Michael Schmitt Address: Fakultät für Mathematik Lehrstuhl Mathematik & Informatik Ruhr-Universität Bochum D-44780 Bochum Germany Office: NA 1/71 eMail: mschmitt [AT] lmi [DOT] ruhr-uni-bochum [DOT] de Telephone: 0234-32-23209 Fax: 0234-32-14465

Publications

Journals

• On the complexity of learning lexicographic strategies, by Michael Schmitt and Laura Martignon. Journal of Machine Learning Research 7(Jan), pages 55-83, 2006. [Abstract]

• Inner product spaces for Bayesian networks, by Atsuyoshi Nakamura, Michael Schmitt, Niels Schmitt, and Hans Ulrich Simon. Journal of Machine Learning Research 6(Sep), pages 1383-1403, 2005. [Abstract]

• On the capabilities of higher-order neurons: A radial basis function approach, by Michael Schmitt. Neural Computation 17(3), pages 715-729, 2005. [Abstract]

• On the power of Boolean computations in generalized RBF neural networks, by Frauke Friedrichs and Michael Schmitt. Neurocomputing 63, pages 483-498, 2005. [Abstract]

• On the sample complexity of learning for networks of spiking neurons with nonlinear synaptic interactions, by Michael Schmitt. IEEE Transactions on Neural Networks 15(5), pages 995-1001, 2004. [Abstract]

• Some dichotomy theorems for neural learning problems, by Michael Schmitt. Journal of Machine Learning Research 5(Aug), pages 891-912, 2004. [Abstract]

• New designs for the Descartes rule of signs, by Michael Schmitt. American Mathematical Monthly 111(2), pages 159-164, 2004.

• Descartes' rule of signs for radial basis function neural networks, by Michael Schmitt. Neural Computation 14(12), pages 2997-3011, 2002. [Abstract]

• Neural networks with local receptive fields and superlinear VC dimension, by Michael Schmitt. Neural Computation 14(4), pages 919-956, 2002. [Abstract]

• On the complexity of computing and learning with multiplicative neural networks, by Michael Schmitt. Neural Computation 14(2), pages 241-301, 2002. [Abstract]

• On using the Poincaré polynomial for calculating the VC dimension of neural networks, by Michael Schmitt. Neural Networks 14(10), page 1465, 2001.

• Simplicity and robustness of fast and frugal heuristics, by Laura Martignon and Michael Schmitt, Minds and Machines 9(4), pages 565-593, 1999. [Abstract]

• On the sample complexity for nonoverlapping neural networks, by Michael Schmitt. Machine Learning 37(2), pages 131-141, 1999. [Abstract]

• On the complexity of learning for spiking neurons with temporal coding, by Wolfgang Maass and Michael Schmitt. Information and Computation 153, pages 26-46, 1999. [Abstract]

• On computing Boolean functions by a spiking neuron, by Michael Schmitt. Annals of Mathematics and Artificial Intelligence 24, pages 181-191, 1998. [Abstract]

• Self-organization of spiking neurons using action potential timing, by Berthold Ruf and Michael Schmitt. IEEE Transactions on Neural Networks 9(3), pages 575-578, 1998. [Abstract]

• Identification criteria and lower bounds for Perceptron-like learning rules, by Michael Schmitt. Neural Computation 10(1), pages 235-250, 1998. [Abstract]

• Proving hardness of neural network training problems, by Michael Schmitt. Neural Networks 10(8), pages 1533-1534, 1997.

• Learning temporally encoded patterns in networks of spiking neurons, by Berthold Ruf and Michael Schmitt. Neural Processing Letters 5(1), pages 9-18, 1997. [Abstract]

• Exact VC-dimension of Boolean monomials, by Thomas Natschläger and Michael Schmitt. Information Processing Letters 59, pages 19-20, 1996. Erratum ibid. 60, page 107, 1996. [Abstract]

Conferences

• On the accuracy of bounded rationality: How far from optimal is fast and frugal?, by Michael Schmitt and Laura Martignon. In Y. Weiss, B. Schölkopf, and J. C. Platt (eds.), Advances in Neural Information Processing Systems 18, to appear, MIT Press, Cambridge, MA, 2006. [Abstract]

• An improved VC dimension bound for sparse polynomials, by Michael Schmitt. In J. Shawe-Taylor and Y. Singer (eds.), Proceedings of the 17th Annual Conference on Learning Theory COLT 2004, Lecture Notes in Artificial Intelligence, volume 3120, pages 393-407, Springer-Verlag, Berlin, 2004. [Abstract]

• Bayesian networks and inner product spaces, by Atsuyoshi Nakamura, Michael Schmitt, Niels Schmitt, and Hans Ulrich Simon. In J. Shawe-Taylor and Y. Singer (eds.), Proceedings of the 17th Annual Conference on Learning Theory COLT 2004, Lecture Notes in Artificial Intelligence, volume 3120, pages 518-533, Springer-Verlag, Berlin, 2004. [Abstract]

