May 2026

“You can’t always get what you want. But sometimes you get what you need.” — The Rolling Stones Circular functions and hyperbolic functions aren’t invertible, but we invert them anyway. These functions map many points in the domain to each point in the range, and we invert them by mapping a point in the range back to some point in the domain. Often this works as expected, but sometimes it doesn’t. In the previous post I said You can […]

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Modern smart grids rely on dense measurement infrastructures, communication links, and intelligent field devices. Although this improves supervision and control, it also increases vulnerability to cyber-physical disruptions. Operators must distinguish physical incidents, such as faults or line disturbances, from malicious actions, such as false data injection or unauthorized command execution. This chapter investigates this problem using the well-known MSU/ORNL Power System Attack Dataset. The proposed method combines machine learning with genetic-algorithm-based feature selection. The objective is twofold: to […]

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Autonomous systems have achieved superhuman performance in isolation or simulation, yet they remain brittle in shared, dynamic real-world spaces. This failure stems from the dominant single-agent paradigm for physical applications, where other actors are ignored or treated as environmental noise, preventing effective coordination. Here we show that multi-agent reinforcement learning provides the essential safety scaffolding required for real-world interaction. Using high-speed quadrotor racing as a high-stakes testbed, we train agents to navigate complex aerodynamic interactions and strategic maneuvering […]

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Real-world sensor-based learning systems require uncertainty estimation that is both reliable and computationally efficient. Evidential Deep Learning (EDL) provides single-pass uncertainty estimation by modeling the class probabilities via Dirichlet distributions, where the Dirichlet parameters are predicted by a learned neural network mapping. However, this approach can lead to computational challenges, as Dirichlet expected objectives are more complex than standard supervised learning losses, complicating their analysis and implementation. We address this issue by approximating the objective of the first-order […]

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We study the approximation and statistical complexity of learning collections of operators in a shared multi-task setting, with a focus on the Multiple Neural Operators (MNO) architecture. For broad classes of Lipschitz multiple operator maps, we derive near-optimal upper bounds for approximation and statistical generalization. On the lower-bound side, we establish a curse of parametric complexity and prove corresponding minimax rates. Together, these results show that shared representations across tasks do not increase the overall cost: multi-task operator […]

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