Localization reveals geometric and analytic properties of the Witten genus.
problem Understanding the Witten genus and its modularity properties.
method Equivariant localization techniques and geometric interpretations.
result Identifies the elliptic Bismut-Chern character as a candidate target.
A new method analyzes topological B-model on a torus using doubled geometry.
problem Reproduce derived category of coherent sheaves on a torus.
method Double field theory and T-duality in doubled geometry framework.
result Correctly computes BRST cohomology and derived Hom-spaces of line bundles.
Revisits superfields and geometry, offering new formulations and interpretations.
problem Exploring the connection between N=(2,2) superfields and geometry. method Combining different superfield formulations, using a doubled target space, and interpreting equations of motion geometrically.
result Shows that the doubled geometry is Donaldson's deformation of the original Kähler manifold.
By doubling the target space of a canonical Courant algebroid and subsequently projecting down to a specific subbundle, we identify the data of double field theory (DFT) and hence define its algebroid structure. We specify the properties of the DFT algebroid. We show that one of the Courant algebroid properties plays t…
Double descent in transfer learning explained for linear regression problems.
problem Understanding generalization errors in transferring parameters between overparameterized linear regression tasks.
method Analytical characterization of generalization error in terms of transfer learning factors.
result Generalization error follows a two-dimensional double descent trend controlled by transfer learning factors.
Study topological G₂ and Spin(7) strings at 1-loop using double complexes.
problem Calculate topological string partition functions at 1-loop.
method Define double complexes for supersymmetric backgrounds using generalised geometry, compute partition functions as alternating products of determinants of Laplacians.
result Reproduce known results for G₂ string and predict for Spin(7) string.
We give a concise summary of the para-Hermitian geometry that describes a doubled target space fit for a covariant description of T-duality in string theory. This provides a generalized differentiable structure on the doubled space and leads to a kinematical setup which allows for the recovery of the physical spacetime…
New estimators for causal effects in DAGs with hidden variables, addressing computational and statistical challenges.
problem Estimating causal effects in DAGs with hidden variables beyond traditional criteria.
method Introduces novel one-step corrected plug-in and targeted minimum loss-based estimators for causal effects in DAGs with hidden variables.
result Root-n consistent causal effect estimates with desirable statistical properties.
We define a new geometric framework for string theory.
problem String theory and its symmetries.
method Para-Hermitian geometry and Born geometry.
result A geometric interpretation of string theory symmetries.
The use of target networks has been a popular and key component of recent deep Q-learning algorithms for reinforcement learning, yet little is known from the theory side. In this work, we introduce a new family of target-based temporal difference (TD) learning algorithms and provide theoretical analysis on their conver…
The paper tackles fairness in data and algorithms, expanding on prior work.
problem Discrimination and disparate treatment in data and algorithms.
method Targeted learning for nonparametric inference of fairness in the data generating process.
result Derivation and validation of estimators for fairness metrics like demographic parity and equal opportunity.
We consider the problem of search through comparisons, where a user is presented with two candidate objects and reveals which is closer to her intended target. We study adaptive strategies for finding the target, that require knowledge of rank relationships but not actual distances between objects. We propose a new str…
Paper addresses underestimation bias in double Q-learning, proposing a method to improve learning performance.
problem Underestimation bias in double Q-learning leading to non-optimal fixed points.
method Proposes a simple approach using approximate dynamic programming to bound the target value.
result Significant improvement in learning performance over baseline algorithms in Atari benchmark tasks.
It has been known for a while that the effective geometrical description of compactified strings on d-dimensional target spaces implies a generalization of geometry with a doubling of the sets of tangent space directions. This generalized geometry involves an O(d,d) pairing η and an O(2d) generalized metric $\m…
Evaluating prediction models under covariate shift and selective labels
problem Model performance evaluation under distribution shift and selection bias
method Double machine learning
result Accurate estimation of target risk
TKRR improves KRR performance by aligning target functions with kernels.
problem Improving kernel ridge regression performance through target alignment.
method Focuses on truncated kernel ridge regression (TKRR) with an additional spectral truncation parameter.
result TKRR can achieve faster rates than full KRR, reaching parametric rates.
