We thank the reviewers for their helpful comments. We completely agree and will be sure to make this point very early in a revised manuscript. We will be sure to include both numbers and figures in a revision. We prove (Section 4) that the IJ approximation error increases smoothly with the error in the initial fit. Our neural CRF experiments in Section 5 provide empirical confirmation.

Cyber-physical systems (CPS) designed in simulators, often consisting of multiple interacting agents (e.g. in multi-agent formations), behave differently in the real-world. We want to verify these systems during runtime when they are deployed. We thus propose robust predictive runtime verification (RPRV) algorithms for: (1) general stochastic CPS under signal temporal logic (STL) tasks, and (2) stochastic multi-agent systems (MAS) under spatio-temporal logic tasks. The RPRV problem presents the following challenges: (1) there may not be sufficient data on the behavior of the deployed CPS, (2) predictive models based on design phase system trajectories may encounter distribution shift during real-world deployment, and (3) the algorithms need to scale to the complexity of MAS and be applicable to spatio-temporal logic tasks. To address the challenges, we assume knowledge of an upper bound on the statistical distance between the trajectory distributions of the system at deployment and design time. We are motivated by our prior work [1, 2] where we proposed an accurate and an interpretable RPRV algorithm for general CPS, which we here extend to the MAS setting and spatio-temporal logic tasks. Specifically, we use a learned predictive model to estimate the system behavior at runtime and robust conformal prediction to obtain probabilistic guarantees by accounting for distribution shifts. Building on [1], we perform robust conformal prediction over the robust semantics of spatio-temporal reach and escape logic (STREL) to obtain centralized RPRV algorithms for MAS. We empirically validate our results in a drone swarm simulator, where we show the scalability of our RPRV algorithms to MAS and analyze the impact of different trajectory predictors on the verification result. To the best of our knowledge, these are the first statistically valid algorithms for MAS under distribution shift.

Ludwig Cancer Research scientists have developed a new and more accurate method to identify the molecular signs of cancer likely to be presented to helper T cells, which stimulate and orchestrate the immune response to tumors and infectious agents. The study, led by David Gfeller and Michal Bassani-Sternberg of the Lausanne Branch of the Ludwig Institute for Cancer Research, is reported in the current issue of Nature Biotechnology. The new method combines two powerful new technologies. One is a mass spectrometry technology developed by Bassani-Sternberg's lab to rapidly and inexpensively obtain the amino acid sequences of thousands of peptide antigens--or protein fragments--bound to a molecular complex known as HLA that is expressed on the surface of cells. The other is a novel computational tool developed in Gfeller's lab that is based on machine learning, the computational approach that powers face-recognition software, among other things.

Let's go over the Algorithm: 1. The algorithm takes an input x and a classifier f . And the loop variable to 1. 4. Start and continue loop while the true label and the label of the adversarially perturbed image is the same. 5. Calculate the projection of the input onto the closest hyperplane. With multiclass classifiers, let's say the input is x and for each class there is a hyperplane (straight plane that divides one class from the others) and based on the place in the space where x lies it is classified into a class. Now, all this algorithm does is, it finds the closest hyperplane, and then projects x onto that hyperplane and pushes it a bit beyond, thus misclassifying it with the minimal perturbation possible.