# 227-0423-00L Neural Network Theory

Semester | Autumn Semester 2022 |

Lecturers | H. Bölcskei |

Periodicity | yearly recurring course |

Course | Does not take place this semester. |

Language of instruction | English |

### Courses

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

227-0423-00 V | Neural Network Theory Does not take place this semester. Will be offered again in autumn 2023. | 2 hrs | H. Bölcskei | |

227-0423-00 U | Neural Network Theory Does not take place this semester. Will be offered again in autumn 2023. | 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, capacity of separating surfaces, generalization, fundamental limits of deep neural network learning, VC dimension. |

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 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. Vapnik-Chervonenkis (VC) dimension 7. VC dimension of neural networks 8. Generalization error in neural network learning |

Lecture notes | Detailed lecture notes are available on the course web page Link |

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 only offered in the session after the course unit. Repetition only possible after re-enrolling. |

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 | Lecture Website |

Only public learning materials are listed. |

### Groups

No information on groups available. |

### Restrictions

There are no additional restrictions for the registration. |