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Incorporating learning based components in the current state-of-the-art cyber-physical systems (CPS) has been a challenge due to the brittleness of the underlying deep neural networks. On the bright side, if executed correctly with safety guarantees, this has the ability to revolutionize domains like autonomous systems, medicine, and other safety-critical domains. This is because it would allow system designers to use high-dimensional outputs from sensors like camera and LiDAR. The trepidation in deploying systems with vision and LiDAR components comes from incidents of catastrophic failures in the real world. Recent reports of self-driving cars running into difficult to handle scenarios is ingrained in the software components which handle such sensor inputs.

The ability to handle such high-dimensional signals is due to the explosion of algorithms which use deep neural networks. Sadly, the reason behind the safety issues is also due to deep neural networks themselves. The pitfalls occur due to possible over-fitting and lack of awareness about the blind spots induced by the training distribution. Ideally, system designers would wish to cover as many scenarios during training as possible. However, achieving a meaningful coverage is impossible. This naturally leads to the following question: is it feasible to flag out-of-distribution (OOD) samples without causing too many false alarms? Such an OOD detector should be executable in a fashion that is computationally efficient. This is because OOD detectors often are executed as frequently as the sensors are sampled.

Our aim in this article is to build an effective anomaly detector. To this end, we propose the idea of a memory bank to cache data samples which are representative enough to cover most of the in-distribution data. The similarity with respect to such samples can be a measure of familiarity of the test input. This is made possible by an appropriate choice of distance function tailored to the type of sensor we are interested in. Additionally, we adapt conformal anomaly detection framework to capture the distribution shifts with a guarantee of false alarm rate. We report the performance of our technique on two challenging scenarios: a self-driving car setting implemented inside the simulator CARLA with image inputs and autonomous racing car navigation setting with LiDAR inputs. From the experiments, it is clear that a deviation from the in-distribution setting can potentially lead to unsafe behavior. It should be noted that not all OOD inputs lead to precarious situations in practice, but staying in-distribution is akin to staying within a safety bubble and predictable behavior. An added benefit of our memory-based approach is that the OOD detector produces interpretable feedback for a human designer. This is of utmost importance since it recommends a potential fix for the situation as well. In other competing approaches, such feedback is difficult to obtain due to reliance on techniques which use variational autoencoders. 

We present an approach for the synthesis and verification of neural network controllers for closed loop dynamical systems, modelled as an ordinary differential equation. Feedforward neural networks are ubiquitous when it comes to approximating functions, especially in the machine learning literature. The proposed verification technique tries to construct an over-approximation of the system trajectories using a combination of tools, such as, Sherlock and Flow*. In addition to computing reach sets, we incorporate counter examples or bad traces into the synthesis phase of the controller as well. We go back and forth between verification and counter example generation until the system outputs a fully verified controller, or the training fails to terminate in a neural network which is compliant with the desired specifications. We demonstrate the effectiveness of our approach over a suite of benchmarks ranging from 2 to 17 variables. 

In this paper, we provide an approach to data-driven control for artificial pancreas systems by learning neural network models of human insulin-glucose physiology from available patient data and using a mixed integer optimization approach to control blood glucose levels in real-time using the inferred models. First, our approach learns neural networks to predict the future blood glucose values from given data on insulin infusion and their resulting effects on blood glucose levels. However, to provide guarantees on the resulting model, we use quantile regression to fit multiple neural networks that predict upper and lower quantiles of the future blood glucose levels, in addition to the mean. Using the inferred set of neural networks, we formulate a model-predictive control scheme that adjusts both basal and bolus insulin delivery to ensure that the risk of harmful hypoglycemia and hyperglycemia are bounded using the quantile models while the mean prediction stays as close as possible to the desired target. We discuss how this scheme can handle disturbances from large unannounced meals as well as infeasibilities that result from situations where the uncertainties in future glucose predictions are too high. We experimentally evaluate this approach on data obtained from a set of 17 patients over a course of 40 nights per patient. Furthermore, we also test our approach using neural networks obtained from virtual patient models available through the UVA-Padova simulator for type-1 diabetes. 

Given a neural network (NN) and a set of possible inputs to the network described by polyhedral constraints, we aim to compute a safe over-approximation of the set of possible output values. This operation is a fundamental primitive enabling the formal analysis of neural networks that are extensively used in a variety of machine learning tasks such as perception and control of autonomous systems. Increasingly, they are deployed in high-assurance applications, leading to a compelling use case for formal verification approaches. In this paper, we present an efficient range estimation algorithm that iterates between an expensive global combinatorial search using mixed-integer linear programming problems, and a relatively inexpensive local optimization that repeatedly seeks a local optimum of the function represented by the NN. We implement our approach and compare it with Reluplex, a recently proposed solver for deep neural networks. We demonstrate applications of our approach to computing flowpipes for neural network-based feedback controllers. We show that the use of local search in conjunction with mixed-integer linear programming solvers effectively reduces the combinatorial search over possible combinations of active neurons in the network by pruning away suboptimal nodes.