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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,786 papers · 148 categories

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3 results for “Spectrahedra”
Convex Algebraic Geometry of Curvature Operatorsmath.DG

Study curvature operators with sectional curvature bounds using convex algebraic geometry.

problem Characterize algebraic curvature operators with sectional curvature bounds.
method Apply convex algebraic geometry techniques, including spectrahedra and hierarchies of inner and outer approximations.
result For n≥5n \geq 5, the set of curvature operators is a spectrahedron or a spectrahedral shadow, providing counter-examples to the Helton--Nie Conjecture.
Curvature OperatorsSectional CurvatureConvex Algebraic GeometrySpectrahedraSpectrahedral Shadows
2019-08-10abs ↗pdf ↗
Neural Spectrahedra and Semidefinite Lifts: Global Convex Optimization of Polynomial Activation Neural Networks in Fully Polynomial-Timecs.LG

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.
Neural NetworksPolynomial ActivationSemidefinite ProgrammingGlobal OptimizationConvex Optimization
2021-01-07abs ↗pdf ↗
Log-concave Sampling from a Convex Body with a Barrier: a Robust and Unified Dikin Walkcs.DS

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.
samplinglog-concave distributionsconvex bodiesbarrier functionsspectrahedra
2024-10-08abs ↗pdf ↗