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Conditional contrastive learning frameworks consider the conditional sampling procedure that constructs positive or negative data pairs conditioned on specific variables. Fair contrastive learning constructs negative pairs, for example,…
A neural network architecture is presented that exploits the multilevel properties of high-dimensional parameter-dependent partial differential equations, enabling an efficient approximation of parameter-to-solution maps, rivaling…
Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of…
Group Convolutional Neural Networks (G-CNNs) constrain learned features to respect the symmetries in the selected group, and lead to better generalization when these symmetries appear in the data. If this is not the case, however,…
Although provably robust to translational perturbations, convolutional neural networks (CNNs) are known to suffer from extreme performance degradation when presented at test time with more general geometric transformations of inputs.…
For dynamical systems with a non hyperbolic equilibrium, it is possible to significantly simplify the study of stability by means of the center manifold theory. This theory allows to isolate the complicated asymptotic behavior of the system…
Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…
Convolutional neural networks (CNNs) have enabled the state-of-the-art performance in many computer vision tasks. However, little effort has been devoted to establishing convolution in non-linear space. Existing works mainly leverage on the…
In this work we investigate how to achieve equivariance to input transformations in deep networks, purely from data, without being given a model of those transformations. Convolutional Neural Networks (CNNs), for example, are equivariant to…
Neural networks are a promising tool for simulating quantum many body systems. Recently, it has been shown that neural network-based models describe quantum many body systems more accurately when they are constrained to have the correct…
Conditional density estimation is a general framework for solving various problems in machine learning. Among existing methods, non-parametric and/or kernel-based methods are often difficult to use on large datasets, while methods based on…
The lack of anisotropic kernels in graph neural networks (GNNs) strongly limits their expressiveness, contributing to well-known issues such as over-smoothing. To overcome this limitation, we propose the first globally consistent…
In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with…
The purpose of this short and simple note is to clarify a common misconception about convolutional neural networks (CNNs). CNNs are made up of convolutional layers which are shift equivariant due to weight sharing. However, convolutional…
Group equivariant neural networks have been explored in the past few years and are interesting from theoretical and practical standpoints. They leverage concepts from group representation theory, non-commutative harmonic analysis and…
In $\mathbb R^d$, it is well-known that cumulants provide an alternative to moments that can achieve the same goals with numerous benefits such as lower variance estimators. In this paper we extend cumulants to reproducing kernel Hilbert…
Continuous time recurrent neural networks (CTRNN) are systems of coupled ordinary differential equations that are simple enough to be insightful for describing learning and computation, from both biological and machine learning viewpoints.…
The convolutional neural network (CNN) is one of the most commonly used architectures for computer vision tasks. The key building block of a CNN is the convolutional kernel that aggregates information from the pixel neighborhood and shares…
The state-of-the-art CNN models give good performance on sentence classification tasks. The purpose of this work is to empirically study desirable properties such as semantic coherence, attention mechanism and reusability of CNNs in these…
Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…