We study the structure of the set of algebraic curvature operators satisfying a sectional curvature bound under the light of the emerging field of Convex Algebraic Geometry. More precisely, we determine in which dimensions this convex semialgebraic set is a spectrahedron or a spectrahedral shadow; in particular, fo…
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3 results for “spectrahedra”
Paper develops exact convex optimization for neural networks with polynomial activations.
problem Training two-layer neural networks with nonlinear polynomial activations.
method Exact convex optimization using semidefinite programming.
result Global optimization of neural networks is polynomial-time computable.
A new sampling method for log-concave distributions with warm starts and barriers.
problem Sampling from log-concave distributions constrained by convex bodies with barriers.
method Robust sampling framework using spectral approximations to Hessian of barrier functions.
result Improved mixing times for polytopes and spectrahedra, faster than previous methods.