arXiv research

New upper bound for non-trivial links in a cube, geometric approach.

Bayesian optimization outperformed random search in machine learning hyperparameter tuning challenge.

Proves mean curvature flow from conical singularities to shrinkers.

Understanding how a learned black box works is of crucial interest for the future of Machine Learning. In this paper, we pioneer the question of the global interpretability of learned black box models that assign numerical values to symbolic sequential data. To tackle that task, we propose a spectral algorithm for the …

Deep neural networks work well at approximating complicated functions when provided with data and trained by gradient descent methods. At the same time, there is a vast amount of existing functions that programmatically solve different tasks in a precise manner eliminating the need for training. In many cases, it is po…

Study improves curvature estimate for stable marginally outer trapped hypersurfaces with a free boundary.

Paper optimizes Laplacian regularization for sparse network clustering.

Membership inference determines, given a sample and trained parameters of a machine learning model, whether the sample was part of the training set. In this paper, we derive the optimal strategy for membership inference with a few assumptions on the distribution of the parameters. We show that optimal attacks only depe…

A new method for variable importance measures without impossible data.

A novel fact-checking method using debate dynamics on knowledge graphs.

A method for reasoning on knowledge graphs using debate dynamics.

In this article I describe my recent geometric localization argument dealing with actions of NONcompact groups which provides a geometric bridge between two entirely different character formulas for reductive Lie groups and answers the question posed in [Sch]. A corresponding problem in the compact group setting was so…

An odd-dimensional version of the Goldberg conjecture was formulated and proved by Boyer and Galicki, using an orbifold analogue of Sekigawa's formulas, and an approximation argument of K-contact structures with quasi-regular ones. We provide here another proof of this result and give some applications.

In recent years, deep neural networks have revolutionized many application domains of machine learning and are key components of many critical decision or predictive processes. Therefore, it is crucial that domain specialists can understand and analyze actions and pre- dictions, even of the most complex neural network …

Recently V. Ginzburg proved that Calogero phase space is a coadjoint orbit for some infinite dimensional Lie algebra coming from noncommutative symplectic geometry. In this note we generalize this argument to specific quotient varieties of representations of (deformed) preprojective algebras. This result was also obtai…

Stochastic LWTA networks resist adversarial attacks while maintaining accuracy.

We study the asymptotic behavior of Masur-Veech volumes as the genus goes to infinity. We show the existence of a complete asymptotic expansion of these volumes that depends only on the genus and the number of singularities. The computation of the first term of this asymptotics expansion was a long standing problem. Th…

New method turns optimization algorithms into uniformly stable learning algorithms for non-Euclidean norms.

In this article, the author provides full details of the proof of the concordance/isotopy problem. The first published proof, [5], accomplished this task only partially since there was an error, see the erratum [6], which damaged the main argument of [5, Theorem 2.9], and, consequently, the proof of [5, Theorem A].

The book explores essential stats and psychology for quantitative trading.

Taleb (2018) claimed a novel approach to evaluating the quality of probabilistic election forecasts via no-arbitrage pricing techniques and argued that popular forecasts of the 2016 U.S. Presidential election had violated arbitrage boundaries. We show that under mild assumptions all such political forecasts are arbitra…

This article provides a geometric bridge between two entirely different character formulas for reductive Lie groups and answers the question posed by W.Schmid in [Sch]. A corresponding problem in the compact group setting was solved by N.Berline, E.Getzler and M.Vergne in [BGV] by an application of the theory of equiva…

In this paper, we study the problem of how to defend classifiers against adversarial attacks that fool the classifiers using subtly modified input data. In contrast to previous works, here we focus on the white-box adversarial defense where the attackers are granted full access to not only the classifiers but also defe…

In this survey paper, we outline the proofs of the rigidity results for simple, thick, hyperbolic P-manifolds found in our three earlier papers math.GR/0506518, math.GT/0410476, and math.GR/0409586. We discuss how the arguments change in the two, three, and higher dimensional settings. This paper was written for the 22…

We derive the sharp Moser-Trudinger-Onofri inequalities on the standard $n$-sphere and CR $(2n+1)$- sphere as the limit of the sharp fractional Sobolev inequalities for all $n\ge 1$. On the $2$-sphere and $4$-sphere, this was established recently by S.-Y. Chang and F. Wang. Our proof uses an alternative and elementary …

TabPFN learns to approximate functions on tabular data.

