We propose a method for formally certifying and quantifying individual fairness of deep neural networks (DNN). Individual fairness guarantees that any two individuals who are identical except for a legally protected attribute (e.g., gender or race) receive the same treatment. While there are existing techniques that provide such a guarantee, they tend to suffer from lack of scalability or accuracy as the size and input dimension of the DNN increase. Our method overcomes this limitation by applying abstraction to a symbolic interval based analysis of the DNN followed by iterative refinement guided by the fairness property. Furthermore, our method lifts the symbolic interval based analysis from conventional qualitative certification to quantitative certification, by computing the percentage of individuals whose classification outputs are provably fair, instead of merely deciding if the DNN is fair. We have implemented our method and evaluated it on deep neural networks trained on four popular fairness research datasets. The experimental results show that our method is not only more accurate than state-of-the-art techniques but also several orders-of-magnitude faster.
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