Related papers: Convolutional Filtering and Neural Networks with N…
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
We present an efficient convolution kernel for Convolutional Neural Networks (CNNs) on unstructured grids using parameterized differential operators while focusing on spherical signals such as panorama images or planetary signals. To this…
A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images,…
We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly…
Geometric variations like rotation, scaling, and viewpoint changes pose a significant challenge to visual understanding. One common solution is to directly model certain intrinsic structures, e.g., using landmarks. However, it then becomes…
This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…
This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on the image classification…
We establish a series of deep convolutional neural networks to automatically analyze position averaged convergent beam electron diffraction patterns. The networks first calibrate the zero-order disk size, center position, and rotation…
Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem -- e.g., factor…
Standard kernels such as Mat\'ern or RBF kernels only encode simple monotonic dependencies within the input space. Spectral mixture kernels have been proposed as general-purpose, flexible kernels for learning and discovering more…
A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalisation of the Leibnitz rules of commutative geometry and uses the bimodule structure of $\Omega^1$. A special role is played…
This work proposes an unsupervised fusion framework based on deep convolutional transform learning. The great learning ability of convolutional filters for data analysis is well acknowledged. The success of convolutive features owes to…
Convolutional neural networks typically consist of many convolutional layers followed by one or more fully connected layers. While convolutional layers map between high-order activation tensors, the fully connected layers operate on…
In this paper we consider a problem of searching a space of predictive models for a given training data set. We propose an iterative procedure for deriving a sequence of improving models and a corresponding sequence of sets of non-linear…
Recovering an image from a noisy observation is a key problem in signal processing. Recently, it has been shown that data-driven approaches employing convolutional neural networks can outperform classical model-based techniques, because…
Fourier embedding has shown great promise in removing spectral bias during neural network training. However, it can still suffer from high generalization errors, especially when the labels or measurements are noisy. We demonstrate that…
Selective unlearning and long-horizon extrapolation remain fragile in modern neural networks, even when tasks have underlying algebraic structure. In this work, we argue that these failures arise not solely from optimization or unlearning…
This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…
Adversarial Attacks are still a significant challenge for neural networks. Recent work has shown that adversarial perturbations typically contain high-frequency features, but the root cause of this phenomenon remains unknown. Inspired by…