Appears in collection : A Multiscale tour of Harmonic Analysis and Machine Learning - To Celebrate Stéphane Mallat's 60th birthday

Machine Learning (ML) has reached an unprecedented performance in various inference problems arising in practice. The sample complexity and that of the model have, however, increasingly emerged as a serious limitation. Given the importance of a number of problems where these issues are central, we have revisited the Conv-net fundamental principle and have reformulated it from a Volterra Series perspective using a polynomial functional paradigm*. We propose a computational Convolutional Network solution which requires no activation function and provides a very competitive inference performance (often better) at a fraction of the sample and model complexity of the most competitive CNN architecture. * Homogeneous Polynomial Functional were first developed and formalized by Frechet