Related papers: Building Function Approximators on top of Haar Sca…

Deep learning based on deep neural networks has been very successful in many practical applications, but it lacks enough theoretical understanding due to the network architectures and structures. In this paper we establish some analysis for…

We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…

Estimating the normal of a point requires constructing a local patch to provide center-surrounding context, but determining the appropriate neighborhood size is difficult when dealing with different data or geometries. Existing methods…

Scattering networks are a class of designed Convolutional Neural Networks (CNNs) with fixed weights. We argue they can serve as generic representations for modelling images. In particular, by working in scattering space, we achieve…

Scattering Transforms (or ScatterNets) introduced by Mallat are a promising start into creating a well-defined feature extractor to use for pattern recognition and image classification tasks. They are of particular interest due to their…

Designing scalable estimation algorithms is a core challenge in modern statistics. Here we introduce a framework to address this challenge based on parallel approximants, which yields estimators with provable properties that operate on the…

This work addresses two fundamental limitations in neural network approximation theory. We demonstrate that a three-dimensional network architecture enables a significantly more efficient representation of sawtooth functions, which serves…

Multi-channel satellite imagery, from stacked spectral bands or spatiotemporal data, have meaningful representations for various atmospheric properties. Combining these features in an effective manner to create a performant and trustworthy…

While exploring desirable properties of hash functions in cryptography, the author was led to investigate three notions of functions with scattering or "diffusive" properties, where the functions map between binary strings of fixed finite…

Using random walks for sampling has proven advantageous in assessing the characteristics of large and unknown social networks. Several algorithms based on random walks have been introduced in recent years. In the practical application of…

Deep neural networks have proven to be particularly effective in visual and audio recognition tasks. Existing models tend to be computationally expensive and memory intensive, however, and so methods for hardware-oriented approximation have…

Geometric scattering has recently gained recognition in graph representation learning, and recent work has shown that integrating scattering features in graph convolution networks (GCNs) can alleviate the typical oversmoothing of features…

Vision-based object detection is one of the fundamental functions in numerous traffic scene applications such as self-driving vehicle systems and advance driver assistance systems (ADAS). However, it is also a challenging task due to the…

We consider the problem of multi-task learning in the high dimensional setting. In particular, we introduce an estimator and investigate its statistical and computational properties for the problem of multiple connected linear regressions…

Ranking functions used in information retrieval are primarily used in the search engines and they are often adopted for various language processing applications. However, features used in the construction of ranking functions should be…

Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…

Ensuring the trustworthiness and interpretability of machine learning models is critical to their deployment in real-world applications. Feature attribution methods have gained significant attention, which provide local explanations of…

Feature foundation models - usually vision transformers - offer rich semantic descriptors of images, useful for downstream tasks such as (interactive) segmentation and object detection. For computational efficiency these descriptors are…

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher…

We investigate the existence of approximation algorithms for maximization of submodular functions, that run in fixed parameter tractable (FPT) time. Given a non-decreasing submodular set function $v: 2^X \to \mathbb{R}$ the goal is to…