Related papers: NIL: Learning Nonlinear Interpolants
Complementary-label learning (CLL) is a weakly supervised paradigm where instances are labeled with classes they do not belong to. Despite a decade of research, CLL methods remain competitive mainly on 10-class classification, with scaling…
Various algebraic multigrid algorithms have been developed for solving problems in scientific and engineering computation over the past decades. They have been shown to be well-suited for solving discretized partial differential equations…
Large pretrained language models (LMs) have shown impressive In-Context Learning (ICL) ability, where the model learns to do an unseen task via a prompt consisting of input-output examples as the demonstration, without any parameter…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
This paper provides approximation orders for a class of nonlinear interpolation procedures for univariate data sampled over $\sigma$ quasi-uniform grids. The considered interpolation is built using both essentially nonoscillatory (ENO) and…
In the article \The State of SAT", the authors asked whether a procedure dramatically different from DPLL can be found for handling unsatisfiable instances. This study proposes a new linear programming approach to address this issue…
We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…
For visual object recognition tasks, the illumination variations can cause distinct changes in object appearance and thus confuse the deep neural network based recognition models. Especially for some rare illumination conditions, collecting…
Although some preconditioners are available for solving dense linear systems, there are still many matrices for which preconditioners are lacking, in particular in cases where the size of the matrix $N$ becomes very large. There remains…
Class Incremental Learning (CIL) based on pre-trained models offers a promising direction for open-world continual learning. Existing methods typically rely on correlation-based strategies, where an image's classification feature is used as…
We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable…
We consider the problem of synthesizing provably non-overflowing integer arithmetic expressions or Boolean relations among integer arithmetic expressions. First we use a numerical abstract domain to infer numerical properties among program…
Interpolation theory for complex polynomials is well understood. In the non-commutative quaternionic setting, the polynomials can be evaluated "on the left" and "on the right". If the interpolation problem involves interpolation conditions…
We present HyperFLINT (Hypernetwork-based FLow estimation and temporal INTerpolation), a novel deep learning-based approach for estimating flow fields, temporally interpolating scalar fields, and facilitating parameter space exploration in…
Flow matching is a scalable generative framework for characterizing continuous normalizing flows with wide-range applications. However, current state-of-the-art methods are not well-suited for modeling dynamical systems, as they construct…
Given a neural network, training data, and a threshold, it was known that it is NP-hard to find weights for the neural network such that the total error is below the threshold. We determine the algorithmic complexity of this fundamental…
A multiresolution analysis is a nested chain of related approximation spaces.This nesting in turn implies relationships among interpolation bases in the approximation spaces and their derived wavelet spaces. Using these relationships, a…
Many imitation learning (IL) algorithms use inverse reinforcement learning (IRL) to infer a reward function that aligns with the demonstration. However, the inferred reward functions often fail to capture the underlying task objectives. In…
Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to…
This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence…