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We introduce a data-free quantization method for deep neural networks that does not require fine-tuning or hyperparameter selection. It achieves near-original model performance on common computer vision architectures and tasks. 8-bit…
We focus on semiparametric regression that has played a central role in statistics, and exploit the powerful learning ability of deep neural networks (DNNs) while enabling statistical inference on parameters of interest that offers…
How to train deep neural networks (DNNs) to generalize well is a central concern in deep learning, especially for severely overparameterized networks nowadays. In this paper, we propose an effective method to improve the model…
Computing the critical points of a polynomial function $q\in\mathbb Q[X_1,\ldots,X_n]$ restricted to the vanishing locus $V\subset\mathbb R^n$ of polynomials $f_1,\ldots, f_p\in\mathbb Q[X_1,\ldots, X_n]$ is of first importance in several…
Weighting methods are widely used to adjust for covariates in observational studies, sample surveys, and regression settings. In this paper, we study a class of recently proposed weighting methods which find the weights of minimum…
The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite…
Hilbert schemes of zero-dimensional ideals in a polynomial ring can be covered with suitable affine open subschemes whose construction is achieved using border bases. Moreover, border bases have proved to be an excellent tool for describing…
Acquiring labels are often costly, whereas unlabeled data are usually easy to obtain in modern machine learning applications. Semi-supervised learning provides a principled machine learning framework to address such situations, and has been…
Quantized Neural Networks (QNNs), which use low bitwidth numbers for representing parameters and performing computations, have been proposed to reduce the computation complexity, storage size and memory usage. In QNNs, parameters and…
Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields. Traditional methods like Gr\"obner and Border bases are fundamental but suffer from high…
We consider the problem of computing sample points in each connected component of a semi-algebraic set defined by the non-vanishing or the positivity of an n-variate polynomial of degree d, with rational coefficients of bit size bounded by…
Generalization bounds which assess the difference between the true risk and the empirical risk, have been studied extensively. However, to obtain bounds, current techniques use strict assumptions such as a uniformly bounded or a Lipschitz…
Variational data assimilation in ocean models depends on the ability to model general correlation operators in the presence of coastlines. Grid-point filters based on diffusion operators are widely used for this purpose, but come with a…
As the deep neural networks are being applied to complex tasks, the size of the networks and architecture increases and their topology becomes more complicated too. At the same time, training becomes slow and at some instances inefficient.…
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…
Compressing large Neural Networks (NN) by quantizing the parameters, while maintaining the performance is highly desirable due to reduced memory and time complexity. In this work, we cast NN quantization as a discrete labelling problem, and…
In this work, we propose to employ information-geometric tools to optimize a graph neural network architecture such as the graph convolutional networks. More specifically, we develop optimization algorithms for the graph-based…
Two aspects of neural networks that have been extensively studied in the recent literature are their function approximation properties and their training by gradient descent methods. The approximation problem seeks accurate approximations…
We are given a uniformly elliptic coefficient field that we regard as a realization of a stationary and finite-range (say, range unity) ensemble of coefficient fields. Given a (deterministic) right-hand-side supported in a ball of size…
The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…