  Estimating the Lipschitz constant of deep neural networks is of growing
interest as it is useful for informing on generalisability and adversarial
robustness. Convolutional neural networks (CNNs) in particular, underpin much
of the recent success in computer vision related applications. However,
although existing methods for estimating the Lipschitz constant can be tight,
they have limited scalability when applied to CNNs. To tackle this, we propose
a novel method to accelerate Lipschitz constant estimation for CNNs. The core
idea is to divide a large convolutional block via a joint layer and width-wise
partition, into a collection of smaller blocks. We prove an upper-bound on the
Lipschitz constant of the larger block in terms of the Lipschitz constants of
the smaller blocks. Through varying the partition factor, the resulting method
can be adjusted to prioritise either accuracy or scalability and permits
parallelisation. We demonstrate an enhanced scalability and comparable accuracy
to existing baselines through a range of experiments.
