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.
Figures & tables
Fig. 1: probabilistic abstract interpretation with two-step abstraction
Fig. 2: Two centroids of clusters
Fig. 3: Two centroids of clusters after layer propagation