# 227-0423-00L Neural Network Theory

Semester | Autumn Semester 2020 |

Lecturers | H. Bölcskei |

Periodicity | yearly recurring course |

Language of instruction | English |

### Courses

Number | Title | Hours | Lecturers | ||||
---|---|---|---|---|---|---|---|

227-0423-00 V | Neural Network Theory «Hybrid». Up to 150 students can attend the course on-site. Further information will be announced to enrolled students by e-mail in the week before the semester starts. The first lecture is on 21.9. | 2 hrs |
| H. Bölcskei | |||

227-0423-00 U | Neural Network Theory «Hybrid». Up to 150 students can attend the course on-site. Further information will be announced to enrolled students by e-mail in the week before the semester starts. The first lecture is on 21.9. | 1 hrs |
| H. Bölcskei |

### Catalogue data

Abstract | The class focuses on fundamental mathematical aspects of neural networks with an emphasis on deep networks: Universal approximation theorems, basics of approximation theory, fundamental limits of deep neural network learning, geometry of decision surfaces, capacity of separating surfaces, dimension measures relevant for generalization, VC dimension of neural networks. |

Objective | After attending this lecture, participating in the exercise sessions, and working on the homework problem sets, students will have acquired a working knowledge of the mathematical foundations of (deep) neural networks. |

Content | 1. Universal approximation with single- and multi-layer networks 2. Introduction to approximation theory: Fundamental limits on compressibility of signal classes, Kolmogorov epsilon-entropy of signal classes, non-linear approximation theory 3. Fundamental limits of deep neural network learning 4. Geometry of decision surfaces 5. Separating capacity of nonlinear decision surfaces 6. Dimension measures: Pseudo-dimension, fat-shattering dimension, Vapnik-Chervonenkis (VC) dimension 7. Dimensions of neural networks 8. Generalization error in neural network learning |

Lecture notes | Detailed lecture notes will be provided. |

Prerequisites / Notice | This course is aimed at students with a strong mathematical background in general, and in linear algebra, analysis, and probability theory in particular. |

### Performance assessment

Performance assessment information (valid until the course unit is held again) | |

Performance assessment as a semester course | |

ECTS credits | 4 credits |

Examiners | H. Bölcskei |

Type | session examination |

Language of examination | English |

Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |

Mode of examination | written 180 minutes |

Written aids | None |

This information can be updated until the beginning of the semester; information on the examination timetable is binding. |

### Learning materials

Main link | Course website |

Only public learning materials are listed. |

### Groups

No information on groups available. |

### Restrictions

There are no additional restrictions for the registration. |