For a smooth projective toric surface we determine the Donaldson invariants and their wallcrossing in terms of the Nekrasov partition function. Using the solution of the Nekrasov conjecture math.AG/0306198, hep-th/0306238, math.AG/0409441 and its refinement math.AG/0311058, we apply this result to give a generating fun…

New method estimates selection event for black-box models.

Research tackles safety of deep learning in safety-critical tasks.

In this paper, we construct a family of asymptotically hyperbolic manifolds with horizons and with scalar curvature equal to -6. The manifolds we constructed can be arbitrary close to anti-de Sitter-Schwarzschild manifolds at infinity. Hence, the mass of our manifolds can be very large or very small. The main arguments…

Canonical correlation analysis was proposed by Hotelling [6] and it measures linear relationship between two multidimensional variables. In high dimensional setting, the classical canonical correlation analysis breaks down. We propose a sparse canonical correlation analysis by adding l1 constraints on the canonical vec…

Regulated curves on Banach manifolds with continuous projections and regulated derivatives are studied.

We revisit an example of a semi-Riemannian geodesic that was discussed by Musso, Pejsachowicz and Portaluri in 2007 to show that not every conjugate point is a bifurcation point. We point out a mistake in their argument, showing that on this geodesic actually every conjugate point is a bifurcation point. Finally, we pr…

In this paper, we obtain a positivity result of a quasi-local mass integral as proposed by Shi and Tam in general dimensions. The main argument is based on the monotonicity of a mass integral in a foliation of quasi-spherical metrics and a positive mass type theorem which was proved by Wang and Yau in the three dimensi…

Optimizes latent space of VAEs using decoder uncertainty to generate valid objects.

We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains a $\mathbb{Z}^\infty$-subgroup and a $\mathbb{Z}$-summand. Our proof proceeds by introducing an algebraic variant of the involutive Heegaard Floer package of He…

In math.GT/0106017 it was shown that thin position on Heegaard spines can be a useful tool for analyzing the topology of knots in 3-space. The proof there (specifically, of the Goda-Teragaito conjecture) requires masses of technical detail; it is easy to lose track of the underlying ideas. The present paper gives an ov…

New model improves deep learning robustness against adversarial attacks.

Deep convolutional neural networks have recently achieved state-of-the-art performance on a number of image recognition benchmarks, including the ImageNet Large-Scale Visual Recognition Challenge (ILSVRC-2012). The winning model on the localization sub-task was a network that predicts a single bounding box and a confid…

Continuous latent time series models are prevalent in Bayesian modeling; examples include the Kalman filter, dynamic collaborative filtering, or dynamic topic models. These models often benefit from structured, non mean field variational approximations that capture correlations between time steps. Black box variational…

Numerous methods for crafting adversarial examples were proposed recently with high success rate. Since most existing machine learning based classifiers normalize images into some continuous, real vector, domain firstly, attacks often craft adversarial examples in such domain. However, "adversarial" examples may become…

In [dLMu05], DeLellis and Müller proved a quantitative version of Codazzi's theorem, namely for a smooth embedded surface $\ Σ\subseteq \mathbb{R}^3\$ with area normalized to $\ {\cal H}^2(Σ) = 4 π$, it was shown that $\ \parallel A_Σ- id \parallel_{L^2(Σ)} \leq C \parallel A^0_Σ\parallel_{L^2(Σ)}\$, and building on…

Paper shows perturbed Taub-Bolt metric becomes singularity under Ricci flow.

In this appraisal paper, we evaluate the efficacy of SHIELD, a compression-based defense framework for countering adversarial attacks on image classification models, which was published at KDD 2018. Here, we consider alternative threat models not studied in the original work, where we assume that an adaptive adversary …

Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data. Convergence problems during training are overcome by Wasserstein GANs which minimize the distance between the model and the empirical distribution in terms of a dif…

John Morgan and G,Tian pointed out a mistake in the concluding argument for our paper entitled "$C_1$ in [2] is zero", which was recently published in arXiv:1512.02098. We hereby acknowledge this mistake and correct the computation, leading to the conclusion that $C_1$ is non-zero and that their reference [2] does inde…

In this paper we prove genus bounds for closed embedded minimal surfaces in a closed 3-dimensional manifold constructed via min-max arguments. A stronger estimate was announced by Pitts and Rubistein but to our knowledge its proof has never been published. Our proof follows ideas of Simon and uses an extension of a fam…

Methods for interpreting machine learning black-box models increase the outcomes' transparency and in turn generates insight into the reliability and fairness of the algorithms. However, the interpretations themselves could contain significant uncertainty that undermines the trust in the outcomes and raises concern abo…