Efficient Sum-Check Protocol for Convolution Operation

Abstract

Convolutional Neural Networks (CNNs) are made up of sequential operations including activation, pooling, convolution, and fully connected layer that can result in enormous computation. When a user with insufficient computer capacity delegates certain tasks to a server with sufficient computing power, the user may want to verify the correctness of the delegated computation of CNNs. Specifically, we focus on the verifiable computation of matrix multiplication for operations in CNNs. We use the method [22] to verify the matrix multiplication operations and present a predicate function based on the insight that the sequence of operations can be viewed as a sequential matrix operation. Furthermore, we provide an efficient sum-check protocol for a convolution operation. As a result, we can lower the cost of proving by splitting the convolution operation into two halves and we achieve asymptotically optimal proving cost.