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

Zhuofan Zhang, Herbert Wiklicky

Abstract

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.

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

Abstract

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.

Paper Structure

This paper contains 10 sections, 53 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Abstract Domains
  3. Distribution Approximation as Abstract Domain
  4. Polynomial Regression
  5. Radial Basis Functions
  6. Fourier Transform
  7. Clusters Approximation as Abstract Domain
  8. K-means
  9. Gaussian Mixture Model
  10. Conclusions and Future Work

Figures (3)

  • Figure 1: probabilistic abstract interpretation with two-step abstraction
  • Figure 2: Two centroids of clusters
  • Figure 3: Two centroids of clusters after layer propagation