Study mirrors descent's early stopping for linear and kernel models, improving risk guarantees.
problem Understanding the statistical performance of early-stopped mirror descent algorithms.
method Characterized convexity of squared loss, identified link between offset Rademacher complexities and mirror descent convergence.
result Excess risk guarantees for mirror descent iterates traced by the path, expressed in terms of offset complexities.
Bayesian approach controls FDR in high-dimensional models.
problem High-dimensional variable selection and inference.
method Adapted Mirror Statistic to Bayesian framework for FDR control.
result Effective FDR control without data splitting.
Information geometry applies concepts in differential geometry to probability and statistics and is especially useful for parameter estimation in exponential families where parameters are known to lie on a Riemannian manifold. Connections between the geometric properties of the induced manifold and statistical properti…
NGMs create mirrored features to assess neural network feature importance.
problem Lack of feature relevance information in DNNs limits their applicability.
method Structured perturbation and kernel-based conditional dependence measure for feature importance evaluation.
result Controls feature selection error rate and maintains high selection power with correlated features.
New algorithm for optimizing statistical utilities in bandits.
problem Optimizing statistical functionals of long-run reward distributions.
method Influence-function calculus for stochastic gradient estimation, entropic mirror-ascent algorithm.
result Regret bounds that separate optimization and estimation errors.
CatNet controls FDR in LSTM models using SHAP feature importance and Gaussian mirrors.
problem Controlling False Discovery Rate (FDR) in LSTM models with feature selection.
method CatNet uses SHAP values for feature importance and Gaussian Mirror algorithm for FDR control. It introduces a kernel-based independence measure to handle feature correlations.
result CatNet reduces overfitting and improves model interpretability on simulated and real-world data.
New framework controls FDR for grouped features in sequential models.
problem FDR control for grouped features in sequential models.
method Grouped-feature FDR control framework for sequential and grouped models using mirror statistics and Permutation SHAP.
result FDR control for low- and high-dimensional grouped linear models and improved power under correlated signals.
Paper uses Stochastic Mirror Descent for large-scale sparse recovery problems.
problem Statistical estimation of high-dimensional sparse parameters.
method Non-Euclidean Composite Stochastic Mirror Descent (CSMD) algorithm for solving penalized stochastic optimization problems.
result The proposed algorithm achieves optimal convergence in sparse Generalized Linear Regression problems.
Study shows Stochastic Mirror Descent optimizes convex problems with infinite noise variance.
problem Optimizing convex problems with infinite noise variance.
method Stochastic Mirror Descent algorithm with uniformly convex mirror maps.
result Demonstrates convergence rate quantified in terms of iterations, dimensionality, and geometric parameters.
Paper tackles private optimization for non-smooth objectives efficiently.
problem Private stochastic convex optimization for non-smooth objectives.
method Noisy mirror descent algorithm.
result Achieves optimal rates in statistical complexity and number of queries.
DDO-RM improves reward-based policies by converting reward scores into a target distribution.
problem Improving reward-based policies when the reward function is simpler than the policy.
method Converts reward scores into a target distribution and uses KL-regularized mirror-descent updates.
result DDO-RM outperforms DPO in pair accuracy and mean margin.
VRSMD improves SMD convergence and has implicit regularization.
problem Efficiently estimating models with large datasets.
method Variance reduction in stochastic mirror descent.
result VRSMD converges to the minimum mirror interpolant.
The MAP estimate's log-likelihood sub-optimality is hard to bound in general.
problem Bounding the expected log-likelihood sub-optimality of MAP for exponential families.
method Interpreting MAP as stochastic mirror descent and analyzing convergence rates.
result Current convergence results do not apply to standard examples of exponential families.
New inequalities help optimize first-order algorithms for statistical risk analysis.
problem Optimizing first-order iterative algorithms for statistical risk analysis.
method Introducing basic inequalities that connect implicit and explicit regularization.
result The basic inequalities translate the number of iterations into an effective regularization coefficient.
