Learning Two-layer Neural Networks with Symmetric Inputs

We give a new algorithm for learning a two-layer neural network under a general class of input distributions. Assuming there is a ground-truth two-layer network $$y = A \sigma(Wx) + \xi,$$ where $A,W$ are weight matrices, $\xi$ represents noise, and the number of neurons in the hidden layer is no larger than the input or output, our algorithm is guaranteed to recover the parameters $A,W$ of the ground-truth network. The only requirement on the input $x$ is that it is symmetric, which still allows highly complicated and structured input. Our algorithm is based on the method-of-moments framework and extends several results in tensor decompositions. We use spectral algorithms to avoid the complicated non-convex optimization in learning neural networks. Experiments show that our algorithm can robustly learn the ground-truth neural network with a small number of samples for many symmetric input distributions

Convolutional Neural Networks over Tree Structures for Programming Language Processing

Programming language processing (similar to natural language processing) is a hot research topic in the field of software engineering; it has also aroused growing interest in the artificial intelligence community. However, different from a natural language sentence, a program contains rich, explicit, and complicated structural information. Hence, traditional NLP models may be inappropriate for programs. In this paper, we propose a novel tree-based convolutional neural network (TBCNN) for programming language processing, in which a convolution kernel is designed over programs' abstract syntax trees to capture structural information. TBCNN is a generic architecture for programming language processing; our experiments show its effectiveness in two different program analysis tasks: classifying programs according to functionality, and detecting code snippets of certain patterns. TBCNN outperforms baseline methods, including several neural models for NLP.Comment: Accepted at AAAI-1