arXiv research

This paper tackles the 'Clever Hans' effect in anomaly detection models.

Unsupervised learning models can produce accurate but misleading predictions.

Deep neural networks have shown excellent performances in many real-world applications. Unfortunately, they may show "Clever Hans"-like behavior -- making use of confounding factors within datasets -- to achieve high performance. In this work, we introduce the novel learning setting of "explanatory interactive learning…

Current learning machines have successfully solved hard application problems, reaching high accuracy and displaying seemingly "intelligent" behavior. Here we apply recent techniques for explaining decisions of state-of-the-art learning machines and analyze various tasks from computer vision and arcade games. This showc…

CLEVER (Cross-Lipschitz Extreme Value for nEtwork Robustness) is an Extreme Value Theory (EVT) based robustness score for large-scale deep neural networks (DNNs). In this paper, we propose two extensions on this robustness score. First, we provide a new formal robustness guarantee for classifier functions that are twic…

The robustness of neural networks to adversarial examples has received great attention due to security implications. Despite various attack approaches to crafting visually imperceptible adversarial examples, little has been developed towards a comprehensive measure of robustness. In this paper, we provide a theoretical…

A key problem in research on adversarial examples is that vulnerability to adversarial examples is usually measured by running attack algorithms. Because the attack algorithms are not optimal, the attack algorithms are prone to overestimating the size of perturbation needed to fool the target model. In other words, the…

Han discusses variants of digital covering maps and their equivalences.

Corrects errors in Hans' pseudocovering spaces paper.

By studying modular invariance properties of some characteristic forms, we prove some new anomaly cancellation formulas which generalize the Han-Zhang and Han-Liu-Zhang anomaly cancellation formulas

The Han-Li conjecture states that: Let $(M,g_0)$ be an $n$-dimensional $(n\geq 3)$ smooth compact Riemannian manifold with boundary having positive (generalized) Yamabe constant and $c$ be any real number, then there exists a conformal metric of $g_0$ with scalar curvature $1$ and boundary mean curvature $c$. Combining…

Hans Duistermaat was scheduled to lecture in the 2010 School on Poisson Geometry at IMPA, but passed away suddenly. This is a record of a talk I gave at the 2010 Conference on Poisson Geometry (the week after the School) to share some of my memories of him and to give a brief assessment of his impact on the subject.

Clever sampling methods can be used to improve the handling of big data and increase its usefulness. The subject of this study is remote sensing, specifically airborne laser scanning point clouds representing different classes of ground cover. The aim is to derive a supervised learning model for the classification usin…

We discuss the constant $σ_{2}$ problem for conic 4-spheres. Based on earlier works of Chang-Han-Yang and Han-Li-Teixeira, we are able to find a necessary condition for the existence problem. In particular, when the condition is sharp, we have the uniqueness result similar to that of Troyanov in dimension 2. It indicat…

Frank-Wolfe algorithms for convex minimization have recently gained considerable attention from the Optimization and Machine Learning communities, as their properties make them a suitable choice in a variety of applications. However, as each iteration requires to optimize a linear model, a clever implementation is cruc…

We introduce HUBERT which combines the structured-representational power of Tensor-Product Representations (TPRs) and BERT, a pre-trained bidirectional Transformer language model. We show that there is shared structure between different NLP datasets that HUBERT, but not BERT, is able to learn and leverage. We validate …

Estimates solutions to Hessian quotient equations on HKT manifolds.

Correlation matrices play a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. Although Pearson's sample correlation matrix enjoys various good prop…

We establish the family rigidity and vanishing theorems on the equivariant $K$-theory level for the Witten type operators on String$^c$ manifolds introduced by Chen-Han-Zhang.

In (Yang et al. 2016), a hierarchical attention network (HAN) is created for document classification. The attention layer can be used to visualize text influential in classifying the document, thereby explaining the model's prediction. We successfully applied HAN to a sequential analysis task in the form of real-time m…

Ultra-wideband (UWB) radar systems nowadays typical operate in the low frequency spectrum to achieve penetration capability. However, this spectrum is also shared by many others communication systems, which causes missing information in the frequency bands. To recover this missing spectral information, we propose a gen…

This work establishes a new upper bound on the number of samples sufficient for PAC learning in the realizable case. The bound matches known lower bounds up to numerical constant factors. This solves a long-standing open problem on the sample complexity of PAC learning. The technique and analysis build on a recent brea…

We study asymptotic behaviors of positive solutions to the Yamabe equation and the $σ$k-Yamabe equation near isolated singular points and establish expansions up to arbitrary orders. Such results generalize an earlier pioneering work by Caffarelli, Gidas, and Spruck, and a work by Korevaar, Mazzeo, Pacard, and Schoen, …

We consider the optimization of active extension portfolios. For this purpose, the optimization problem is rewritten as a stochastic programming model and solved using a clever multi-start local search heuristic, which turns out to provide stable solutions. The heuristic solutions are compared to optimization results o…

Study proves curvature prescription on spheres for k ≥ n/2.

