Related papers: Nonlocal Kernel Network (NKN): a Stable and Resolu…
Neural Tangent Kernel (NTK) theory is widely used to study the dynamics of infinitely-wide deep neural networks (DNNs) under gradient descent. But do the results for infinitely-wide networks give us hints about the behavior of real…
Despite their immense promise in performing a variety of learning tasks, a theoretical understanding of the limitations of Deep Neural Networks (DNNs) has so far eluded practitioners. This is partly due to the inability to determine the…
Non-local methods exploiting the self-similarity of natural signals have been well studied, for example in image analysis and restoration. Existing approaches, however, rely on k-nearest neighbors (KNN) matching in a fixed feature space.…
This paper addresses the scalability problem of Bayesian deep neural networks. The performance of deep neural networks is undermined by the fact that these algorithms have poorly calibrated measures of uncertainty. This restricts their…
The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in a neural ordinary differential equation (NODE) is considered, that means finding the weights of a residual network with time continuous…
We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced-order space and…
Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a…
Expressiveness and generalization of deep models was recently addressed via the connection between neural networks (NNs) and kernel learning, where first-order dynamics of NN during a gradient-descent (GD) optimization were related to…
In the realm of computational science and engineering, constructing models that reflect real-world phenomena requires solving partial differential equations (PDEs) with different conditions. Recent advancements in neural operators, such as…
We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the…
The training dynamics and generalization properties of neural networks (NN) can be precisely characterized in function space via the neural tangent kernel (NTK). Structural changes to the NTK during training reflect feature learning and…
Deep Convolutional Neural Networks (CNN) have exhibited superior performance in many visual recognition tasks including image classification, object detection, and scene label- ing, due to their large learning capacity and resistance to…
Numerically solving partial differential equations typically requires fine discretization to resolve necessary spatiotemporal scales, which can be computationally expensive. Recent advances in deep learning have provided a new approach to…
Deep neural networks typically treat nonlinearities as fixed primitives (e.g., ReLU), limiting both interpretability and the granularity of control over the induced function class. While recent additive models (like KANs) attempt to address…
Deep neural networks (DNNs) enable innovative applications of machine learning like image recognition, machine translation, or malware detection. However, deep learning is often criticized for its lack of robustness in adversarial settings…
Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to…
Recently, quantum neural networks or quantum-classical neural networks (qcNN) have been actively studied, as a possible alternative to the conventional classical neural network (cNN), but their practical and theoretically-guaranteed…
Structural equation models (SEMs) have been widely adopted for inference of causal interactions in complex networks. Recent examples include unveiling topologies of hidden causal networks over which processes such as spreading diseases, or…
Performant Convolutional Neural Network (CNN) architectures must be tailored to specific tasks in order to consider the length, resolution, and dimensionality of the input data. In this work, we tackle the need for problem-specific CNN…
We present Shape-Tailored Deep Neural Networks (ST-DNN). ST-DNN extend convolutional networks (CNN), which aggregate data from fixed shape (square) neighborhoods, to compute descriptors defined on arbitrarily shaped regions. This is natural…