Optimistic bilevel optimization with manifold lower-level minimizers is differentiable if the optimistic selection is unique, yielding a pseudoinverse hyper-gradient and a convergent HG-MS algorithm whose rate depends on intrinsic manifold dimension.
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The free subgroup of higher smooth surgery structure sets of complex projective spaces is determined in all dimensions up to extension problems, together with the forgetful map to topological versions in low dimensions.
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Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets
Optimistic bilevel optimization with manifold lower-level minimizers is differentiable if the optimistic selection is unique, yielding a pseudoinverse hyper-gradient and a convergent HG-MS algorithm whose rate depends on intrinsic manifold dimension.
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Higher Smooth Surgery Structure Sets of Complex Projective Spaces, Part I
The free subgroup of higher smooth surgery structure sets of complex projective spaces is determined in all dimensions up to extension problems, together with the forgetful map to topological versions in low dimensions.