On the complexity of shallow and deep neural network classifiers

By Monica Bianchini, Franco Scarselli. 2014

55 citations recorded by the source corpus.

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In Scaling & Learning Theory

Citations in the corpus

Wide Residual Networks (2016, background): “…increase of the number of layers in the last few years, starting from AlexNet [14], VGG [24], Inception [28] to Residual [9] networks, corresponding to improvements in many image recognition tasks. a The superiority of deep networks has been spotted in several works in the recent years [3, 20].”
The Power of Depth for Feedforward Neural Networks (2015, background): “(2014) consider the number of linear regions which can be expressed by ReLU networks of a given width and size, and Bianchini and Scarselli (2014) consider the topological complexity (via Betti numbers) of networks with certain activation functions, as a function of the depth.”
Depth-Width Tradeoffs in Approximating Natural Functions with Neural Networks (2016, background): “…ones (e.g. (Cohen et al., 2016; De-lalleau & Bengio, 2011; Martens & Medabalimi, 2014)), measuring quantities other than approximation error (e.g. (Bianchini & Scarselli, 2014; Poole et al., 2016)), focusing only on approximation upper bounds (e.g. (Shaham et al., 2016)), or measuring…”
The Nonlinearity Coefficient - Predicting Generalization in Deep Neural Networks (2018, background): “Depth A large body of work has detailed the benefits of depth in neural networks (e.g. Montafur et al. (2014); Delalleau & Bengio (2011); Martens et al. (2013); Bianchini & Scarselli (2014); Shamir & Eldan (2015); Telgarsky (2015); Mhaskar & Shamir (2016)).”
On the Origin of Deep Learning (2017, background): “Further, Bianchini and Scarselli (2014) extended this study to a general neural network with many major activation functions including tanh and sigmoid.”