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.

In the context of assistive robotics, myocontrol is one of the so-far unsolved problems of upper-limb prosthetics. It consists of swiftly, naturally and reliably converting biosignals, non-invasively gathered from an upper-limb disabled subject, into control commands for an appropriate self-powered prosthetic device. Despite decades of research, traditional surface electromyography cannot yet detect the subject's intent to an acceptable degree of reliability, that is, enforce an action exactly when the subject wants it to be enforced.In this work we tackle one such kind of mismatch between the subject's intent and the response by the myocontrol system, and show that Formal Verification can indeed be used to mitigate it. Eighteen intact subjects were engaged in two Target Achievement Control tests in which a standard myocontrol system was compared with two "repaired" ones, one based on a non-formal technique, and thus enforcing no guarantee of safety, and the other using the Satisfiability Modulo Theories (SMT) technology to rigorously enforce the desired property. The experimental results indicate that both repaired systems exhibit better reliability than the non-repaired one. The SMT-based system causes only a modest increase in the required computational resources with respect to the non-formal technique; as opposed to this, the non-formal technique can be easily implemented in existing myocontrol systems, potentially increasing their reliability.

Formal verification of neural networks is a promising technique to improve their dependability for safety critical applications. Autonomous driving is one such application where the controllers supervising different functions in a car should undergo a rigorous certification process. In this paper we present an example about learning and verification of an adaptive cruise control function on an autonomous car. We detail the learning process as well as the attempts to verify various safety properties using the tool NeVer2 a new framework that integrates learning and verification in a single easy-to-use package intended for practictioners rather than experts in formal methods and/or machine learning.

Despite the increasing popularity of Machine Learning methods, their usage in safety-critical applications is sometimes limited by the impossibility of providing formal guarantees on their behaviour. In this work we focus on one such application, where Kernel Ridge Regression with Random Fourier Features is used to learn controllers for a prosthetic hand. Due to the non-linearity of the activation function used, these controllers sometimes fail in correctly identifying users' intention. Under specific circumstances muscular activation levels may be misinterpreted by the method, resulting in the prosthetic hand not behaving as intended. To alleviate this problem, we propose a novel method to verify the presence of this kind of intent detection mismatch and to repair controllers leveraging off-the-shelf LP technology without using additional data. We demonstrate the feasibility of our approach using datasets gathered from human participants.

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