organizing neural trees. In International Joint Conference on Neural Networks, pages 329–334, 1992.
C.W. Omlin and C.L. Giles. Constructing deterministic finite-state automata in recurrent neural networks. Journal of the ACM, 43(6):937–972, 1996.
M. P. Perrone. A soft-competitive splitting rule for adaptive tree-structured neural networks. In International Joint Conference on Neural Networks, pages 689–693, 1992.
M. P. Perrone and N. Intrator. Unsupervised splitting rules for neural tree classifiers. In International Joint Conference on Neural Networks, pages 820–825, 1992.
J. B. Pollack. Recursive distributed representations. Artificial Intelligence, 46(1–2):77–106, 1990.
D. E. Rumelhart and J. L. McClelland. Parallel Distributed Processing: Explorations in the Micro structure of Cognition. MIT Press, 1986.
A. Sankar and R. Mammone. Neural Tree Networks, pages 281–302. Neural Networks: Theory and Applications. Academic Press, 1991.
S. Schulz, A. Küchler, and C. Goller. Some Experiments on the Applicability of Folding Architecture Networks to Guide Theorem Proving. In Proceedings of the 10th International FLAIRS Conference, 1997.
I. K. Sethi. Entropy nets: From decision trees to neural networks. Proceeding of the IEEE, 78:1605–1613, 1990.
H. T. Siegelmann and E. D. Sontag. On the computational power of neural nets. Journal of Computer and System Sciences, 50(1):132–150, 1995.
J. A. Sirat and J-P. Nadal. Neural trees: a new tool for classification. Network, 1:423–438, 1990.
K.-Y. Siu, V. Roychowdhury, and T. Kailath. Discrete Neural Computation. Englewood Cliffs, New Jersey: Prentice Hall, 1995.
A. Sperduti and A. Starita. Supervised neural networks for the classification of structures. IEEE Transactions on Neural Networks, 8(3):714–735, 1997.
A. Sperduti, A. Starita, and C. Goller. Learning distributed representations for the classification of terms. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 509–515, 1995.
J. W. Thatcher. Tree automata: An informal survey. In A. V. Aho, editor, Currents in the Theory of Computing. Prentice-Hall, Englewood Cliffs, NJ, 1973.
R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1:270–280, 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sperduti, A. (1998). Neural networks for processing data structures. In: Giles, C.L., Gori, M. (eds) Adaptive Processing of Sequences and Data Structures. NN 1997. Lecture Notes in Computer Science, vol 1387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0053997
Download citation
DOI: https://doi.org/10.1007/BFb0053997
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64341-8
Online ISBN: 978-3-540-69752-7
eBook Packages: Springer Book Archive