arXiv research

Optimal square matrices for image approximation under translation and rotation.

Study invariant $λ$-translators in Lorentz-Minkowski space.

The paper classifies invariant translators for a specific curvature flow.

GCNNs gain rotation invariance with more training augmentation, making SVD-Universal more effective.

Overview of methods for rotating 2D and 3D data.

The paper classifies special surfaces in a 3D space.

Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map translations. This is not the case for rotations. Global rotation equivariance is typic…

A $λ$-translating soliton with density vector $\vec{v}$ is a surface in Euclidean space whose mean curvature $H$ satisfies $2H=2λ+\langle N,\vec{v}\rangle$, where $N$ is the Gauss map. We classify all $λ$-translating solitons that are invariant by a one-parameter group of translations and a one-parameter group of rotat…

In this paper we show that all conformal metrics to a pseudo-euclidean space invariant under the translation group, and all the conformal metrics product manifold also invariant by translation where F m it is Ricci flat semi-Riemannian manifold, are gradient Ricci almost soliton. We also proved that all conformal metri…

Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated, flipped, etc. However, coming up with exact models of how to rotate a 3 x 3 filter…

New neural network processes 3D volumes with improved equivariance.

Helicoidal surfaces rotate and translate under mean curvature flow.

The paper classifies surfaces in the Heisenberg space invariant under specific isometries.

Generates valid Euclidean distance matrices for molecular structures.

Patch ranking improves CNN performance by focusing on object content, not location.

Classifies timelike translating solitons in Minkowski space.

The study classifies horo-shrinkers in hyperbolic space under different isometries.

The projection body operator Π, which associates with every convex body in Euclidean space Rn its projection body, is a continuous valuation, it is invariant under translations and equivariant under rotations. It is also well known that Π maps the set of polytopes in Rn into itself. We show that Π is the only non-trivi…

This paper presents a novel approach to exploit the distinctive invariant features in convolutional neural network. The proposed CNN model uses Scale Invariant Feature Transform (SIFT) descriptor instead of the max-pooling layer. Max-pooling layer discards the pose, i.e., translational and rotational relationship betwe…

Researchers classify translators and rotators in hyperbolic 3-space for mean curvature flow.

The paper classifies invariant gradient $k$-Yamabe solitons in pseudo-Euclidean spaces.

The effectiveness of Convolutional Neural Networks stems in large part from their ability to exploit the translation invariance that is inherent in many learning problems. Recently, it was shown that CNNs can exploit other invariances, such as rotation invariance, by using group convolutions instead of planar convoluti…

3D capsule network for point clouds handles rotations and translations.

Researchers classify and describe $K^α$-translators in Euclidean space.

The paper classifies rotational K^α-translators in Minkowski space.

INO learns physical models with momentum conservation laws.

The study finds translators for higher order mean curvature flows in Euclidean and hyperbolic spaces.

Symmetry augmentation speeds up learning in robotics tasks.

This paper shows how rotating, cropping, and translating images improves a reinforcement learning agent's ability to generalize.

New families of translating solitons found in hyperbolic space.

Finite translation surfaces can be classified by the order of their singularities. When generalizing to infinite translation surfaces, however, the notion of order of a singularity is no longer well-defined and has to be replaced by new concepts. This article discusses the nature of two such concepts, recently introduc…

The paper proves Hessian estimates for specific geometric flows.

Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab-initio calculations) and at speeds suitable for molecular dynam- ics simulation. Best performance is achieved when the known physical constraints are encoded in the mac…

Classifies and constructs translators for curvature flows.

Transforms improve CNNs' invariance to image transformations.

Improves reinforcement learning extrapolation in Gridworlds.

3D Convolutional Neural Networks are sensitive to transformations applied to their input. This is a problem because a voxelized version of a 3D object, and its rotated clone, will look unrelated to each other after passing through to the last layer of a network. Instead, an idealized model would preserve a meaningful r…

We give explicit formulæ for Noether invariants associated to Killing vector fields for the variational problem of minimal and constant mean curvature surfaces in 3-manifolds. In the case of homogeneous spaces, such invariants are the flux (associated to translations) and the torque (associated to rotations). Then we f…

Classifies hypersurfaces with positive constant mean curvature in hyperbolic space.

We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM margin. We provide rigorous guarantees for optimality and generalization, interpret…

A general machine learning architecture is introduced that uses wavelet scattering coefficients of an inputted three dimensional signal as features. Solid harmonic wavelet scattering transforms of three dimensional signals were previously introduced in a machine learning framework for the regression of properties of sm…

New MCMC method improves sampling efficiency across diverse structural models.

Characterizes geodesic completeness for landmark spaces.

A novel approach learns goal-conditioned policies for locomotion using batch RL.

The paper classifies and characterizes special surfaces in a 3D space.

Proposes local coordinate frames for improving model performance in complex dynamical systems.

Constructing solutions to geometric flows with rotational symmetry.

For many tasks and data types, there are natural transformations to which the data should be invariant or insensitive. For instance, in visual recognition, natural images should be insensitive to rotation and translation. This requirement and its implications have been important in many machine learning applications, a…