We construct branched double coverings by certain direct products of manifolds for connected sums of copies of sphere bundles over the 2-sphere. As an application we answer a question of Kotschick and Loeh up to dimension five. More precisely, we show that: (1) every simply connected, closed four-manifold admits a bran…
We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown that a double vector bundle can be realized as the associated bundle of its frame bundle. Also dual structures, gauge transformations and conne…
The paper develops a theory for one-step Wasserstein-guided models for PDE-induced measures.
problem Theoretical understanding of generative models' accuracy in scientific computing.
method Regularity theory for optimal transport between doubling measures, excess-risk bounds.
result One-step Wasserstein-guided generative models can approximate PDE-induced measures with Hölder continuity.
Defines doubling conditions for Lorentzian spaces linked to curvature bounds.
problem Relating doubling conditions to curvature bounds in Lorentzian geometry.
method Defines doubling conditions using chronological diamonds and proves implications with timelike curvature bounds.
result Relates doubling to curvature bounds in Lorentzian geometry.
The paper characterizes Pfaffian embeddings from 2,3,5-manifolds to 7-dimensional isotropic spaces.
problem Characterizing Pfaffian embeddings from (2,3,5)-into flat (4,7)-geometries.
method Analyzing Pfaffian embeddings with specific geometric constraints.
result A generic (2,3,5)-manifold does not embed, with the first obstruction being a double root in the Cartan quartic.
Deep networks can interpolate noisy data without losing generalization.
problem Characterizing the relationship between interpolation and generalization in overparameterized deep networks.
method Analyzing the loss landscape of neural network functions over volumes around training data points, varying model parameters and training epochs.
result Loss sharpness in the input space follows a double descent, with large models predicting noisy targets over larger volumes around training data points.
We develop some theory of double fibration transforms where the cycle space is a smooth manifold and apply it to complex projective space.
Paper proposes FPG algorithm for unbiased off-policy PG estimation.
problem Challenges in off-policy policy gradient estimation.
method Double Fitted PG estimation (FPG) algorithm for arbitrary policy parameterization.
result Empirically, FPG significantly outperforms existing methods.
Unified super-symmetry and higher fluxes using super-Lie-infinity algebras.
problem Unified extended super-symmetry and higher flux densities.
method Using super-Lie-infinity algebras and their extensions and cyclifications.
result Derivation of topological T-duality laws from super-Lie-infinity structure.
A Klein surface is a surface with a dianalytic structure. A double of a Klein surface X is a Klein surface Y such that there is a degree two morphism (of Klein surfaces) Y→X. There are many doubles of a given Klein surface and among them the so-called natural doubles which are: the complex double, the …
Classifies generalized Seifert fiber spaces and their branched covers.
problem Classifying generalized Seifert fiber spaces and their topological properties.
method Symbolic classification and computation of invariants.
result Canonical double branched cover of non-manifold spaces is a Seifert manifold.
Method estimates dynamic treatment effects using machine learning and g-estimation.
problem Estimating treatment effects over time with multiple treatments and potential future outcomes.
method Double/debiased machine learning framework for dynamic treatment effects, extending Neyman orthogonal cross-fitted g-estimation. result Provides finite sample guarantees and allows for non-linear effect heterogeneity and high-dimensional parameterizations.
The paper reviews a correspondence between Double Field Theory and bundle gerbes.
problem Exploring a geometric interpretation of Double Field Theory.
method Interpreting Double Field Theory as a field theory on the total space of bundle gerbes.
result Double Field Theory can be seen as a higher geometric field theory.
The study finds infinitely many counterexamples to a generalized Double Soul Conjecture.
problem The Double Soul Conjecture for non-simply connected manifolds.
method Analysis of double disk bundles and counterexamples.
result Infinitely many counterexamples to the generalized Double Soul Conjecture.
Paper tackles efficient off-policy evaluation in long-horizon settings.
problem Efficient off-policy evaluation in long-horizon settings with diminishing overlap.
method Derives efficiency bounds for OPE under Markovian and time-invariant structures, develops a new DRL estimator.
result DRL estimator provides efficient OPE even with just one dependent trajectory in time-invariant Markov decision processes.
Researchers describe how special conic bundles deform into double solids.
problem Understanding the versal deformation of conic bundles over 3CP2. method Explicit description of deformation in a general context.
result Explicit description of the deformation of conic bundles into double solids.
