Applies optimal transport to bound OOD generalization error in Transformers via Lipschitz continuity and TC^0 circuit depth lower bounds for Dyck-k backtracking, supported by evaluations on 54 configurations.
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A generalized zeroth-order method samples random directions on the sphere to optimize quotients of quadratics, estimates Riemannian derivatives with surrogates, and yields an accelerated algorithm outperforming prior work.
A certificate of unboundedness is introduced for arbitrary polynomial optimization problems to detect cases with no finite lower bound.
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A Measure-Theoretic Analysis of Reasoning: Structural Generalization and Approximation Limits
Applies optimal transport to bound OOD generalization error in Transformers via Lipschitz continuity and TC^0 circuit depth lower bounds for Dyck-k backtracking, supported by evaluations on 54 configurations.
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Generalization of Zeroth-Order Method for Quotients of Quadratic Functions
A generalized zeroth-order method samples random directions on the sphere to optimize quotients of quadratics, estimates Riemannian derivatives with surrogates, and yields an accelerated algorithm outperforming prior work.
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A Certificate of Unboundedness for Polynomial Optimization Problems
A certificate of unboundedness is introduced for arbitrary polynomial optimization problems to detect cases with no finite lower bound.