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This paper develops a PAC-Bayesian framework for physics-informed machine learning, providing high-probability generalization guarantees for unbounded losses. It proposes a multi-task perspective that jointly handles data fidelity, PDE residuals, and boundary conditions, and introduces a self-bounding learning algorithm.
This paper develops a PAC-Bayesian framework for test-time adaptation that uses MMD-balls as credal sets, providing formal generalization bounds and separating epistemic from aleatoric uncertainty under distribution shift.
This paper studies generalization in learning through the lens of bounded-rational decision theory, where the learner's response law induces a tradeoff between training loss and sample dependence. The authors show that this tradeoff is governed by an f-divergence regularizer and that generalization can be certified from the learner's hedging behavior.