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One little-explored frontier of image generation and editing is the task of interpolating between two input images, a feature missing from all currently deployed image generation pipelines. We argue that such a feature can expand the…
In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…
A set of arbitrarily high-order WENO schemes for reconstructions on nonuniform grids is presented. These non-linear interpolation methods use simple smoothness indicators with a linear cost with respect to the order, making them easy to…
We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a…
The reduced-order modeling of a system from data (also known as system identification) is a classical task in system and control theory and well understood for standard linear systems with the so-called Loewner framework as one of many…
This paper attempts a more formal approach to the legibility of text based programming languages, presenting, with proof, minimum possible ways of representing structure in text interleaved with information. This presumes that a minimalist…
The recently introduced polynomial time integration framework proposes a novel way to construct time integrators for solving systems of first-order ordinary differential equation by using interpolating polynomials in the complex time plane.…
Feature selection is an important problem in high-dimensional data analysis and classification. Conventional feature selection approaches focus on detecting the features based on a redundancy criterion using learning and feature searching…
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…
This research endeavors to offer insights into unlocking the further potential of transformer-based architectures. One of the primary motivations is to offer a geometric interpretation for the attention mechanism in transformers. In our…
In order to generate novel 3D shapes with machine learning, one must allow for interpolation. The typical approach for incorporating this creative process is to interpolate in a learned latent space so as to avoid the problem of generating…
In this paper we introduce a framework for option model composition. Option models are temporal abstractions that, like macro-operators in classical planning, jump directly from a start state to an end state. Prior work has focused on…
This work considers the problem of selecting overlapping control structures to remove decentralized fixed modes. The selection of such controller is conventionally carried out based on minimal overlapping communications. In this paper, this…
Multiple importance sampling estimators are widely used for computing intractable constants due to its reliability and robustness. The celebrated balance heuristic estimator belongs to this class of methods and has proved very successful in…
In this paper, we present an interpolation framework for structure-preserving model order reduction of parametric bilinear dynamical systems. We introduce a general setting, covering a broad variety of different structures for parametric…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
Diffractive lenses have recently been applied to the domain of multispectral imaging in the X-ray and UV regimes where they can achieve very high resolution as compared to reflective and refractive optics. Conventionally, spectral…
Transformer architectures have achieved remarkable success across language, vision, and multimodal tasks, and there is growing demand for them to address in-context compositional learning tasks. In these tasks, models solve the target…
This paper proposes a frequency-domain system identification method for learning low-order systems. The identification problem is formulated as the minimization of the l2 norm between the identified and measured frequency responses, with…
The method of reconstruction of an attractor from a set of short time series ({\it clusters}) is proposed and discussed. This method is most useful for correlation dimension estimation of experimental data.