Syntactic vs Semantic Linear Abstraction and Refinement of Neural
  Networks
Calvin Chau Jan Křetínský Stefanie Mohr
Abstraction is a key verification technique to improve scalability. However,
its use for neural networks is so far extremely limited. Previous approaches
for abstracting classification networks replace several neurons with one of
them that is similar enough. We can classify the similarity as defined either
syntactically (using quantities on the connections between neurons) or
semantically (on the activation values of neurons for various inputs).
Unfortunately, the previous approaches only achieve moderate reductions, when
implemented at all. In this work, we provide a more flexible framework where a
neuron can be replaced with a linear combination of other neurons, improving
the reduction. We apply this approach both on syntactic and semantic
abstractions, and implement and evaluate them experimentally. Further, we
introduce a refinement method for our abstractions, allowing for finding a
better balance between reduction and precision.