相关论文: Aliasing in Convnets: A Frame-Theoretic Perspectiv…
Group convolutional layers with respect to some group $G$ are modeled by convolutions or cross-correlations with a filter, and they provide the fundamental building block for group convolutional neural networks. For entirely unconstrained…
The construction of Parseval fusion frames is highly desirable in a wide range of signal processing applications. In this paper, we study the problem of modifying the weights of a fusion frame in order to generate a Parseval fusion frame.…
In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…
In this paper we introduce and study the algebraic generalization of non commutative convolutional neural networks. We leverage the theory of algebraic signal processing to model convolutional non commutative architectures, and we derive…
Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…
Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are…
Convolution is a broadly useful operation with applications including signal processing, machine learning, probability, optics, polynomial multiplication, and efficient parsing. Usually, however, this operation is understood and implemented…
Efficient estimators of Fourier-space statistics for large number of objects rely on Fast Fourier Transforms (FFTs), which are affected by aliasing from unresolved small scale modes due to the finite FFT grid. Aliasing takes the form of a…
Most existing human pose estimation (HPE) methods exploit multi-scale information by fusing feature maps of four different spatial sizes, \ie $1/4$, $1/8$, $1/16$, and $1/32$ of the input image. There are two drawbacks of this strategy: 1)…
Neural networks, specifically deep convolutional neural networks, have achieved unprecedented performance in various computer vision tasks, but the rationale for the computations and structures of successful neural networks is not fully…
Ocular biometric systems working in unconstrained environments usually face the problem of small within-class compactness caused by the multiple factors that jointly degrade the quality of the obtained data. In this work, we propose an…
We consider regression in which one predicts a response $Y$ with a set of predictors $X$ across different experiments or environments. This is a common setup in many data-driven scientific fields and we argue that statistical inference can…
Accurate stabilization of facial motion is essential for applications in photoreal avatar construction for 3D games, virtual reality, movies, and training data collection. For the latter, stabilization must work automatically for the…
We investigate the convective stability of a thin, infinite fluid layer with a rectangular cross-section, subject to imposed heat fluxes at the top and bottom and fixed temperature along the vertical sides. The instability threshold depends…
Despite strong empirical performance for image classification, deep neural networks are often regarded as ``black boxes'' and they are difficult to interpret. On the other hand, sparse convolutional models, which assume that a signal can be…
Regular sampling in the time domain results in aliasing in the frequency domain that complicates the accurate determination of the periods of astrophysical variables. We propose to actively break the regularity of this sampling by providing…
Image convolutions have been a cornerstone of a great number of deep learning advances in computer vision. The research community is yet to settle on an equivalent operator for sparse, unstructured continuous data like point clouds and…
Frames are the foundation of the linear operators used in the decomposition and reconstruction of signals, such as the discrete Fourier transform, Gabor, wavelets, and curvelet transforms. The emergence of sparse representation models has…
Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…
In the context of training neural network-based approximations of solutions of parameter-dependent PDEs, we investigate the effect of preconditioning via well-conditioned frame representations of operators and demonstrate a significant…