ReluDiff: Differential Verification of Deep Neural Networks
This addresses the need for formal guarantees in neural network compression, particularly for safety-critical applications, though it is an incremental improvement over existing verification techniques.
The paper tackles the problem of verifying the equivalence of compressed and original deep neural networks by introducing ReluDiff, a differential verification method that exploits structural similarities and gradient differences to achieve orders-of-magnitude speedup and prove more properties than existing tools.
As deep neural networks are increasingly being deployed in practice, their efficiency has become an important issue. While there are compression techniques for reducing the network's size, energy consumption and computational requirement, they only demonstrate empirically that there is no loss of accuracy, but lack formal guarantees of the compressed network, e.g., in the presence of adversarial examples. Existing verification techniques such as Reluplex, ReluVal, and DeepPoly provide formal guarantees, but they are designed for analyzing a single network instead of the relationship between two networks. To fill the gap, we develop a new method for differential verification of two closely related networks. Our method consists of a fast but approximate forward interval analysis pass followed by a backward pass that iteratively refines the approximation until the desired property is verified. We have two main innovations. During the forward pass, we exploit structural and behavioral similarities of the two networks to more accurately bound the difference between the output neurons of the two networks. Then in the backward pass, we leverage the gradient differences to more accurately compute the most beneficial refinement. Our experiments show that, compared to state-of-the-art verification tools, our method can achieve orders-of-magnitude speedup and prove many more properties than existing tools.