Probabilistic Abstract Interpretation on Neural Networks via Grids Approximation

Probabilistic abstract interpretation is a theory used to extract particular properties of a computer program when it is infeasible to test every single inputs. In this paper we apply the theory on neural networks for the same purpose: to analyse density distribution flow of all possible inputs of a neural network when a network has uncountably many or countable but infinitely many inputs. We show how this theoretical framework works in neural networks and then discuss different abstract domains and corresponding Moore-Penrose pseudo-inverses together with abstract transformers used in the framework. We also present experimental examples to show how this framework helps to analyse real world problems.

Distribution and Clusters Approximations as Abstract Domains in Probabilistic Abstract Interpretation to Neural Network Analysis

The probabilistic abstract interpretation framework of neural network analysis analyzes a neural network by analyzing its density distribution flow of all possible inputs. The grids approximation is one of abstract domains the framework uses which abstracts concrete space into grids. In this paper, we introduce two novel approximation methods: distribution approximation and clusters approximation. We show how these two methods work in theory with corresponding abstract transformers with help of illustrations of some simple examples.

Comparison of Syntactic and Semantic Representations of Programs in Neural Embeddings

Neural approaches to program synthesis and understanding have proliferated widely in the last few years; at the same time graph based neural networks have become a promising new tool. This work aims to be the first empirical study comparing the effectiveness of natural language models and static analysis graph based models in representing programs in deep learning systems. It compares graph convolutional networks using different graph representations in the task of program embedding. It shows that the sparsity of control flow graphs and the implicit aggregation of graph convolutional networks cause these models to perform worse than naive models. Therefore it concludes that simply augmenting purely linguistic or statistical models with formal information does not perform well due to the nuanced nature of formal properties introducing more noise than structure for graph convolutional networks.