For more information about this meeting, contact Svetlana Katok, Becky Halpenny.

Title: | Neural networks and labeled trees |

Seminar: | PMASS Colloquium |

Speaker: | Manfred Denker, Penn State |

Abstract: |

It has been observed in experiments that the number of active neurons in a neural network obeys a power law: The chances of having L of them is proportional to L^{-3/2}. I will discuss the question how this can be derived in a mathematically rigorous way from simple assumptions. It turns out that this question is related to an old theorem of Caylay (in 1889) about the number of labeled trees with a fixed number of vertices.
The mathematical tools used in the talk are taken from combinatorics (placing balls in boxes), binomial coefficients, and analysis (differentiation). |

### Room Reservation Information

Room Number: | MB113 |

Date: | 01 / 16 / 2014 |

Time: | 02:30pm - 03:20pm |