Related papers: Estimating the Probability of Sampling a Trained N…

Large margin nearest neighbor (LMNN) is a metric learner which optimizes the performance of the popular $k$NN classifier. However, its resulting metric relies on pre-selected target neighbors. In this paper, we address the feasibility of…

Although deep learning based approximation algorithms have been applied very successfully to numerous problems, at the moment the reasons for their performance are not entirely understood from a mathematical point of view. Recently,…

The classical statistical learning theory implies that fitting too many parameters leads to overfitting and poor performance. That modern deep neural networks generalize well despite a large number of parameters contradicts this finding and…

In this work, we propose a new training method for finding minimum weight norm solutions in over-parameterized neural networks (NNs). This method seeks to improve training speed and generalization performance by framing NN training as a…

We suggest a general approach to quantification of different forms of aleatoric uncertainty in regression tasks performed by artificial neural networks. It is based on the simultaneous training of two neural networks with a joint loss…

Although the recent progress in the deep neural network has led to the development of learnable local feature descriptors, there is no explicit answer for estimation of the necessary size of a neural network. Specifically, the local feature…

We consider the problem of estimating the volume of a compact domain in a Euclidean space based on a uniform sample from the domain. We assume the domain has a boundary with positive reach. We propose a data splitting approach to correct…

Understanding the internal mechanisms of large language models (LLMs) remains a challenging and complex endeavor. Even fundamental questions, such as how fine-tuning affects model behavior, often require extensive empirical evaluation. In…

In this paper we propose a Bayesian method for estimating architectural parameters of neural networks, namely layer size and network depth. We do this by learning concrete distributions over these parameters. Our results show that regular…

Deciding what to sense is a crucial task, made harder by dependencies and by a nonadditive utility function. We develop approximation algorithms for selecting an optimal set of measurements, under a dependency structure modeled by a…

It has been experimentally observed in recent years that multi-layer artificial neural networks have a surprising ability to generalize, even when trained with far more parameters than observations. Is there a theoretical basis for this?…

This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hyperparameters are optimized,…

To measure the volume of specific image structures, a typical approach is to first segment those structures using a neural network trained on voxel-wise (strong) labels and subsequently compute the volume from the segmentation. A more…

We say that a classifier is \emph{adversarially robust} to perturbations of norm $r$ if, with high probability over a point $x$ drawn from the input distribution, there is no point within distance $\le r$ from $x$ that is classified…

We present a formal measure-theoretical theory of neural networks (NN) built on probability coupling theory. Our main contributions are summarized as follows. * Built on the formalism of probability coupling theory, we derive an algorithm…

Local algorithms are common tools for estimating intrinsic volumes from black-and-white digital images. However, these algorithms are typically biased in the design based setting, even when the resolution tends to infinity. Moreover, images…

The idea that many important classes of signals can be well-represented by linear combinations of a small set of atoms selected from a given dictionary has had dramatic impact on the theory and practice of signal processing. For practical…

In order to estimate the specific intrinsic volumes of a planar Boolean model from a binary image, we consider local digital algorithms based on weighted sums of $2\times 2$ configuration counts. For Boolean models with balls as grains,…

One explanation for the strong generalization ability of neural networks is implicit bias. Yet, the definition and mechanism of implicit bias in non-linear contexts remains little understood. In this work, we propose to characterize…

The anchor words algorithm performs provably efficient topic model inference by finding an approximate convex hull in a high-dimensional word co-occurrence space. However, the existing greedy algorithm often selects poor anchor words,…