Function Feature Learning of Neural Networks

We present a Function Feature Learning (FFL) method that can measure the similarity of non-convex neural networks. The function feature representation provides crucial insights into the understanding of the relations between different local solutions of identical neural networks. Unlike existing methods that use neuron activation vectors over a given dataset as neural network representation, FFL aligns weights of neural networks and projects them into a common function feature space by introducing a chain alignment rule. We investigate the function feature representation on Multi-Layer Perceptron (MLP), Convolutional Neural Network (CNN), and Recurrent Neural Network (RNN), finding that identical neural networks trained with different random initializations on different learning tasks by the Stochastic Gradient Descent (SGD) algorithm can be projected into different fixed points. This finding demonstrates the strong connection between different local solutions of identical neural networks and the equivalence of projected local solutions. With FFL, we also find that the semantics are often presented in a bottom-up way. Besides, FFL provides more insights into the structure of local solutions. Experiments on CIFAR-100, NameData, and tiny ImageNet datasets validate the effectiveness of the proposed method.