  As neural networks (NNs) are increasingly introduced into safety-critical
domains, there is a growing need to formally verify NNs before deployment. In
this work we focus on the formal verification problem of NN equivalence which
aims to prove that two NNs (e.g. an original and a compressed version) show
equivalent behavior. Two approaches have been proposed for this problem: Mixed
integer linear programming and interval propagation. While the first approach
lacks scalability, the latter is only suitable for structurally similar NNs
with small weight changes.
  The contribution of our paper has four parts. First, we show a theoretical
result by proving that the epsilon-equivalence problem is coNP-complete.
Secondly, we extend Tran et al.'s single NN geometric path enumeration
algorithm to a setting with multiple NNs. In a third step, we implement the
extended algorithm for equivalence verification and evaluate optimizations
necessary for its practical use. Finally, we perform a comparative evaluation
showing use-cases where our approach outperforms the previous state of the art,
both, for equivalence verification as well as for counter-example finding.
