Dempster-Shafer Zonotopic Probability Bounds Analysis of Neural Networks in Julia.

Code (see notebooks in the examples directory) to reproduce the examples of: A Zonotopic Dempster-Shafer Approach to the Quantitative Verification of Neural Networks, Eric Goubault, Sylvie Putot, 2024.

Builds in particular on:

• the LazySets package for calculus with convex sets
• the ProbabilityBoundsAnalysis package for p-boxes analysis relying on Dempster-Shafer interval structures
• the NeuralVerification package

Retrieve the DSZAnalysis directory and run in this directory the command:

docker build . -f Dockerfile

An image sha256:... is built, which you can execute by:

docker run -it --name FM sha256:...

This should open Julia through docker, in which you can run the examples by:

• include("ToyExample.jl")
• include("ACASXu.jl")
• include("RocketLander.jl")

These files been executed with Julia 1.8.1 and the following Julia packages and versions:

Pkg.add(name="ProbabilityBoundsAnalysis", version="0.2.11"); 
Pkg.add(url="https://github.com/sisl/NeuralVerification.jl"); 
Pkg.add(name="LazySets", version="2.11.3"); 
Pkg.add(name="IntervalArithmetic",version="0.20.9"); 
Pkg.add(name="Distributions", version = "0.25.107"); 
Pkg.add(name="DataFrames", version="1.6.1"); 
Pkg.add(name="SplitApplyCombine",version="1.2.3"); 
Pkg.add(name="PyPlot", version = "2.11.2"); 
Pkg.add(name="Plots", version="1.39.0 »)