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Safety is a critical concern for the next generation of autonomy that is likely to rely heavily on deep neural networks for perception and control. This paper proposes a method to repair unsafe ReLU DNNs in safety-critical systems using reachability analysis. Our repair method uses reachability analysis to calculate the unsafe reachable domain of a DNN, and then uses a novel loss function to construct its distance to the safe domain during the retraining process. Since subtle changes of the DNN parameters can cause unexpected performance degradation, we also present a minimal repair approach where the DNN deviation is minimized. Furthermore, we explore applications of our method to repair DNN agents in deep reinforcement learning (DRL) with seamless integration with learning algorithms. Our method is evaluated on the ACAS Xu benchmark and a rocket lander system against the state-of-the-art method ART. Experimental results show that our repair approach can generate provably safe DNNs on multiple safety specifications with negligible performance degradation, even in the absence of training data (Code is available online at https://github.com/Shaddadi/veritex.git). 

The nuclear two-photon or double-gamma ( $2\gamma$) decay is a second-order electromagnetic process whereby a nucleus in an excited state emits two gamma rays simultaneously. To be able to directly measure the $2\gamma$decay rate in the low-energy regime below the electron-positron pair-creation threshold, we combined the isochronous mode of a storage ring with Schottky resonant cavities. The newly developed technique can be applied to isomers with excitation energies down to $\sim 100\mathrm{keV}$and half-lives as short as $\sim 10\mathrm{ms}$. The half-life for the $2\gamma$decay of the first-excited $0^{+}$state in bare ${}^{72}\mathrm{Ge}$ions was determined to be 23.9(6) ms, which strongly deviates from expectations. Published by the American Physical Society2024