Publications related to Bilinear interpolation

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in orthologic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based pro ...

Cham2024

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in ortho- logic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based p ...

2024

Stable Nonconvex-Nonconcave Training via Linear Interpolation

Volkan Cevher, Thomas Michaelsen Pethick, Wanyun Xie

This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss lan ...

2023

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

Alfio Quarteroni, Francesco Regazzoni

The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

Lausanne2023

Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems

Jan Sickmann Hesthaven, Junming Duan

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for time-dependent n ...

San Diego2023

Benign Overfitting in Deep Neural Networks under Lazy Training

Volkan Cevher, Grigorios Chrysos, Fanghui Liu, Zhenyu Zhu

This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayesoptimal test error for classification while obtaining (nearly) zero-trai ...

2023

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Joao Pedro Gonçalves Ramos, Martin Peter Stoller

We obtain new Fourier interpolation and uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa [11] and the second author [12]. We show that the only Schwartz function which, together with its Fourier transform ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

pyFFS: A Python Library for Fast Fourier Series Computation and Interpolation with GPU Acceleration

Martin Vetterli, Paul Hurley, Eric Bezzam, Sepand Kashani, Matthieu Martin Jean-André Simeoni

Fourier transforms are an often necessary component in many computational tasks, and can be computed efficiently through the fast Fourier transform (FFT) algorithm. However, many applications involve an underlying continuous signal, and a more natural choi ...

2022

Choreography Controlled (ChoCo) brain MRI artifact generation for labeled motion-corrupted datasets

Michel Kocher, François Lazeyras, Bastien Chopard, Sébastien Courvoisier, Julien Songeon

MRI is a non-invasive medical imaging modality that is sensitive to patient motion, which constitutes a major limitation in most clinical applications. Solutions may arise from the reduction of acquisition times or from motion-correction techniques, either ...

ELSEVIER SCI LTD2022

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Bilinear interpolation

Interpolation and Quantifiers in Ortholattices

Interpolation and Quantifiers in Ortholattices

Stable Nonconvex-Nonconcave Training via Linear Interpolation

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems

Benign Overfitting in Deep Neural Networks under Lazy Training

Perturbed Fourier uniqueness and interpolation results in higher dimensions

pyFFS: A Python Library for Fast Fourier Series Computation and Interpolation with GPU Acceleration

Choreography Controlled (ChoCo) brain MRI artifact generation for labeled motion-corrupted datasets

Graph Chatbot

Chat with Graph Search

Interpolation and Quantifiers in Ortholattices

Stable Nonconvex-Nonconcave Training via Linear Interpolation

Interpolation and Quantifiers in Ortholattices

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Benign Overfitting in Deep Neural Networks under Lazy Training

Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems

pyFFS: A Python Library for Fast Fourier Series Computation and Interpolation with GPU Acceleration

Choreography Controlled (ChoCo) brain MRI artifact generation for labeled motion-corrupted datasets