Adversarial testing methods based on Projected Gradient Descent (PGD) are widely used for searching norm-bounded perturbations that cause the inputs of neural networks to be misclassified. This paper takes a deeper look at these methods and explains the effect of different hyperparameters (i.e., optimizer, step size an…

Note on new cancellation formulas for manifolds.

We extend the theory of the universal eta-invariant to the case of relative bordism groups of manifolds with boundaries. This allows the construction of secondary descendants of the universal eta-invariant. We obtain an interpretation of Laures' f-invariant as an example of this general construction. As an aside we imp…

Let $(X^{n},g_+)$ $(n\geq 3)$ be a Poincaré-Einstein manifold which is $C^{3,α}$ conformally compact with conformal infinity $(\partial X, [\hat{g}])$. On the conformal compactification $(\overline{X}, \bar g=ρ^2g_+)$ via some boundary defining function $ρ$, there are two types of Yamabe constants: $Y(\overline{X},\pa…

Unified theory for causal inference using various methods.

New proof shows exotic 4-manifolds exist without complex calculations.

BR-SNIS reduces bias in self-normalized IS without increasing variance.

We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their frictionless counterparts - the deviation has Ornstein-Uhlenbeck dynamics for quadr…

New rigidity theorems for spin^c manifolds using modular invariance.

Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all possible adversarial perturbations. While these techniques show promise, they often res…

Manipulating video content is easier than ever. Due to the misuse potential of manipulated content, multiple detection techniques that analyze the pixel data from the videos have been proposed. However, clever manipulators should also carefully forge the metadata and auxiliary header information, which is harder to do …

In this paper, we revisit the analyses of Antonie Stern (1925) and Hans Lewy (1977) devoted to the construction of spherical harmonics with two or three nodal domains. Our method yields sharp quantitative results and a better understanding of the occurrence of bifurcations in the families of nodal sets.This paper is a …

Recently Hui et al. (\cite{HAP}, \cite{HAN}) studied contact CR-warped product submanifolds and also warped product pseudo-slant submanifolds of a $(LCS)_n$-manifold $\bar{M}$. In this paper we have studied the characterization for both these classes of warped product submanifolds. It is also shown that there do not ex…

A multilayer perceptron can behave as a generative classifier by applying bidirectional learning (BL). It consists of training an undirected neural network to map input to output and vice-versa; therefore it can produce a classifier in one direction, and a generator in the opposite direction for the same data. The lear…

Deep learning method improves numerical approximation of FBSDEs with jumps.

Assume that the compact Riemannian spin manifold $(M^n,g)$ admits a $G$-structure with characteristic connection $\nabla$ and parallel characteristic torsion ($\nabla T=0$), and consider the Dirac operator $D^{1/3}$ corresponding to the torsion $T/3$. This operator plays an eminent role in the investigation of such man…

New Witten rigidity theorems for elliptic genus in various dimensions.

Study proposes a new method to estimate bias-correction term for ATE estimation.

We study the topology of (properly) immersed complete minimal surfaces $P^2$ in Hyperbolic and Euclidean spaces which have finite total extrinsic curvature, using some isoperimetric inequalities satisfied by the extrinsic balls in these surfaces, (see \cite{Pa}). We present an alternative and partially unified proof of…

This paper improves the Diversification Quotient (DQ) for better risk management.

We demonstrate that the use of asymptotic expansion as prior knowledge in the "deep BSDE solver", which is a deep learning method for high dimensional BSDEs proposed by Weinan E, Han & Jentzen (2017), drastically reduces the loss function and accelerates the speed of convergence. We illustrate the technique and its imp…

The paper solves a curvature problem on a ball's surface near constant values.

The study sets limits on heat equation solutions' Hessians on curved spaces.