Participating group members: |
Ralf Eichhorn, Peter Reimann |

Main external cooperation partners: |
Chris Van den Broeck, Géza Györgyi, Michael Biehl |

Order parameter function x(q) of a model neuron beyond its storage capacity (continuous replica symmetry broken phase) for different inverse temperatures beta. |

General context: neural networks, modeling of learning and data-analysis by means of methods from classical statistics and statistical mechanics, especially replica-techniques. In particular: new concepts and optimization of so-called unsupervised learning. Unified description of memorization and generalization problems. Theoretical limits for learning (Bayes limit) and their practical implementation as learning algorithms. Generalization for neural network setups of replica-symmetry-breaking methods, originally introduced by G. Parisi in the context of spin glass theory.

Main publications:

P. Reimann and C. Van den Broeck

*Learning by Examples from a
Non-Uniform Distribution*

Phys. Rev. E **53**, 3989 (1996)

C. Van den Broeck and P. Reimann

*Unsupervised Learning by Examples: On-line versus Off-line*

Phys. Rev. Lett. **76**, 2188 (1996)

G. Györgyi and P. Reimann

*Parisi Phase in a Neuron*

Phys. Rev. Lett. **79**, 2746 (1997)

M. Copelli, R. Eichhorn, O. Kinouchi, M. Biehl, R. Simonetti,
P. Riegler and N. Caticha

*Noise robustness in multilayer neural networks*

Europhys. Lett. **37**, 427 (1997)

P. Reimann

*Unsupervised Learning of Distributions*

Europhys. Lett. **40**, 251 (1997)

G. Györgyi and P. Reimann

*Beyond Storage Capacity in a Single Model Neuron:
Continuous Replica Symmetry Breaking*

J. Stat. Phys. **101**, 679 (2000)

*Last update on August 4, 2004.*