相关论文: bispectrum: Selective $G$-Bispectra Made Practical

An important problem in signal processing and deep learning is to achieve \textit{invariance} to nuisance factors not relevant for the task. Since many of these factors are describable as the action of a group $G$ (e.g. rotations,…

In many computer vision and shape analysis tasks, practitioners are interested in learning from the shape of the object in an image, while disregarding the object's orientation. To this end, it is valuable to define a rotation-invariant…

Much work has been devoted to devising architectures that build group-equivariant representations, while invariance is often induced using simple global pooling mechanisms. Little work has been done on creating expressive layers that are…

This paper develops the theory behind the bispectrum, a concept that is well established in statistical signal processing but not, until recently, extended to computer vision as a source of frequency-domain invariants. Recent papers on…

We address the problem of improving the performance and in particular the sample complexity of deep neural networks by enforcing and guaranteeing invariances to symmetry transformations rather than learning them from data. Group-equivariant…

We study how group symmetry helps improve data efficiency and generalization for end-to-end differentiable planning algorithms when symmetry appears in decision-making tasks. Motivated by equivariant convolution networks, we treat the path…

We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that…

We introduce a method to design a computationally efficient $G$-invariant neural network that approximates functions invariant to the action of a given permutation subgroup $G \leq S_n$ of the symmetric group on input data. The key element…

We design and implement a Python library to help the non-expert using all these powerful tools in a way that is efficient, extensible, and simple to incorporate into the workflow of the data scientist, practitioner, and applied researcher.…

Machine learning models often have uneven performance among subpopulations (a.k.a., groups) in the data distributions. This poses a significant challenge for the models to generalize when the proportions of the groups shift during…

We propose a new set of rotationally and translationally invariant features for image or pattern recognition and classification. The new features are cubic polynomials in the pixel intensities and provide a richer representation of the…

The bispectrum stands out as a revolutionary tool in frequency domain analysis, leaping the usual power spectrum by capturing crucial phase information between frequency components. In our innovative study, we have utilized the bispectrum…

In response to the increasingly critical demand for accurate prediction of GPU memory resources in deep learning tasks, this paper deeply analyzes the current research status and innovatively proposes a deep learning model that integrates…

We present a neural network architecture, Bispectral Neural Networks (BNNs) for learning representations that are invariant to the actions of compact commutative groups on the space over which a signal is defined. The model incorporates the…

In this paper, we introduce McTorch, a manifold optimization library for deep learning that extends PyTorch. It aims to lower the barrier for users wishing to use manifold constraints in deep learning applications, i.e., when the parameters…

This paper presents the design, implementation, and evaluation of the PyTorch distributed data parallel module. PyTorch is a widely-adopted scientific computing package used in deep learning research and applications. Recent advances in…

Generalized Category Discovery (GCD) aims to identify novel categories in unlabeled data while leveraging a small labeled subset of known classes. Training a parametric classifier solely on image features often leads to overfitting to old…

Building practical filtrations on objects to detect topological and geometric features is an important task in the field of Topological Data Analysis (TDA). In this paper, leveraging the ability of the Laplacian of Gaussian operator to…

Despite the prevalence of symmetry in scientific linear systems, these structural properties are often underutilized by standard computational software. This paper introduces PySymmetry, an open-source Sage/Python framework that implements…

Unsupervised skill discovery aims to acquire behavior primitives that improve exploration and accelerate downstream task learning. However, existing approaches often ignore the geometric symmetries of physical environments, leading to…