arXiv research

Study on topological rigidity of ALE vector bundles with specific conditions.

A central question for active learning (AL) is: "what is the optimal selection?" Defining optimality by classifier loss produces a new characterisation of optimal AL behaviour, by treating expected loss reduction as a statistical target for estimation. This target forms the basis of model retraining improvement (MRI), …

New functional proves mass positivity for ALE metrics.

Classifies ancient and expanding Ricci flows with specific groups.

Study on stability of ALE Ricci-flat metrics using a modified Perelman's λ-functional.

Active Learning (AL) methods seek to improve classifier performance when labels are expensive or scarce. We consider two central questions: Where does AL work? How much does it help? To address these questions, a comprehensive experimental simulation study of Active Learning is presented. We consider a variety of tasks…

The paper classifies and proves properties of ALE manifolds and orbifolds.

Refined asymptotics of scalar-flat ALE four-manifolds

Study ALE spaces via nodal curves and compactifications.

Existence proved for specific types of gravitational instantons.

Active Learning (AL) is increasingly important in a broad range of applications. Two main AL principles to obtain accurate classification with few labeled data are refinement of the current decision boundary and exploration of poorly sampled regions. In this paper we derive a novel AL scheme that balances these two pri…

We prove a Kuranishi-type theorem for deformations of complex structures on ALE Kähler surfaces. This is used to prove that for any scalar-flat Kähler ALE surface, all small deformations of complex structure also admit scalar-flat Kähler ALE metrics. A local moduli space of scalar-flat Kähler ALE metrics is then constr…

Sharp mass bounds for ALE and ALF toric 4-manifolds.

Sharp convergence theorem for Yang-Mills flow on ALE manifolds proved.

The paper studies a special sphere in ALE spaces.

Survey on AL strategies for cost-effective annotation in classification.

Active learning (AL) is a promising ML paradigm that has the potential to parse through large unlabeled data and help reduce annotation cost in domains where labeling data can be prohibitive. Recently proposed neural network based AL methods use different heuristics to accomplish this goal. In this study, we demonstrat…

Proves unique ALE instanton with toric Hermitian structure.

Proposes a method to imitate active learning heuristics for better performance.

We prove that if an ALE Ricci-flat manifold $(M,g)$ is linearly stable and integrable, it is dynamically stable under Ricci flow, i.e. any Ricci flow starting close to g exists for all time and converges modulo diffeomorphism to an ALE Ricci-flat metric close to $g$. By adapting Tian's approach in the closed case, we s…

The underlying complex structure of an ALE Kähler manifold is exhibited as a resolution of a deformation of an isolated quotient singularity. As a consequence, there exist only finitely many diffeomorphism types of minimal ALE Kähler surfaces with a given group at infinity.

Our main result in this article is a compactness result which states that a noncollapsed sequence of asymptotically locally Euclidean (ALE) scalar-flat Kähler metrics on a minimal Kähler surface whose Kähler classes stay in a compact subset of the interior of the Kähler cone must have a convergent subsequence. As an ap…

Since the debut of Evolution Strategies (ES) as a tool for Reinforcement Learning by Salimans et al. 2017, there has been interest in determining the exact relationship between the Evolution Strategies gradient and the gradient of a similar class of algorithms, Finite Differences (FD).(Zhang et al. 2017, Lehman et al. …

The study calculates harmonic functions and 1-forms on specific 4D spaces.

The popular Alternating Least Squares (ALS) algorithm for tensor decomposition is efficient and easy to implement, but often converges to poor local optima---particularly when the weights of the factors are non-uniform. We propose a modification of the ALS approach that is as efficient as standard ALS, but provably rec…

Active learning (AL) is a widely-used training strategy for maximizing predictive performance subject to a fixed annotation budget. In AL one iteratively selects training examples for annotation, often those for which the current model is most uncertain (by some measure). The hope is that active sampling leads to bette…

In many classification problems unlabelled data is abundant and a subset can be chosen for labelling. This defines the context of active learning (AL), where methods systematically select that subset, to improve a classifier by retraining. Given a classification problem, and a classifier trained on a small number of la…

Motivated by concerns that machine learning algorithms may introduce significant bias in classification models, developing fair classifiers has become an important problem in machine learning research. One important paradigm towards this has been providing algorithms for adversarially learning fair classifiers (Zhang e…

In this paper, we consider derivative free optimization problems, where the objective function is smooth but is computed with some amount of noise, the function evaluations are expensive and no derivative information is available. We are motivated by policy optimization problems in reinforcement learning that have rece…

The paper classifies 4D Ricci-flat ALE manifolds and their properties.

This paper is the sequel of our previous article "From ALE to ALF gravitational instantons", where we constructed ALF hyperkahler metrics on minimal resolutions of dihedral Kleinian singularities. In the present article we generalize the construction to smooth deformations of these Kleinian singularities, with help of …

MetAL improves graph classification models with fewer labeled data.

We introduce a natural definition of the renormalized volume of a 4-dimensional Ricci-flat ALE space. We then prove that the renormalized volume is always less or equal than zero, with equality if and only if the ALE space is isometric to its asymptotic cone. Currently the only known examples of 4-dimensional Ricci-fla…

A new method speeds up ALS for recommender systems by subsampling key elements.

We address the online linear optimization problem when the actions of the forecaster are represented by binary vectors. Our goal is to understand the magnitude of the minimax regret for the worst possible set of actions. We study the problem under three different assumptions for the feedback: full information, and the …

New gauge-theoretic construction of 4D hyperkähler ALE spaces.

Study examines Kähler immersions of ALE Kähler metrics into complex space forms.

The paper shows how to create scalar flat metrics with very large ADM mass.

AL$\ell_0$CORE tensor decomposition reduces computational cost for sparse count data.

Study toric gravitational instantons using rod structures and inequalities.

We propose a novel algorithm for sequential matrix completion in a recommender system setting, where the $(i,j)$th entry of the matrix corresponds to a user $i$'s rating of product $j$. The objective of the algorithm is to provide a sequential policy for user-product pair recommendation which will yield the highest pos…

In this small note we use results derived in Berestycki et al. to correct the celebrated formulae of Hagan et al. We derive explicitly the correct zero order term in the expansion of the implied volatility in time to maturity. The new term is consistent as $β\to 1$. Furthermore, numerical simulations show that it reduc…

Solves geodesic equations on special Kähler manifolds, proving global regularity.

We give an ADHM type description of instantons on ALE spaces for classical groups as an extension of the description in [KN90] for unitary groups.

Stability and rigidity of Ricci-flat ALE manifolds proven.

There is a broad range of BioNLP tasks for which active learning (AL) can significantly reduce annotation costs and a specific AL algorithm we have developed is particularly effective in reducing annotation costs for these tasks. We have previously developed an AL algorithm called ClosestInitPA that works best with tas…

We prove that the only exact Lagrangian submanifolds in an ALE space are spheres. ALE spaces are the simply connected hyperkahler manifolds which at infinity look like C^2/G for any finite subgroup G of SL(2,C). They can be realized as the plumbing of copies of the cotangent bundle of a 2-sphere according to ADE Dynkin…

Revisits CP tensor decomposition for noisy, non-orthogonal data.