### Abstract

In this paper we introduce and investigate a mathematically rigorous theory of learning curves that is based on ideas from statistical mechanics. The advantage of our theory over the well-established Vapnik-Chervonenkis theory is that our bounds can be considerably tighter in many cases, and are also more reflective of the true behavior (functional form) of learning curves. This behavior can often exhibit dramatic properties such as phase transitions, as well as power law asymptotics not explained by the VC theory. The disadvantages of our theory are that its application requires knowledge of the input distribution, and it is limited so far to finite cardinality function classes. We illustrate our results with many concrete examples of learning curve bounds derived from our theory.

Original language | English (US) |
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Title of host publication | Proceedings of the 7th Annual Conference on Computational Learning Theory, COLT 1994 |

Publisher | Association for Computing Machinery |

Pages | 76-87 |

Number of pages | 12 |

ISBN (Electronic) | 0897916557 |

DOIs | |

State | Published - Jul 16 1994 |

Event | 7th Annual Conference on Computational Learning Theory, COLT 1994 - New Brunswick, United States Duration: Jul 12 1994 → Jul 15 1994 |

### Publication series

Name | Proceedings of the Annual ACM Conference on Computational Learning Theory |
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Volume | Part F129415 |

### Other

Other | 7th Annual Conference on Computational Learning Theory, COLT 1994 |
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Country | United States |

City | New Brunswick |

Period | 7/12/94 → 7/15/94 |

### All Science Journal Classification (ASJC) codes

- Software
- Theoretical Computer Science
- Artificial Intelligence

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## Cite this

*Proceedings of the 7th Annual Conference on Computational Learning Theory, COLT 1994*(pp. 76-87). (Proceedings of the Annual ACM Conference on Computational Learning Theory; Vol. Part F129415). Association for Computing Machinery. https://doi.org/10.1145/180139.181018