• RBF neural networks and Descartes' rule of signs, by Michael Schmitt. In N. Cesa-Bianchi, M. Numao, and R. Reischuk (eds.), Proceedings of the 13th International Conference on Algorithmic Learning Theory ALT02, Lecture Notes in Artificial Intelligence, volume 2533, pages 321-335, Springer-Verlag, Berlin, 2002. [Abstract]

• Computing time lower bounds for recurrent sigmoidal neural networks, by Michael Schmitt. In T. G. Dietterich, S. Becker, and Z. Ghahramani (eds.), Advances in Neural Information Processing Systems 14, volume 1, pages 503-510, MIT Press, Cambridge, MA, 2002. [Abstract]

• Complexity of learning for networks of spiking neurons with nonlinear synaptic interactions, by Michael Schmitt. In G. Dorffner, H. Bischof, and K. Hornik (eds.), Proceedings of the International Conference on Artificial Neural Networks ICANN 2001, Lecture Notes in Computer Science, volume 2130, pages 247-252, Springer-Verlag, Berlin, 2001. [Abstract]

• Product unit neural networks with constant depth and superlinear VC dimension, by Michael Schmitt. In G. Dorffner, H. Bischof, and K. Hornik (eds.), Proceedings of the International Conference on Artificial Neural Networks ICANN 2001, Lecture Notes in Computer Science, volume 2130, pages 253-258, Springer-Verlag, Berlin, 2001. [Abstract]

• Radial basis function neural networks have superlinear VC dimension, by Michael Schmitt. In D. Helmbold and B. Williamson (eds.), Proceedings of the 14th Annual Conference on Computational Learning Theory COLT 2001 and 5th European Conference on Computational Learning Theory EuroCOLT 2001, Lecture Notes in Artificial Intelligence, volume 2111, pages 14-30, Springer-Verlag, Berlin, 2001. [Abstract]

• Lower bounds on the complexity of approximating continuous functions by sigmoidal neural networks, by Michael Schmitt. In S. A. Solla, T. K. Leen, and K.-R. Müller (eds.), Advances in Neural Information Processing Systems 12, pages 328-334, MIT Press, Cambridge, MA, 2000. [Abstract]

• VC dimension bounds for product unit networks, by Michael Schmitt. In Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks IJCNN'2000, volume IV, pages 165-170, IEEE Computer Society, Los Alamitos, CA, 2000. [Abstract]

• VC dimension bounds for higher-order neurons, by Michael Schmitt. In Proceedings of the 9th International Conference on Artificial Neural Networks ICANN99, volume 2, pages 563-568, IEE Conference Publication No. 470, Institution of Electrical Engineers, London, 1999. [Abstract]

• On the implications of delay adaptability for learning in pulsed neural networks, by Michael Schmitt. In J. Demiris and G. Westermann (eds.), Proceedings of the Workshop on Biologically-Inspired Machine Learning, pages 28-37, Chania, Greece, 1999. [Abstract]

• VC dimension bounds for networks of spiking neurons, by Michael Schmitt. In M. Verleysen (ed.), Proceedings of the 7th European Symposium on Artificial Neural Networks ESANN'99, pages 429-434, D-Facto, Brussels, 1999. [Abstract]

• On the sample complexity for neural trees, by Michael Schmitt. In M. M. Richter, C. H. Smith, R. Wiehagen and T. Zeugmann (eds.), Proceedings of the 9th International Conference on Algorithmic Learning Theory ALT'98, Lecture Notes in Artificial Intelligence, volume 1501, pages 375-384, Springer-Verlag, Berlin, 1998. [Abstract]

• Complexity of Boolean computations for a spiking neuron, by Michael Schmitt. In L. Niklasson, M. Bodén and T. Ziemke (eds.), Proceedings of the 8th International Conference on Artificial Neural Networks ICANN 98, volume 2, pages 585-590, Perspectives in Neural Computing, Springer-Verlag, London, 1998. [Abstract]

• On the complexity of computing and learning with networks of spiking neurons, by Wolfgang Maass and Michael Schmitt. In Electronic Proceedings of the Fifth International Symposium on Artificial Intelligence and Mathematics, http://rutcor.rutgers.edu/~amai/, 1998. [Abstract]

• Self-organizing maps of spiking neurons using temporal coding, by Berthold Ruf and Michael Schmitt. In J. M. Bower (ed.), Computational Neuroscience: Trends in Research, 1998, pages 509-514, Plenum Press, New York, 1998. [Abstract]

• Improving the performance of satisficing cognitive algorithms, by Michael Schmitt and Laura Martignon. Annual Meeting of the Society for Judgement and Decision Making J/DM, 1997. [Abstract]

• Unsupervised learning in networks of spiking neurons using temporal coding, by Berthold Ruf and Michael Schmitt. In W. Gerstner, A. Germond, M. Hasler and J.-D. Nicoud (eds.), Proceedings of the 7th International Conference on Artificial Neural Networks - ICANN'97, Lecture Notes in Computer Science, volume 1327, pages 361-366, Springer-Verlag, Berlin, 1997. [Abstract]