Unified framework for non-Euclidean CPD under scalable stochastic mirror descent.
problem Handling non-Euclidean losses in tensor decomposition.
method Tensor fiber sampling strategy-based stochastic mirror descent.
result Global convergence to a stationary point under reasonable conditions.
Mirror flows converge to a limiting flow with a convex potential.
problem Incremental learning in mirror flows
method Rescaled trajectories converge to a limiting mirror flow
result Primal variable minimizes the loss over a time-dependent hypothesis set
New mirror maps improve PMD performance in reinforcement learning.
problem Limited exploration of PMD's full potential due to focus on negative entropy.
method Evolutionary strategies to identify and learn more efficient mirror maps.
result Learned mirror maps outperform negative entropy in various environments.
Study mirror symmetry on manifolds with exceptional holonomy groups.
problem Construct mirrors for Spin(7) and G2 manifolds.
method Apply mirror symmetry to pairs of non-compact manifolds and use CFT analysis.
result Confirm geometric mirror constructions for Spin(7) and G2 manifolds.
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.
problem No specific problem stated; focuses on derivation.
method Derives Mirror Descent from gradient flow on a Riemannian manifold with a natural discretization.
result Generalizes Mirror Descent to non-Hessian metrics.
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.
problem Homological mirror symmetry for Hirzebruch surfaces F k \mathbb{F}_k F k . method Using Strominger-Yau-Zaslow construction and Morse homotopy.
result Homological mirror symmetry holds for Hirzebruch surfaces F k \mathbb{F}_k F k . This paper deforms complex tori and their mirrors using gerbes.
problem Deforming complex tori and their mirror partners.
method Using flat gerbes to deform complex tori and their mirrors, constructing holomorphic line bundles over deformed objects.
result Deformed complex tori and their mirrors can be studied using flat gerbes.
Constructs mirror pairs for solvmanifolds using Lie groups.
problem Finding mirror pairs for non-Kaehler solvmanifolds.
method Left-invariant affine structures on Lie groups.
result Explicitly finds SYZ mirror symmetric partners for all known compact 6D solvmanifolds.
New analysis shows GMD can converge linearly under PL-like conditions.
problem Establishing linear convergence for generalized mirror descent.
method PL-based analysis for time-dependent mirrors, Taylor-series approach for stochastic GMD.
result Linear convergence of stochastic GMD under PL-like conditions.
Homological mirror symmetry for toric Fano surfaces using Morse homotopy.
problem Establishing homological mirror symmetry for toric Fano surfaces.
method Applying SYZ construction and using Morse homotopy of the moment polytope.
result Homological mirror symmetry achieved for toric Fano surfaces.
Researchers explore mirror symmetries for twisted G 2 G_2 G 2 manifolds.
problem Exploring mirror symmetries for compactified Type II superstrings on G 2 G_2 G 2 manifolds. method Revisits construction, discusses autoequivalence and duality, clarifies B-field role, tests conjectures against Joyce orbifold examples.
result Evidence for generalized mirror symmetries and massless spectra respectivity.
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.
problem Optimizing classification problems with separable data using mirror flow.
method Examine mirror flow on linearly separable classification problems, focusing on the horizon function of the mirror potential.
result Mirror flow converges to a maximum margin classifier for separable data under certain conditions.
Study connects mirror symmetry invariants to K-stability for toric manifolds.
problem Relating invariants from mirror symmetry to K-stability for toric polarized manifolds.
method Analyzes expansions involving base loci of linear systems from Landau-Ginzburg potentials.
result Shows Z-stability naturally arises from mirror symmetry considerations.
Reparameterizes mirror descent as gradient descent for efficient sparse learning.
problem Efficiently training small sparse networks with mirror descent.
method Develops a framework to convert mirror descent updates into gradient descent updates on different parameters.
result Mirror descent can be reparameterized as gradient descent on modified parameters, facilitating standard backpropagation.
