pyNeVer: A Framework for Learning and Verification of Neural Networks

Abstract

Automated verification of neural networks (NNs) was first proposed in [1] and it is an established research topic with several contributions to date -see, e.g., [2]. The taxonomy proposed in [2] suggests a division among verification tools providing deterministic guarantees, e.g., Marabou [3], and those providing sound approximations, e.g., ERAN [4] and NNV [5]. pyNeVer borrows basic techniques from [5] and casts them into an abstraction approach inspired by [4]; like ERAN and NNV, it features complete verification methods, but it features a distinctive abstraction mechanism. Networks comprising layers of affine transformations and layers of activation functions such as Rectified Linear Units (Re-LUs) and sigmoids are abstracted to mappings between polytopes represented as generalized star sets [6]; the main novelty is that the abstraction level of each layer can be controlled down to a single neuron to support various refinement policies. Additionally, pyNeVer can also load popular datasets and NN models in ONNX [7] and PyTorch [8] formats, and supports training of NNs carried out transparently through PyTorch. Additionally, NNs can be manipulated through network slimming and weight pruning to ease verification -see [9].Here we focus on verification with pyNeVer and provide a brief experimental account. pyNeVer sources, documentation and examples are accessible at https://github.com/NeVerTools/pyNeVerIn the remainder of this section, we briefly introduce some basic definitions and notation used in the paper.

Digital Twins for Lighting Analysis: Literature Review, Challenges, and Research Opportunities

“…However, the complete setting in algorithm 1 potentially causes the exponential blow-up in the number of stars generated, and thus the computation might simply not be feasible. The mixed setting strikes a trade-off between complete and over-approximated setting: using an heuristic detailed in [GPT21], NEVER2 tries to concretize the least number of stars that enable proving the property without blowing the computation time. In our experiments, we consider two different sub-settings for mixed, called mixed and mixed2 which differ in the number of neurons to refine, either 1 or 2, respectively.…”

RISOPA: Rapid Imperceptible Strong One-Pixel Attacks in Deep Neural Networks

“…The formal verification of neural networks [19][20][21][22][23][24] is another valuable research direction for enhancing neural network robustness. Pulina and Tacchella [19] introduced a pivotal study on formal verification for neural networks.…”

NeVer2: Learning and Verification of Neural Networks

“…• properties about the network can be attached to it -again, visually through the addition of special blocks in the graphical interface -and the network can be verified using our backend pyNeVer (Guidotti et al, 2021) in a "pushbutton" fashion; also in this case, the user configures pyNeVer through dialog boxes which are meant to simplify the interaction as much as possible.…”

“…Guidotti et al, 2021) defines the abstract mapping of a functional layer with n ReLU activation functions and adapts the methodology proposed inTran et al (2019).The function compute layer takes as input an indexed list of N stars Θ 1 , . .…”