• On the complexity of learning for a spiking neuron, by Wolfgang Maass and Michael Schmitt. Proceedings of the Tenth Annual Conference on Computational Learning Theory COLT'97, pages 54-61, ACM Press, New York, 1997. [Abstract]

• Hebbian learning in networks of spiking neurons using temporal coding, by Berthold Ruf and Michael Schmitt. In J. Mira, R. Moreno-Díaz and J. Cabestany (eds.), Biological and Artificial Computation: From Neuroscience to Technology. Proceedings of the International Work-Conference on Artificial and Natural Neural Networks IWANN'97, Lecture Notes in Computer Science, volume 1240, pages 380-389, Springer-Verlag, Berlin, 1997. [Abstract]

• Lower bounds on identification criteria for Perceptron-like learning rules, by Michael Schmitt. In Robert Trappl, editor, Proceedings of the Thirteenth European Meeting on Cybernetics and Systems Research EMCSR '96, volume 2, pages 1049-1054, Vienna, 1996. [Abstract]

• On methods to keep learning away from intractability, by Michael Schmitt. In F. Fogelman-Soulié and P. Gallinari, editors, Proceedings of the International Conference on Artificial Neural Networks ICANN '95, volume 1, pages 211-216, EC2 & Cie., Paris, 1995. [Abstract]

• On the size of weights for McCulloch-Pitts neurons, by Michael Schmitt. In E. R. Caianiello, editor, Proceedings of the Sixth Italian Workshop on Neural Nets WIRN VIETRI-93, pages 241-246, World Scientific, Singapore, 1994. [Abstract]

Contributions to Books

• Unsupervised learning and self-organization in networks of spiking neurons, by Thomas Natschläger, Berthold Ruf, and Michael Schmitt. In U. Seiffert and L. C. Jain (eds.), Self-Organizing Neural Networks: Recent Advances and Applications, Studies in Fuzziness and Soft Computing, vol. 78, pages 45-73, Physica-Verlag, Heidelberg, 2002. [Abstract]

• Abzählbarkeit; Axiom; Backpropagation; Explosion, kombinatorische; Formalismus; Gödelscher Satz; Gradientenmethode; Kalkül; Knoten; Knoten, verborgene, Neuronen, verborgene; Lernregel; Netzarchitektur; Rekursionstheorie, Theorie rekursiver Funktionen; System, formales; Theorem; Widerspruchsfreiheit,Konsistenz; XOR-Problem.
  In Gerhard Strube u.a. (Hrsg.), Wörterbuch der Kognitionswissenschaft. Klett-Cotta, Stuttgart, 1996.

A Survey Paper

• Einführung in die Komplexität des Rechnens und Lernens mit neuronalen Netzen, von Michael Schmitt. In Georg Dorffner, Knut Möller, Gerhard Paaß, Raúl Rojas und Stephan Vogel (Hrsg.), Konnektionismus und Neuronale Netze: Beiträge zur Herbstschule HeKoNN96, Münster/Westf., S. 41-52, St. Augustin, 1996. GMD-Studien Nr. 300, GMD-Forschungszentrum Informationstechnik GmbH.

  An earlier version appeared as

• Die Komplexität des Rechnens und Lernens mit neuronalen Netzen - Ein Kurzführer, von Michael Schmitt. In Georg Dorffner, Knut Möller, Gerhard Paaß und Stephan Vogel (Hrsg.), Konnektionismus und Neuronale Netze: Beiträge zur Herbstschule HeKoNN95, Münster/Westf., S. 83-93, St. Augustin, 1995. GMD-Studien Nr. 272, GMD-Forschungszentrum Informationstechnik GmbH.

Unpublished Technical Reports

• Complexity of lexicographic strategies on binary cues, by Michael Schmitt and Laura Martignon. Preprint, 1999.

• Unwind Property von Algebren endlicher Wörter und Mengen bezüglich polynomiell zeitbeschränkter Programme, von Michael Schmitt und Volker Sperschneider. Interner Bericht Nr. 8/87, Fakultät für Informatik der Universität Karlsruhe, März 1987.

Doctoral Dissertation

• Komplexität neuronaler Lernprobleme, von Michael Schmitt. Dissertation, Universität Ulm, 1994. [English abstract]

  Also available as

• Komplexität neuronaler Lernprobleme, von Michael Schmitt. Band 20 der Europäischen Hochschulschriften, Reihe XLI. Peter Lang Verlag, Frankfurt am Main, 1996. (ISBN 3-631-49906-X)

Diploma Thesis

• Untere Schranken für Schaltkreise und die Polynomielle Hierarchie, von Michael Schmitt. Diplomarbeit an der Fakultät für Informatik der Universität Karlsruhe, Institut für Logik, Komplexität und Deduktionssysteme, 1988.