Related papers: Efficient Representations of Signals in Nonlinear …

This paper presents an efficient reversible algorithm for linear regression, both with and without ridge regression. Our reversible algorithm matches the asymptotic time and space complexity of standard irreversible algorithms for this…

We address in this paper the following two closely related problems: 1. How to represent functions with singularities (up to a prescribed accuracy) in a compact way? 2. How to reconstruct such functions from a small number of measurements?…

The key to success in machine learning (ML) is the use of effective data representations. Traditionally, data representations were hand-crafted. Recently it has been demonstrated that, given sufficient data, deep neural networks can learn…

Implicit Neural Representations (INRs) have revolutionized signal processing and computer vision by modeling signals as continuous, differentiable functions parameterized by neural networks. However, INRs are prone to the spectral bias…

Sampling of signals belonging to a low-dimensional subspace has well-documented merits for dimensionality reduction, limited memory storage, and online processing of streaming network data. When the subspace is known, these signals can be…

By the recent advances in computer technology leading to the invention of more powerful processors, the importance of creating models using data training is even greater than ever. Given the significance of this issue, this work tries to…

After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an…

We propose a nonlinear, wavelet based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multi-reference alignment problem and generalizations thereof, we analyze the…

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially…

The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines and results of simulink-modeling is presented. The advantages of this paper is that…

Over the past decade, deep learning models have exhibited considerable advancements, reaching or even exceeding human-level performance in a range of visual perception tasks. This remarkable progress has sparked interest in applying deep…

Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces in representation learning,…

The effective representation, processing, analysis, and visualization of large-scale structured data, especially those related to complex domains such as networks and graphs, are one of the key questions in modern machine learning. Graph…

We propose a graph spectral representation of time series data that 1) is parsimoniously encoded to user-demanded resolution; 2) is unsupervised and performant in data-constrained scenarios; 3) captures event and event-transition structure…

Attention layers, as commonly used in transformers, form the backbone of modern deep learning, yet there is no mathematical description of their benefits and deficiencies as compared with other architectures. In this work we establish both…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

Geographic data is fundamentally local. Disease outbreaks cluster in population centers, ecological patterns emerge along coastlines, and economic activity concentrates within country borders. Machine learning models that encode geographic…

Efficient representations of multivariate functions are critical for the design of state-of-the-art methods of data restoration and image reconstruction. In this work, we consider the representation of spatio-temporal data such as temporal…

Implicit neural representation (INR) has proven to be accurate and efficient in various domains. In this work, we explore how different neural networks can be designed as a new texture INR, which operates in a continuous manner rather than…