# SOLVING NUMBER SERIES - Architectural Properties of Successful Artificial Neural Networks

### Marco Ragni, Andreas Klein

#### Abstract

Any mathematical pattern can be the generation principle for number series. In contrast to most of the application fields of artificial neural networks (ANN) a successful solution does not only require an approximation of the underlying function but to correctly predict the exact next number. We propose a dynamic learning approach and evaluate our method empirically on number series from the Online Encyclopedia of Integer Sequences. Finally, we investigate research questions about the performance of ANNs, structural properties, and the adequate architecture of the ANN to deal successfully with number series.

#### References

- Connor, J. T., Martin, R. D., and Atlas, L. E. (1994). Recurrent neural networks and robust time series prediction. IEEE Transaction on Neural Networks, 51(2):240- 254.
- Farmer, J. D. and Sidorowich, J. J. (1987). Predicting chaotic time series. Phys. Rev. Lett., 59(8):845-848.
- Franco, L. (2006). Generalization ability of boolean functions implemented in feedforward neural networks. Neurocomputing, 70:351-361.
- Gómez, I., Franco, L., and Jérez, J. M. (2009). Neural network architecture selection: Can function complexity help ? Neural Processing Letters, 30(2):71-87.
- Marr, D. (1982). Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. Freeman, New York.
- Martinetz, T. M., Berkovich, S. G., and Schulten, K. J. (1993). “Neuralgas” network for vector quantization and its application to time-series prediction. IEEE Transaction on Neural Networks, 4:558-569.
- McCulloch, W. S. and Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5:115-133.
- Ragni, M. and Klein, A. (2011). Predicting numbers: An AI approach to solving number series. In Edelkamp, S. and Bach, J., editors, KI-2011.
- Russell, S. and Norvig, P. (2003). Artificial Intelligence: A Modern Approach. Prentice Hall, 2nd edition.
- Sloane, N. J. A. (2003). The on-line encyclopedia of integer sequences. Notices of the American Mathematical Society, 50(8):912-915.
- Tatuzov, A. L. (2006). Neural network models for teaching multiplication table in primary school. In IJCNN 7806. International Joint Conference on Neural Networks, 2006, pages 5212 - 5217, Vancouver, BC, Canada.

#### Paper Citation

#### in Harvard Style

Ragni M. and Klein A. (2011). **SOLVING NUMBER SERIES - Architectural Properties of Successful Artificial Neural Networks** . In *Proceedings of the International Conference on Neural Computation Theory and Applications - Volume 1: NCTA, (IJCCI 2011)* ISBN 978-989-8425-84-3, pages 224-229. DOI: 10.5220/0003682302240229

#### in Bibtex Style

@conference{ncta11,

author={Marco Ragni and Andreas Klein},

title={SOLVING NUMBER SERIES - Architectural Properties of Successful Artificial Neural Networks},

booktitle={Proceedings of the International Conference on Neural Computation Theory and Applications - Volume 1: NCTA, (IJCCI 2011)},

year={2011},

pages={224-229},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003682302240229},

isbn={978-989-8425-84-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Neural Computation Theory and Applications - Volume 1: NCTA, (IJCCI 2011)

TI - SOLVING NUMBER SERIES - Architectural Properties of Successful Artificial Neural Networks

SN - 978-989-8425-84-3

AU - Ragni M.

AU - Klein A.

PY - 2011

SP - 224

EP - 229

DO - 10.5220/0003682302240229