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…
Proposes φ φ φ -balancing for more balanced expert utilization in MoE models.
problem Balanced expert utilization in MoE models to avoid bias.
method Directly targets population-level balance by minimizing a convex potential function.
result Consistently outperforms prior methods in stability and effectiveness.
The paper discusses a solution to homological mirror symmetry for complex tori, especially when the matrix is singular.
problem Homological mirror symmetry for complex tori, particularly when the matrix is singular.
method Proposes a new approach to define a mirror partner for complex tori of dimension n ≥ 2 n \geq 2 n ≥ 2 when the matrix is singular. result Proposes a method to avoid the problem of defining a mirror partner for complex tori of higher dimensions when the matrix is singular.
Find first (0,2) mirror symmetry examples on Hopf surfaces.
problem Find (0,2) mirror symmetry on compact non-Kähler manifolds.
method Use Borisov's approach with vertex algebras and chiral de Rham complex. Study Killing spinors on quadratic Lie algebras and embeddings of superconformal vertex algebras.
result Construct first (0,2) mirror pairs of 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.
problem Optimizing complex, non-smooth, non-convex functions efficiently.
method SVRAMD: Variance Reduced Adaptive Mirror Descent.
result Variance reduction accelerates convergence in adaptive mirror descent.
Mirror descent algorithm recovers low-rank matrices in matrix sensing.
problem Matrix sensing with low-rank matrices under certain conditions.
method Discrete-time mirror descent applied to empirical risk with Bregman divergence analysis.
result Mirror descent converges to a matrix minimizing a specific nuclear norm-related quantity.
Paper analyzes convergence of OMD algorithms with geometric conditions.
problem Analyzing convergence of online mirror descent algorithms.
method Presented necessary and sufficient conditions for convergence of OMD with step size sequences.
result Established conditions for convergence and linear convergence under specific variances.
New algorithm improves sampling from constrained spaces.
problem Sampling from constrained spaces efficiently.
method Metropolis-adjusted Mirror Langevin algorithm.
result Unbiased sampling with improved mixing time.
Develops parameter-free online mirror descent for optimal dynamic regret.
problem Optimal online linear optimization in unbounded domains.
method Modified online mirror descent framework for parameter-free algorithms.
result First unconstrained online linear optimization achieving optimal dynamic regret.
Study shows Calabi-Yau manifolds are non-hyperbolic via mirror symmetry.
problem Proving non-hyperbolicity of Calabi-Yau manifolds.
method Using mirror symmetry, entire curves are found on Calabi-Yau manifolds.
result Calabi-Yau manifolds are Kobayashi non-hyperbolic.
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.
problem Matching complex affine structures in SYZ fibrations of Del Pezzo surfaces.
method Floer-theoretical gluing method to construct mirrors using immersed Lagrangians.
result The constructed mirror agrees with Carl-Pomperla-Siebert's mirror.
Continuous-time mirror descent solves sparse phase retrieval efficiently.
problem Recovering sparse signals from magnitude-only measurements.
method Continuous-time mirror descent applied to unconstrained empirical risk minimization problem.
result Mirror descent recovers k k k -sparse vectors with minimum non-zero entry order of ∥ x ⋆ ∥ 2 / k \| \mathbf{x}^\star \|_2/\sqrt{k} ∥ x ⋆ ∥ 2 / k from k 2 k^2 k 2 Gaussian measurements. Paper explains scattering diagrams' role in mirror symmetry.
problem Reconstruction problem in mirror symmetry.
method Introduction of scattering diagrams and their role in SYZ and HMS conjectures.
result Scattering diagrams help in understanding mirror symmetry.
Mathematical framework for brane quantization using SYZ mirror symmetry.
problem Developing a mathematical framework for brane quantization.
method Applying SYZ mirror symmetry to construct and analyze branes.
result Established a mathematical definition of endomorphism algebras and their isomorphisms.