DML addresses biases in machine learning by estimating nuisance functions.
problem Bias in machine learning models due to nuisance functions.
method Double/Debiased Machine Learning (DML) approach to reduce biases.
result DML allows flexible estimation of nuisance functions without auxiliary assumptions.
Study of generalized double Bruhat cells and their integrations.
problem Understanding and integrating generalized double Bruhat cells in Lie groups.
method Integrating Poisson groupoids to symplectic double groupoids, relating to fission spaces of irregular singularities.
result Explicit integrations of Poisson groupoids and Morita equivalence of double groupoids.
In a recent paper (math.DG/0701278) we constructed a series of new Moishezon twistor spaces which is a kind of variant of the famous LeBrun twistor spaces. In this paper we explicitly give projective models of another series of Moishezon twistor spaces on nCP^2 for arbitrary n>2, which can be regarded as a generalizati…
Let M be a Riemannian manifold and PM be the space of all smooth paths on M. We describe geodesics on path space PM. Normal neighbourhood structure on PM has been discussed. We identify paths on M under "back-track" equivalence. Under this identification we show that if M …
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation and basic examples come from Analytical Mechanics, where double affine bundles hav…
We construct a C-space associated with every closed 3-form on a spacetime M and show that it depends on the class of the form in H3(M,Z). We also demonstrate that C-spaces have a relation to generalized geometry and to gerbes. C-spaces are constructed after introducing additional coordinates at the open sets and …
In this paper we investigate Moishezon twistor spaces which have a structure of double covering over a very simple rational threefold. These spaces can be regarded as a direct generalization of the twistor spaces studied by Poon and Kreussler-Kurke to the case of arbitrary signature. In particular, the branch divisor o…
A new double quasi-Poisson bracket on surface groups.
problem Constructing a new mathematical structure on surface groups.
method Proposing and proving a double quasi-Poisson bracket on group algebras.
result The double quasi-Poisson bracket is a noncommutative generalization of the Goldman bracket.
Characterizes when almost smooth spaces become RCD spaces.
problem Understanding conditions for almost smooth spaces to be RCD spaces.
method Characterizations via local volume doubling and Poincaré inequality.
result Characterizes Einstein 4-orbifolds.
New method estimates precision matrices without models, achieving dense, consistent, and model-free properties.
problem Lack of methods that are dense, consistent, and model-free for precision matrix estimation.
method General class of estimators that unify dense, consistent, and model-free properties within a nonasymptotic framework.
result Ridgeless regression exhibits the double descent phenomenon, establishing a precision matrix analogue to linear regression's double descent.
Let S be a compact oriented surface with boundary together with finitely many marked points on the boundary, and let S∘ be the same surface equipped with the opposite orientation. We consider the double SD obtained by gluing the surfaces S and S∘ along corresponding boundary components. W…
Consider the case that one observes a single time-series, where at each time t one observes a data record O(t) involving treatment nodes A(t), possible covariates L(t) and an outcome node Y(t). The data record at time t carries information for an (potentially causal) effect of the treatment A(t) on the outcome Y(t), in…
Ancient caloric functions on manifolds with polynomial growth are studied under volume doubling barrier.
problem Analyzing ancient caloric functions on manifolds beyond volume doubling.
method Time polynomial structure result on ancient caloric functions with polynomial growth.
result Finiteness result for ancient caloric functions is essentially sharp, except for multi-end cases.
The paper explores geodesics on doubled polygons and their existence.
problem Existence and behavior of 1/k-geodesics on doubled polygons.
method Investigation of 1/k-geodesics on doubled polygons, focusing on regular polygons.
result Every doubled regular n-gon admits a 1/2n-geodesic, and for odd primes p, conjectures k=2p as minimum for 1/k-geodesics.
We use symplectic reduction to give a new construction of the core C of a symplectic double groupoid D as the common leaf space of characteristic foliations associated to various coisotropic submanifolds of D. In the case of the cotangent double groupoid of a Lie groupoid G, the canonical relations arising from…
We consider (local) parametrizations of Teichmuller space Tg,n (of genus g hyperbolic surfaces with n boundary components) by lengths of 6g−6+3n geodesics. We find a large family of suitable sets of 6g−6+3n geodesics, each set forming a special structure called "admissible double pants decomposition". For …