Related papers: Reconstruction of rational functions made simple
Rational-function simplification is key bottlenecks in integration-by-parts (IBP) reduction of Feynman integrals. We study denominator factorization patterns appearing in IBP coefficients and develop practical algorithms for extracting and…
Reinforcement learning algorithms can solve dynamic decision-making and optimal control problems. With continuous-valued state and input variables, reinforcement learning algorithms must rely on function approximators to represent the value…
Our overall goal is to unify and extend some results in the literature related to the approximation of generating functions of finite and infinite sequences over a field by rational functions. In our approach, numerators play a significant…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
Finite-rate-of-innovation (FRI) signals are ubiquitous in applications such as radar, ultrasound, and time of flight imaging. Due to their finite degrees of freedom, FRI signals can be sampled at sub-Nyquist rates using appropriate sampling…
Reasoning LLMs often spend substantial tokens on long intermediate reasoning traces (e.g., chain-of-thought) when solving new problems. We propose to summarize and store reusable reasoning skills distilled from extensive deliberation and…
The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…
Limited angular resolution is one of the main obstacles for practical applications of light fields. Although numerous approaches have been proposed to enhance angular resolution, view selection strategies have not been well explored in this…
In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
A variety of modeling techniques have been developed in the past decade to reduce the computational expense and improve the accuracy of modeling. In this study, a new framework of modeling is suggested. Compared with other popular methods,…
A method is described which allows to evaluate efficiently a polynomial in a (possibly trivial) extension of the finite field of its coefficients. Its complexity is shown to be lower than that of standard techniques when the degree of the…
The work is devoted to the construction of a new type of intervals -- functional intervals. These intervals are built on the idea of expanding boundaries from numbers to functions. Functional intervals have shown themselves to be promising…
We propose a simple, interpretable framework for solving a wide range of image reconstruction problems such as denoising and deconvolution. Given a corrupted input image, the model synthesizes a spatially varying linear filter which, when…
Functional decomposition is a powerful tool for systems analysis because it can reduce a function of arbitrary input dimensions to the sum and superposition of functions of a single variable, thereby mitigating (or potentially avoiding) the…
In this paper, we address the problem of sampling from a set and reconstructing a set stored as a Bloom filter. To the best of our knowledge our work is the first to address this question. We introduce a novel hierarchical data structure…
In this paper we present a fast and efficient method for the reconstruction of Magnetic Resonance Images (MRI) from severely under-sampled data. From the Compressed Sensing theory we have mathematically modeled the problem as a constrained…
Generic 3D reconstruction from a single image is a difficult problem. A lot of data loss occurs in the projection. A domain based approach to reconstruction where we solve a smaller set of problems for a particular use case lead to greater…
Many machine learning models depend on solving a large scale optimization problem. Recently, sub-sampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness…
We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis. As we…