Sampling theorems of neural networks: from one neuron to deep networks
A lecture within Identification of Artificial Neural Networks class of the Mathematics for daTa scieNce study plan
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Bio
Ha conseguito il titolo di Dottore di Ricerca in Matematica computazionale nel 2003 presso l'Università di Padova. Dopo aver speso il periodo dal 2003 al 2006 come ricercatore post-doc presso l'Università di Vienna e l'Università di Roma "La Sapienza", ha preso servizio presso lo Johann Radon Institute for Computational and Applied Mathematics dell'Accademia delle Scienze Austriaca, dove ha lavorato come Senior Scientists fino al marzo 2011. È stato Associate Researcher dal 2006 al 2007 presso il Program in Applied and Computational Mathematics della Princeton University negli USA. Nel 2011 viene chiamato per Chiara Fama come Professore Ordinario di Analisi Applicata e Numerica dalla Technische Universität München in Germania, titolo che ricopre tuttora. È autore di una settantina di articoli scientifici. Ha supervisionato gli studi e le ricerche di 7 studenti di dottorato e di 14 post-dottorandi.Abstract
Identifying a neural network is an NP-hard problem in general. In this talk we address conditions of exact identification of one hidden layer and then deep totally connected feed forward neural networks by means of a number of samples, which scales polynomially with the dimension of the input and network size. The exact identification is obtained by computing second order approximate strong or weak differentials of the network and their unique and stable decomposition into nonorthogonal rank-1 terms. The procedure combines several novel matrix optimization algorithms over the space of second order differentials. As a byproduct we introduce a new whitening procedure for matrices, which allows the stable decomposition of symmetric matrices into nonorthogonal rank-1 decompositions, by reducing the problem to the standard orthonormal decomposition case. We show that this algorithm practically achieve information theoretical recovery bounds. We illustrate the results by several numerical experiments.
This is a joint work with Ingrid Daubechies, Timo Klock, Michael Rauchensteiner, and Jan Vybíral.
Schedule
- 2023/01/19 14.30-16.30, Room A210 @ Povo 1
Details
- Venue: Polo Scientifico e Tecnologico F. Ferrari
- Language: English
- The participation is free. Please send an email to Prof. Claudio Agostinelli. This is important to book the approrpiate room.
- For further information, please contact Prof. Claudio Agostinelli