  We present a training system, which can provably defend significantly larger
neural networks than previously possible, including ResNet-34 and DenseNet-100.
Our approach is based on differentiable abstract interpretation and introduces
two novel concepts: (i) abstract layers for fine-tuning the precision and
scalability of the abstraction, (ii) a flexible domain specific language (DSL)
for describing training objectives that combine abstract and concrete losses
with arbitrary specifications. Our training method is implemented in the DiffAI
system.
