arXiv research

Estimates box dimension of fractal interpolation surfaces using oscillation vectors.

We show that the asymptotic dimension of box spaces behaves (sub)additively with respect to extensions of groups. As a result, we obtain that for an elementary amenable group, the asymptotic dimension of any of its box spaces is bounded above by its Hirsch length. This bound is shown to be an equality for a large subcl…

A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal su…

BBVI converges nearly dimensionally independent for log-concave targets.

New method optimizes black-box functions using generative models and Wasserstein distance.

Efficient method for generating adversarial examples with limited query budget.

Study on Hausdorff dimension and curvature bounds in sub-Lorentzian Heisenberg group.

Proposes a new method to explain complex machine learning models.

We consider scattering by an abstract compactly supported perturbation in R^n. To include the traditional cases of potential, obstacle and metric scattering without going into their particular nature we adopt the "black box" formalism developed jointly with Sjostrand [23]. It is quite likely that one could extend the r…

Given a point (the "spider") on a rectangular box, we would like to find the minimal distance along the surface to its opposite point (the "fly" - the reflection of the spider across the center of the box). Without loss of generality, we can assume that the box has dimensions $1\times a\times b$ with the spider on one …

TREGO improves EGO for global optimization of high-dimensional problems.

Bayesian optimization with cost-awareness using Gittins index.

We focus on the problem of black-box adversarial attacks, where the aim is to generate adversarial examples using information limited to loss function evaluations of input-output pairs. We use Bayesian optimization~(BO) to specifically cater to scenarios involving low query budgets to develop query efficient adversaria…

A new algorithm for optimizing huge-scale black-box problems with reduced memory usage.

In this paper, we study the problem of constrained robust (min-max) optimization ina black-box setting, where the desired optimizer cannot access the gradients of the objective function but may query its values. We present a principled optimization framework, integrating a zeroth-order (ZO) gradient estimator with an a…

Adversarial examples pose a threat to deep neural network models in a variety of scenarios, from settings where the adversary has complete knowledge of the model and to the opposite "black box" setting. Black box attacks are particularly threatening as the adversary only needs access to the input and output of the mode…

Efficiently controls unknown linear systems with black-box interactions.

We derive a representation formula for the tensorial wave equation $\Box_\bg φ^I=F^I$ in globally hyperbolic Lorentzian spacetimes $(\M^{2+1}, \bg)$ by giving a geometric formulation of the method of descent which is applicable for any dimension.

Machine Learning models are often composed of pipelines of transformations. While this design allows to efficiently execute single model components at training time, prediction serving has different requirements such as low latency, high throughput and graceful performance degradation under heavy load. Current predicti…

BOFiP optimizes high-dimensional functions by distributing them into sub-spaces and using game theory.

Ellipsoids approach Gaussian distribution in high dimensions.

GONs improve predictions of maximizers from noisy black-box functions.

New divergences help audit DP in high dimensions.

Study volume growth and asymptotic cones of nonnegative Ricci curvature manifolds.

Proposes an online model for LLM cascading with adaptive API selection.

This work surveys unsupervised learning methods for high-dimensional uncertainty quantification in complex PDEs.

Black box variational inference allows researchers to easily prototype and evaluate an array of models. Recent advances allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive variational distribution that maintains efficient computation? To address this, we …

Deep neural networks (DNNs) are one of the most prominent technologies of our time, as they achieve state-of-the-art performance in many machine learning tasks, including but not limited to image classification, text mining, and speech processing. However, recent research on DNNs has indicated ever-increasing concern o…

Training 3D object detectors for autonomous driving has been limited to small datasets due to the effort required to generate annotations. Reducing both task complexity and the amount of task switching done by annotators is key to reducing the effort and time required to generate 3D bounding box annotations. This paper…

We present DRLViz, a visual analytics interface to interpret the internal memory of an agent (e.g. a robot) trained using deep reinforcement learning. This memory is composed of large temporal vectors updated when the agent moves in an environment and is not trivial to understand due to the number of dimensions, depend…

Many probabilistic models of interest in scientific computing and machine learning have expensive, black-box likelihoods that prevent the application of standard techniques for Bayesian inference, such as MCMC, which would require access to the gradient or a large number of likelihood evaluations. We introduce here a n…

We introduce a family of copulas which are locally piecewise uniform in the interior of the unit cube of any given dimension. Within that family, the simultaneous control of tail dependencies of all projections to faces of the cube is possible and we give an efficient sampling algorithm. The combination of these two pr…

Sharp sample complexity for multiclass PAC learning with bandit feedback.

Let $X$ be an abstract not necessarily compact orientable CR manifold of dimension $2n-1$, $n\geqslant2$, and let $L^k$ be the $k$-th tensor power of a CR complex line bundle $L$ over $X$. Given $q\in\set{0,1,\ldots,n-1}$, let $\Box^{(q)}_{b,k}$ be the Gaffney extension of Kohn Laplacian for $(0,q)$ forms with values i…

Paper improves sparse linear bandits by accounting for noise variance.

New method optimizes expensive simulations for complex systems.

Scout-Nd optimizes parameters of stochastic simulators efficiently.

Paper classifies pillow box isometric deformations preserving crease patterns.

AdaScale-TuRBO improves high-dimensional Bayesian optimization by dynamically scaling the GP lengthscale.

Develops new oracle inequalities for Gaussian ranking estimators.

ODS improves adversarial attacks by maximizing output diversity.

New research shows many recent defenses against adversarial examples are ineffective against black-box attacks.

We give a fast oblivious L2-embedding of $A\in \mathbb{R}^{n x d}$ to $B\in \mathbb{R}^{r x d}$ satisfying $(1-\varepsilon)\|A x\|_2^2 \le \|B x\|_2^2 <= (1+\varepsilon) \|Ax\|_2^2.$ Our embedding dimension $r$ equals $d$, a constant independent of the distortion $\varepsilon$. We use as a black-box any L2-embedding $Π…

Answering complex logical queries on large-scale incomplete knowledge graphs (KGs) is a fundamental yet challenging task. Recently, a promising approach to this problem has been to embed KG entities as well as the query into a vector space such that entities that answer the query are embedded close to the query. Howeve…

A mathematical framework connects neural networks and polynomial regression for better model understanding.

New method improves black-box attacks using pre-trained models.

New approach combines geometric and probabilistic methods to estimate manifold dimension in high-dimensional data.

Study group actions in metric spaces, proving convergence of lens spaces.