arXiv research

Paper proves energy identity and no-neck property for special harmonic maps.

Domain adaptation leverages the knowledge in one domain - the source domain - to improve learning efficiency in another domain - the target domain. Existing heterogeneous domain adaptation research is relatively well-progressed, but only in situations where the target domain contains at least a few labeled instances. I…

Homogenized SGD explains SGD dynamics in high dimensions.

Adapting \cite{strz3}, we define generalized $p$-harmonic maps into Riemannian homogeneous targets, a notion of solutions not belonging to the energy space. Restricting our attention to the subcritical range $p$ greater than the domain dimension $n$, we show a uniform $C^{1,α}$-regularity result for a sequence of such …

We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may arise when trying to preserve symmetries under quantization. The sym…

This paper continues the work of our previous paper [8], where we generalize kth-powers of the Euclidean Dirac operator D_x to higher spin spaces in the case the target space is a degree one homogeneous polynomial space. In this paper, we reconsider the generalizations of D_x^3 and D_x^4 to higher spin spaces in the ca…

A typical domain adaptation approach is to adapt models trained on the annotated data in a source domain (e.g., sunny weather) for achieving high performance on the test data in a target domain (e.g., rainy weather). Whether the target contains a single homogeneous domain or multiple heterogeneous domains, existing wor…

We construct zero-curvature representations for the equations of motion of a class of sigma-models with complex homogeneous target spaces, not necessarily symmetric. We show that in the symmetric case the proposed flat connection is gauge-equivalent to the conventional one.

Study learning halfspaces with Massart noise under Gaussian distribution, improving previous results.

New risk measures adjust for tail risk inadequacies.

The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n).Sp(1), QKT-connection. We study the geometry of QKT-connections. We find conditions to the existence of a QKT-connection and prove that if it …

WaveletGAN improves GANs by homogenizing noise through multi-channel wavelet filtering.

Predicts cryptocurrency pump probability using sequence-based neural networks.

AIS uses a suboptimal extended target distribution, which this paper improves using SGM.

Method learns feature map between source and target domains for high-dimensional regression with missing features.

In this paper we are concerned with harmonic maps and minimal immersions defined on compact Riemannian manifolds and with values in homogenous strongly harmonic manifolds. We show some results on the Morse index by varying these maps along suitable conformal vector fields. We obtain also that they are global maxima on …

We consider the problem of hedging a European contingent claim in a Bachelier model with transient price impact as proposed by Almgren and Chriss. Following the approach of Rogers and Singh and Naujokat and Westray, the hedging problem can be regarded as a cost optimal tracking problem of the frictionless hedging strat…

Deep learning has produced state-of-the-art results for a variety of tasks. While such approaches for supervised learning have performed well, they assume that training and testing data are drawn from the same distribution, which may not always be the case. As a complement to this challenge, single-source unsupervised …

BRACE addresses noncompliance in bandits, offering methods for recommendation and treatment policies.

We develop an adversarial-reinforcement learning scheme for microswimmers in statistically homogeneous and isotropic turbulent fluid flows, in both two (2D) and three dimensions (3D). We show that this scheme allows microswimmers to find non-trivial paths, which enable them to reach a target on average in less time tha…

Given a set of heterogeneous source datasets with their classifiers, how can we quickly find the most useful source dataset for a specific target task? We address the problem of measuring transferability between source and target datasets, where the source and the target have different feature spaces and distributions.…

Distillation is an effective knowledge-transfer technique that uses predicted distributions of a powerful teacher model as soft targets to train a less-parameterized student model. A pre-trained high capacity teacher, however, is not always available. Recently proposed online variants use the aggregated intermediate pr…

Markov random field (MRF) learning is intractable, and its approximation algorithms are computationally expensive. We target a small subset of MRF that is used frequently in computer vision. We characterize this subset with three concepts: Lattice, Homogeneity, and Inertia; and design a non-markov model as an alternati…

In this paper, we give a new generalization error bound of Multiple Kernel Learning (MKL) for a general class of regularizations, and discuss what kind of regularization gives a favorable predictive accuracy. Our main target in this paper is dense type regularizations including \ellp-MKL. According to the recent numeri…

Transfer learning has been demonstrated to be successful and essential in diverse applications, which transfers knowledge from related but different source domains to the target domain. Online transfer learning(OTL) is a more challenging problem where the target data arrive in an online manner. Most OTL methods combine…

We present a new construction for Poisson transforms between vector bundle valued differential forms on homogeneous parabolic geometries and the corresponding Riemannian symmetric space, which can be described in terms of finite dimensional representations of reductive Lie groups. In particular, we use these operators …

Sigma models linked to Gross-Neveu models via quiver varieties.

