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.
Figures & tables
Figure 1: Probabilistic abstract interpretation with Moore-Penrose pseudo-inverse pairs A and G . The left hand side C\xrightarrow{\text{f}}D is the concrete domain and the right hand side C^{\#}\xrightarrow{\text{f^{#}}}D^{\#} is the abstract domain.
Figure 2: lattice of abstract domain
Figure 3: abstract elements through layer
Figure 4: ReLU transformation
Figure 5: (a) A plot of model architecture of digit classifier. (b) A table of model architecture showing total number of weights and number of weights in each layer.