Spline Filters For End-to-End Deep Learning

We propose to tackle the problem of end-to-end learning for raw waveforms signals by introducing learnable continuous time-frequency atoms. The derivation of these filters is achieved by first, defining a functional space with a given smoothness order and boundary conditions. From this space, we derive the parametric analytical filters. Their differentiability property allows gradient-based optimization. As such, one can equip any Deep Neural Networks (DNNs) with these filters. This enables us to tackle in a front-end fashion a large scale bird detection task based on the freefield1010 dataset known to contain key challenges, such as high dimensional inputs ($>100000$) and the presence of multiple sources and soundscapes.