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The integration of Symmetric Positive Definite (SPD) matrices into deep learning has historically relied on fixed algebraic Riemannian metrics. Analogous to hand-crafted features in classical machine learning, these static formulations…
The linear model uses the space defined by the input to project the target or desired signal and find the optimal set of model parameters. When the problem is nonlinear, the adaption requires nonlinear models for good performance, but it…
Many recent efforts have been devoted to designing sophisticated deep learning structures, obtaining revolutionary results on benchmark datasets. The success of these deep learning methods mostly relies on an enormous volume of labeled…
We present a novel method for training score-based generative models which uses nonlinear noising dynamics to improve learning of structured distributions. Generalizing to a nonlinear drift allows for additional structure to be incorporated…
This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic…
Modern Convolutional Neural Networks (CNN) are extremely powerful on a range of computer vision tasks. However, their performance may degrade when the data is characterised by large intra-class variability caused by spatial transformations.…
Neural networks in general, from MLPs and CNNs to attention-based Transformers, are constructed from layers of linear combinations followed by nonlinear operations such as ReLU, Sigmoid, or Softmax. Despite their strength, these…
The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space $V_n$ which approximates well the solution manifold $\mathcal{M}$ consisting of all solutions $u(y)$ with $y$ the…
To deal with non-linear relations between the predictors and the response, we can use transformations to make the data look linear or approximately linear. In practice, however, transformation methods may be ineffective, and it may be more…
Portrait Stylization aims to imbue portrait photos with vivid artistic effects drawn from style examples. Despite the availability of enormous training datasets and large network weights, existing methods struggle to maintain geometric…
Based on its great successes in inference and denosing tasks, Dictionary Learning (DL) and its related sparse optimization formulations have garnered a lot of research interest. While most solutions have focused on single layer…
Asymmetric data naturally exist in real life, such as directed graphs. Different from the common kernel methods requiring Mercer kernels, this paper tackles the asymmetric kernel-based learning problem. We describe a nonlinear extension of…
This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…
Deep neural networks are being increasingly used for short-term traffic flow prediction, which can be generally categorized as convolutional (CNNs) or graph neural networks (GNNs). CNNs are preferable for region-wise traffic prediction by…
Deformable Parts Models and Convolutional Networks each have achieved notable performance in object detection. Yet these two approaches find their strengths in complementary areas: DPMs are well-versed in object composition, modeling…
We revisit the additive model learning literature and adapt a penalized spline formulation due to Eilers and Marx, to train additive classifiers efficiently. We also propose two new embeddings based two classes of orthogonal basis with…
Spatial transformer networks (STNs) were designed to enable convolutional neural networks (CNNs) to learn invariance to image transformations. STNs were originally proposed to transform CNN feature maps as well as input images. This enables…
Deep neural networks based on state space models (SSMs) are attracting significant attention in sequence modeling since their computational cost is much smaller than that of Transformers. While the capabilities of SSMs have been…
Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…
The deep network model, with the majority built on neural networks, has been proved to be a powerful framework to represent complex data for high performance machine learning. In recent years, more and more studies turn to nonneural network…