Optimization Under Symmetry 2021
2021-11-29..2021-12-03
-- online --
who it's for
theoretical computer scientists, applied mathematicians, quantum information researchers, statisticians, machine learning researchers, algebraic geometers, numerical optimization researchers
topics
geodesically convex optimization; matrix scaling and capacity; Harish-Chandra-Itzykson-Zuber sampling; NC-rank computation algorithm; tensor asymptotic spectrum; Kronecker coefficients complexity; continuous maximum-entropy on manifolds; equivariant reinforcement learning; symmetry-adapted Gram spectrahedra
| title | author | length |
|---|---|---|
| Norm Minimization, Invariant Theory, And Quantum Tomography | Cole Franks | 01h 06m |
Shows the exponential rate that the probability of measuring total angular momentum equals zero equals a concrete norm minimization over SL2, and more… | ||
| Computing The Nc-Rank Via Discrete Convex Optimization On Cat(0) Spaces | Hiroshi Hirai | 01h 05m |
Gives a polynomial-time algorithm for NC rank that combines submodular minimization on modular lattices with geodesically convex optimization on non-manifold… | ||
| Continuous Maximum Entropy Distributions | Jonathan Leake | 54m |
Shows that continuous maximum-entropy ensembles on a manifold reduce to a finite-dimensional convex dual that the ellipsoid method can approximate given a… | ||
| Sampling Matrices From Harish-Chandra-Itzykson-Zuber Densities | Colin McSwiggen | 50m |
Proves two efficient samplers for HCIZ/exponential measures on unitary orbits: one achieves total-variation error C in time polynomial in log(1/C), the other… | ||
| A Productization Property/Trick For H-Stable(And Hopefully Strongly Log-Concave) Polynomials | Leonid Gurvits | 01h 02m |
Claims a productization trick that locally expresses many H-stable (real-stable) polynomials as a product of simpler “product polynomials” built from matrices… | ||
| Groups And Symmetries In Statistical Models | Anna Seigal | 52m |
Draws a precise bridge between invariant theory and maximum likelihood for Gaussian models: for reductive groups unstable ↔ likelihood unbounded, semistable ↔… | ||
| Near Optimal Sample Complexity For Matrix And Tensor Normal Models Via Geodesic Convexity | Akshay Ramachandran | 23m |
Proves that maximum-likelihood estimation for matrix/tensor-normal factors attains the same sample scaling as the vector Gaussian case up to a small extra… | ||
| Two Tensor Optimization Problems From Quantum Information | Matthias Christandl | 01h 07m |
Two tensor problems are the focus: deciding transformability under local linear maps via restriction/degeneration and optimizing asymptotic resource rates… | ||
| The Kronecker Coefficients Of The Symmetric Group In Complexity And Combinatorics | Greta Panova | 01h 01m |
Gives concrete complexity and combinatorics: shows characters and Kronecker positivity is NP-hard, Kronecker values sit in GapP (unknown in #P), and uses… | ||
| Matrix Multiplication, And The Asymptotic Spectrum Of Tensors | Avi Wigderson | 01h 08m |
Survey revives Strassen's asymptotic spectra theory, frames tensors as a preordered semiring and proves a strong duality: asymptotic rank equals the maximum… | ||
| Complexity Of Computing Complex Zeros Of Structured Polynomial Systems | Peter Buergisser | 59m |
An algorithm black box solve uses randomized homotopy continuation on unitary-orbit inputs to compute an approximate zero with probability ≥ 1 − ε under a… | ||
| On The Polyhedral Geometry Of Pivot Rules | Raman Sanyal | 57m |
Constructs a concrete polytope that parametrizes how local, memoryless pivot rules vary: the pivot rule polytope records when two weight choices yield the same… | ||
| Optimization On Tensor Network Varieties | Fulvio Gesmundo | 51m |
Defines tensor network varieties as closures of images of linear-evaluation maps on graph tensors and proves: acyclic graphs have no boundary while graphs with… | ||
| Symmetry Adapted Gram Spectrahedra | Serkan Hosten | 33m |
Constructs a symmetry-adapted Gram spectrahedron by restricting Gram matrices to the fixed-point subspace for the symmetric group, uses a representation-theory… | ||
| Equivariant RL | Max Welling | 01h 09m |
Argues that encoding symmetry cuts sample complexity: policies built with group-equivariant convolutions and equivariant graph neural networks learn from far… | ||
| Equivariant Machine Learning Structured Like Classical Physics | Soledad Villar | 59m |
Provides a concrete, dimension-agnostic parameterization: inner products as complete invariants for O(d) and Minkowski variants, and any O(d)-equivariant… | ||
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