no code implementations • 8 Nov 2022 • Massimo Fornasier, Timo Klock, Marco Mondelli, Michael Rauchensteiner
Artificial neural networks are functions depending on a finite number of parameters typically encoded as weights and biases.
no code implementations • 18 Jan 2021 • Christian Fiedler, Massimo Fornasier, Timo Klock, Michael Rauchensteiner
In this paper we approach the problem of unique and stable identifiability of generic deep artificial neural networks with pyramidal shape and smooth activation functions from a finite number of input-output samples.
no code implementations • 30 Jun 2019 • Massimo Fornasier, Timo Klock, Michael Rauchensteiner
Gathering several approximate Hessians allows reliably to approximate the matrix subspace $\mathcal W$ spanned by symmetric tensors $a_1 \otimes a_1 ,\dots, a_{m_0}\otimes a_{m_0}$ formed by weights of the first layer together with the entangled symmetric tensors $v_1 \otimes v_1 ,\dots, v_{m_1}\otimes v_{m_1}$, formed by suitable combinations of the weights of the first and second layer as $v_\ell=A G_0 b_\ell/\|A G_0 b_\ell\|_2$, $\ell \in [m_1]$, for a diagonal matrix $G_0$ depending on the activation functions of the first layer.