We study geometric variational problems for a class of effective models in quantum field theory known as Faddeev-Skyrme models. Mathematically one considers minimizing an energy functional on homotopy classes of maps from closed 3-manifolds into homogeneous spaces of compact Lie groups. The energy minimizers known as H…

Proposes a model to estimate effects of multiple related treatments.

The paper improves classification accuracy by leveraging a shared signal across domains in high-dimensional classification.

We announce a generalization of Zimmer's cocycle superrigidity theorem proven using harmonic map techniques. This allows us to generalize many results concerning higher rank lattices to all lattices in semisimple groups with property $(T)$. In particular, our results apply to SP(1,n) and $F_4^{-20}$ and lattices in tho…

Bayesian methods detect significant IIA violations in similarity choice data.

Improves functional linear regression with shape transfer learning.

We present a novel framework for domain adaptation, whereby both geometric and statistical differences between a labeled source domain and unlabeled target domain can be integrated by exploiting the curved Riemannian geometry of statistical manifolds. Our approach is based on formulating transfer from source to target …

We consider the machine teaching problem in a classroom-like setting wherein the teacher has to deliver the same examples to a diverse group of students. Their diversity stems from differences in their initial internal states as well as their learning rates. We prove that a teacher with full knowledge about the learnin…

Performing inference on data obtained through observational studies is becoming extremely relevant due to the widespread availability of data in fields such as healthcare, education, retail, etc. Furthermore, this data is accrued from multiple homogeneous subgroups of a heterogeneous population, and hence, generalizing…

We succeed in writing 2-dimensional conformally invariant non-linear elliptic PDE (harmonic map equation, prescribed mean curvature equations...etc) in divergence form. This divergence free quantities generalize to target manifolds without symmetries the well known conservation laws for harmonic maps into homogeneous s…

Introduces new types of homogeneous spaces and their properties.

Study on when Bergman metrics of domains are induced by balls.

We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riema…

Introduces homogeneity supermanifolds for studying graded structures.

Transfer learning aims at improving the performance of target learners on target domains by transferring the knowledge contained in different but related source domains. In this way, the dependence on a large number of target domain data can be reduced for constructing target learners. Due to the wide application prosp…

Recently, it is shown that each regular homogeneous Finsler space $M$ admits at least one homogeneous geodesic through any point $o\in M$. The purpose of this article is to study the existence of homogeneous geodesics on singular homogeneous $(α,β)$-spaces, specially, homogeneous Kropina spaces. We show that any homoge…

In this paper, we study homogeneous geodesics in homogeneous Finsler spaces. We first give a simple criterion that characterizes geodesic vectors. We show that the geodesics on a Lie group, relative to a bi-invariant Finsler metric, are the cosets of the one-parameter subgroups. The existence of infinitely many homogen…

Paper characterizes umbilical hypersurfaces using a generalized overdetermined problem.

We prove that the Penrose limit of a spacetime along a homogeneous geodesic is a homogeneous plane wave spacetime and that the Penrose limit of a reductive homogeneous spacetime along a homogeneous geodesic is a Cahen--Wallach space. We then consider several homogenous examples to show that these results are indeed sha…

We prove that under some purely algebraic conditions every locally homogeneous structure modelled on some homogeneous space is induced by a locally homogeneous structure modelled on a different homogeneous space.

Our purpose is to use a Darboux homogenous derivative to understand the harmonic maps with values in homogeneous space. We present a characterization of these harmonic maps from the geometry of homogeneous space. Furthermore, our work covers all type of invariant geometry in homogeneous space.