A complete classification of symmetries in shallow ReLU networks is achieved by using the non-differentiability of ReLU.
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The structure of the inverse system of Gorensteink-algebras
12 Pith papers cite this work. Polarity classification is still indexing.
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Minimal sufficient Jordan algebras characterize sufficiency for positive trace-preserving maps on quantum states, with Neyman-Pearson tests generating them and equality in data-processing inequalities implying Petz recovery.
Extends Steinberg algebras to ample semicategories, relates them to Boolean restriction semigroups, and proves a reconstruction theorem characterizing algebras with quasi-Cartan-like subsemigroups as Steinberg algebras of ultrafilter groupoids.
Constructs equivariant basic cohomology for Lie groupoids with weak actions and uses it to define equivariant Chen-Ruan cohomology on orbifolds.
Bilinear generating function for Wronskians of Hermite polynomials equals the Mehler kernel times a polynomial.
A β-deformed version of motivic Segre classes of Schubert cells is constructed via the connective formal group law, with rational representatives via lattice models and structure constants via Knutson-Tao puzzles proven using quantum group intertwiners for d=1.
Veering triangulations for Anosov flows with orientable foliations admit Legendrian edge realizations in strongly adapted bicontact structures and can be placed in steady position, implying horizontal surgery correspondences via prior author result.
Constructs canonical p-energy measures for strongly local p-energy forms, proves chain/Leibniz rules and uniqueness, and shows coincidence with Korevaar-Schoen-type measures via a p-analogue of Le Jan's domination principle.
Relates the category of quantum Harish-Chandra bimodules at odd roots of unity to affine Soergel bimodules and non-commutative Springer resolution.
Establishes monotone quantities and sharp mass-p-capacity inequalities for p-capacitary functions in 3D AF half-spaces with nonnegative scalar and boundary mean curvature, equality on Schwarzschild half-spaces.
Generalizes Iarrobino's symmetric decomposition to self-dual modules over local algebras, classifies local Hilbert functions for small degrees, and extends Kunte's self-duality criterion.
Studies changes in geometric properties of conv(W · a) for finite Coxeter groups W, with focus on persistent simplices, triangulations, and subdivisions.
citing papers explorer
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A Complete Symmetry Classification of Shallow ReLU Networks
A complete classification of symmetries in shallow ReLU networks is achieved by using the non-differentiability of ReLU.
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Sufficiency and Petz recovery for positive maps
Minimal sufficient Jordan algebras characterize sufficiency for positive trace-preserving maps on quantum states, with Neyman-Pearson tests generating them and equality in data-processing inequalities implying Petz recovery.
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Steinberg Algebras of Ample Semicategories and their Boolean-Cartan Restriction Semigroups
Extends Steinberg algebras to ample semicategories, relates them to Boolean restriction semigroups, and proves a reconstruction theorem characterizing algebras with quasi-Cartan-like subsemigroups as Steinberg algebras of ultrafilter groupoids.
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Equivariant basic cohomology of Lie groupoids
Constructs equivariant basic cohomology for Lie groupoids with weak actions and uses it to define equivariant Chen-Ruan cohomology on orbifolds.
-
Mehler formula for Wronskians of Hermite polynomials
Bilinear generating function for Wronskians of Hermite polynomials equals the Mehler kernel times a polynomial.
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Motivic Segre classes of Schubert cells and the connective formal group law
A β-deformed version of motivic Segre classes of Schubert cells is constructed via the connective formal group law, with rational representatives via lattice models and structure constants via Knutson-Tao puzzles proven using quantum group intertwiners for d=1.
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Legendrian position of veering triangulations
Veering triangulations for Anosov flows with orientable foliations admit Legendrian edge realizations in strongly adapted bicontact structures and can be placed in steady position, implying horizontal surgery correspondences via prior author result.
-
Construction of $p$-energy measures associated with strongly local $p$-energy forms
Constructs canonical p-energy measures for strongly local p-energy forms, proves chain/Leibniz rules and uniqueness, and shows coincidence with Korevaar-Schoen-type measures via a p-analogue of Le Jan's domination principle.
-
Quantum Harish-Chandra bimodules at roots of unity and affine Hecke category
Relates the category of quantum Harish-Chandra bimodules at odd roots of unity to affine Soergel bimodules and non-commutative Springer resolution.
-
Mass-$p$-Capacity Inequalities in Asymptotically Flat Half-Spaces
Establishes monotone quantities and sharp mass-p-capacity inequalities for p-capacitary functions in 3D AF half-spaces with nonnegative scalar and boundary mean curvature, equality on Schwarzschild half-spaces.
-
Iarrobino's symmetric decomposition for self-dual modules
Generalizes Iarrobino's symmetric decomposition to self-dual modules over local algebras, classifies local Hilbert functions for small degrees, and extends Kunte's self-duality criterion.
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Persistent Subdivisions of Coxeter Permutahedra
Studies changes in geometric properties of conv(W · a) for finite Coxeter groups W, with focus on persistent simplices, triangulations, and subdivisions.