Lottery Tickets with Nonzero Biases

The strong lottery ticket hypothesis holds the promise that pruning randomly initialized deep neural networks could offer a computationally efficient alternative to deep learning with stochastic gradient descent. Common parameter initialization schemes and existence proofs, however, are focused on networks with zero biases, thus foregoing the potential universal approximation property of pruning. To fill this gap, we extend multiple initialization schemes and existence proofs to nonzero biases, including explicit 'looks-linear' approaches for ReLU activation functions. These do not only enable truly orthogonal parameter initialization but also reduce potential pruning errors. In experiments on standard benchmark data, we further highlight the practical benefits of nonzero bias initialization schemes, and present theoretically inspired extensions for state-of-the-art strong lottery ticket pruning.