Canonization produces generalization bounds ranging from invariant-optimal to non-invariant depending on regularity, with Hilbert-curve ordering proven to give polynomial covering-number growth for point clouds while lexicographic sorting gives exponential growth.
Robustness and generalization.Machine learning, 86(3):391–423
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Agentic safety fails to generalize across tasks because the task-to-safe-controller mapping has a higher Lipschitz constant than the task-to-controller mapping alone, as proven in linear-quadratic control and demonstrated in quadcopter and LLM experiments.
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When and How to Canonize: A Generalization Perspective
Canonization produces generalization bounds ranging from invariant-optimal to non-invariant depending on regularity, with Hilbert-curve ordering proven to give polynomial covering-number growth for point clouds while lexicographic sorting gives exponential growth.
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Why Does Agentic Safety Fail to Generalize Across Tasks?
Agentic safety fails to generalize across tasks because the task-to-safe-controller mapping has a higher Lipschitz constant than the task-to-controller mapping alone, as proven in linear-quadratic control and demonstrated in quadcopter and LLM experiments.