Related papers: On Explicit Curvature Regularization in Deep Gener…

We give estimates on the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of…

Overparameterized shallow neural networks admit substantial parameter redundancy: distinct parameter vectors may represent the same predictor due to hidden-unit permutations, rescalings, and related symmetries. As a result, geometric…

Convolutional neural networks are capable of learning powerful representational spaces, which are necessary for tackling complex learning tasks. However, due to the model capacity required to capture such representations, they are often…

Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing…

Existing deep learning methods have made significant progress in gait representation learning. Quantization can facilitate the application of gait models as a model-agnostic general compression technique. Typically, appearance-based models…

Currently, deep neural networks are deployed on low-power portable devices by first training a full-precision model using powerful hardware, and then deriving a corresponding low-precision model for efficient inference on such systems.…

Euclidean geometry has historically been the typical "workhorse" for machine learning applications due to its power and simplicity. However, it has recently been shown that geometric spaces with constant non-zero curvature improve…

Recent works in medical image registration have proposed the use of Implicit Neural Representations, demonstrating performance that rivals state-of-the-art learning-based methods. However, these implicit representations need to be optimized…

This paper deals with the concept of curvature of framed space curves, their higher-order derivatives, variations, and co-rotational derivatives. We realize that parametrizing rotation tensor using the Gibbs vector is effective in deriving…

The goal of this paper is to analyze the geometric properties of deep neural network classifiers in the input space. We specifically study the topology of classification regions created by deep networks, as well as their associated decision…

Standard supervised learning optimizes for predictive accuracy but remains agnostic to the internal geometry of learned features, often yielding representations that are entangled and brittle. We propose Class-Conditional Activation…

Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised…

Accurate estimation of spatial derivatives from discrete and noisy data is central to scientific machine learning and numerical solutions of PDEs. We extend kinetic-based regularization (KBR), a localized multidimensional kernel regression…

This paper introduces a generative model for 3D surfaces based on a representation of shapes with mean curvature and metric, which are invariant under rigid transformation. Hence, compared with existing 3D machine learning frameworks, our…

Over-parameterized neural networks generalize well in practice without any explicit regularization. Although it has not been proven yet, empirical evidence suggests that implicit regularization plays a crucial role in deep learning and…

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…

Deep Neural Networks can generalize despite being significantly overparametrized. Recent research has tried to examine this phenomenon from various view points and to provide bounds on the generalization error or measures predictive of the…

Neural-Network (NN) based turbulence closures have been developed for being used as pre-trained surrogates for traditional turbulence closures, with the aim to increase computational efficiency and prediction accuracy of CFD simulations.…

Model compression techniques allow to significantly reduce the computational cost associated with data processing by deep neural networks with only a minor decrease in average accuracy. Simultaneously, reducing the model size may have a…

We consider the problem of learning implicit neural representations (INRs) for signals on non-Euclidean domains. In the Euclidean case, INRs are trained on a discrete sampling of a signal over a regular lattice. Here, we assume that the…