  Deep neural networks (DNNs) play an important role in machine learning due to
its outstanding performance compared to other alternatives. However, DNNs are
not suitable for safety-critical applications since DNNs can be easily fooled
by well-crafted adversarial examples. One promising strategy to counter
adversarial attacks is to utilize spectral normalization, which ensures that
the trained model has low sensitivity towards the disturbance of input samples.
Unfortunately, this strategy requires exact computation of spectral norm, which
is computation intensive and impractical for large-scale networks. In this
paper, we introduce an approximate algorithm for spectral normalization based
on Fourier transform and layer separation. The primary contribution of our work
is to effectively combine the sparsity of weight matrix and decomposability of
convolution layers. Extensive experimental evaluation demonstrates that our
framework is able to significantly improve both time efficiency (up to 60\%)
and model robustness (61\% on average) compared with the state-of-the-art
spectral normalization.
