arXiv research

Mirror flows converge to a limiting flow with a convex potential.

New mirror maps improve PMD performance in reinforcement learning.

Study mirror symmetry on manifolds with exceptional holonomy groups.

We describe mirror symmetry on higher dimensional tori, paying special attention to the behaviour of D-branes under mirror symmetry. To find the mirror D-branes the description of mirror symmetry on D-branes due to Ooguri, Oz en Yin is used. This method allows us to deal with the coisotropic D-branes recently introduce…

Derives Mirror Descent from gradient flow on a Riemannian manifold.

Motivated by Strominger-Yau-Zaslow's mirror symmetry proposal and Kontsevich's homological mirror symmetry conjecture, we study mirror phenomena (in A-model) of certain results from Donaldson-Thomas theory for Calabi-Yau 4-folds.

Study homological mirror symmetry for Hirzebruch surfaces using Morse homotopy.

This paper deforms complex tori and their mirrors using gerbes.

Constructs mirror pairs for solvmanifolds using Lie groups.

Homological mirror symmetry for toric Fano surfaces using Morse homotopy.

New analysis shows GMD can converge linearly under PL-like conditions.

In this article we explore some finer properties of equi-areal mirrors and introduce techniques for developing new mirror surfaces that simultaneously minimize angular and areal distortion.

Mirror flow optimizes separable data problems, converging to a maximum margin classifier.

Study connects mirror symmetry invariants to K-stability for toric manifolds.

Reparameterizes mirror descent as gradient descent for efficient sparse learning.

This paper focuses on a topological version on the Strominger-Yau-Zaslow mirror symmetry conjecture. Roughly put, the SYZ conjecture suggests that mirror pairs of Calabi-Yau manifolds are related by the existence of dual special Lagrangian torus fibrations. We explore this conjecture without reference to the special La…

NGMs create mirrored features to assess neural network feature importance.

We revisit our construction of mirror symmetries for compactifications of Type II superstrings on twisted connected sum $G_2$ manifolds. For a given $G_2$ manifold, we discuss evidence for the existence of mirror symmetries of two kinds: one is an autoequivalence for a given Type II superstring on a mirror pair of $G_2…

The paper discusses a solution to homological mirror symmetry for complex tori, especially when the matrix is singular.

Find first (0,2) mirror symmetry examples on Hopf surfaces.

Inspired by the paper on quantum knots and knot mosaics [23] and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology [2,3,7,24], we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. Tame knot theory is equivalent to knot…

New algorithm reduces optimization complexity in adaptive mirror descent.

Mirror descent algorithm recovers low-rank matrices in matrix sensing.

New algorithm improves sampling from constrained spaces.

Develops parameter-free online mirror descent for optimal dynamic regret.

Study shows Calabi-Yau manifolds are non-hyperbolic via mirror symmetry.

We discuss mirror symmetry in generalized Calabi-Yau compactifications of type II string theories with background NS fluxes. Starting from type IIB compactified on Calabi-Yau threefolds with NS three-form flux we show that the mirror type IIA theory arises from a purely geometrical compactification on a different class…

In this article we discuss the geometry of moduli spaces of (1) flat bundles over special Lagrangian submanifolds and (2) deformed Hermitian-Yang-Mills bundles over complex submanifolds in Calabi-Yau manifolds. These moduli spaces reflect the geometry of the Calabi-Yau itself like a mirror. Strominger, Yau and Zaslow c…

Researchers match complex affine structures in mirror constructions.

Continuous-time mirror descent solves sparse phase retrieval efficiently.

Paper explains scattering diagrams' role in mirror symmetry.

Mirror descent linked to information ratio via Bayesian regret bounds.

Mathematical framework for brane quantization using SYZ mirror symmetry.

New knot invariants discovered using mirror symmetry.

Paper studies early-stopped mirror descent for noisy sparse phase retrieval.

We address the issue why Calabi-Yau manifolds exist with a mirror pair. We observe that the irreducible spinor representation of the Lorentz group Spin(6) requires us to consider the vector spaces of two-forms and four-forms on an equal footing. The doubling of the two-form vector space due to the Hodge duality doubles…

The present paper deals with mirror symmetry aspects of compact ``barely'' $G_2$ manifolds, that is, $G_2$ manifolds of the form (CY$\times S^1)/\mathbb{Z}_2$. We propose that the mirror of any barely $G_2$ manifold is another barely one and which is constructed as a fibration of the \emph{mirror} of the CY base. Also,…

New method improves generative modeling on convex domains using regularized mirror maps and Student-t priors.

CatNet controls FDR in LSTM models using SHAP feature importance and Gaussian mirrors.

Continuous-time distributed mirror descent with integral feedback converges to global optimum.

We explore the intrinsic geometry of tangent bundles and properties of the mirror map.

Study mirrors descent's early stopping for linear and kernel models, improving risk guarantees.

This paper explores a new framework for reinforcement learning based on online convex optimization, in particular mirror descent and related algorithms. Mirror descent can be viewed as an enhanced gradient method, particularly suited to minimization of convex functions in highdimensional spaces. Unlike traditional grad…

The study connects K-stability and large complex structure limits in mirror symmetry.

The paper connects tempering and entropic mirror descent for sampling.

Stochastic mirror descent improves performance on ensemble models.

The mirror of a projective toric manifold $X_Σ$ is given by a Landau-Ginzburg model $(Y,W)$. We introduce a class of Lagrangian submanifolds in $(Y,W)$ and show that, under the SYZ mirror transformation, they can be transformed to torus-invariant hermitian metrics on holomorphic line bundles over $X_Σ$. Through this ge…

The paper explores non-Kähler SYZ mirrors for solvmanifolds, proving cohomological properties and constructing new mirror pairs.