Analyzing neural network behavior through deep statistical model checking

Abstract

Neural networks (NN) are taking over ever more decisions thus far taken by humans, even though verifiable system-level guarantees are far out of reach. Neither is the verification technology available, nor is it even understood what a formal, meaningful, extensible, and scalable testbed might look like for such a technology. The present paper is an attempt to improve on both the above aspects. We present a family of formal models that contain basic features of automated decision-making contexts and which can be extended with further orthogonal features, ultimately encompassing the scope of autonomous driving. Due to the possibility to model random noise in the decision actuation, each model instance induces a Markov decision process (MDP) as verification object. The NN in this context has the duty to actuate (near-optimal) decisions. From the verification perspective, the externally learnt NN serves as a determinizer of the MDP, the result being a Markov chain which as such is amenable to statistical model checking. The combination of an MDP and an NN encoding the action policy is central to what we call “deep statistical model checking” (DSMC). While being a straightforward extension of statistical model checking, it enables to gain deep insight into questions like “how high is the NN-induced safety risk?”, “how good is the NN compared to the optimal policy?” (obtained by model checking the MDP), or “does further training improve the NN?”. We report on an implementation of DSMC inside the ModestToolset in combination with externally learnt NNs, demonstrating the potential of DSMC on various instances of the model family, and illustrating its scalability as a function of instance size as well as other factors like the degree of NN training.

Statistical Model Checking in Process Mining: A Comprehensive Approach to Analyse Stochastic Processes

“…Unlike other verification strategies, such as numerical analysis, SMC is distinguished by its capacity to analyse systems with large state space and to accommodate systems with unspecified implementation components. As a versatile and scalable solution, SMC offers a practical alternative for evaluating the properties of stochastic systems, as highlighted in [28][29][30] and in a comprehensive survey [31].…”

“…The system under study behaves as a black-box that is already deployed, from which sample traces can be passively observed but cannot be manipulated. More applications of SMC in stochastic systems can be found in [28][29][30].…”

Explanation Paradigms Leveraging Analytic Intuition (ExPLAIn)

“…As a result, verifying RL agents requires verifying the agents behavior in context of the environment in which it acts, leading to complex verification tasks. A light-weight, approximate alternative to the verification of RL agents is Deep Statistical Model Checking (DSMC), as proposed in the paper "Analyzing Neural Network Behavior through Deep Statistical Model Checking" [18]. As the authors show, an RL agent acting on a markov decision process, the standard formulation of an in RL, can be modeled as a Markov chain, motivating the use of probabilistic model checking to verify its safety [19].…”