We introduce a new type of artificial neural network (ANN): the trimming neural network (TNN) model. As most ANNs, a TNN is an alternating sequence of linear and nonlinear vectorial operators. Recall that in usual ANN models, nonlinear functions are independently applied on each entry of each layer. In contrast, we design TNNs' nonlinearities as functions of the whole layer: indeed, they are based on sorting all the layer's entries. In particular, we focus on the trimming operation which consists in summing all entries but a certain fraction of the smallest/largest ones. We show that TNNs enjoy convexity properties useful in various statistical learning contexts.
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