Related papers: Polynomial-based rotation invariant features
A very active area of materials research is to devise methods that use machine learning to automatically extract predictive models from existing materials data. While prior examples have demonstrated successful models for some applications,…
The invariant classification of superintegrable systems is reviewed and utilized to construct singular limits between the systems. It is shown, by construction, that all superintegrable systems on conformally flat, 3D complex Riemannian…
Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in…
The topological framework of circuit topology has recently been introduced to complement knot theory and to help in understanding the physics of molecular folding. Naturally evolved linear molecular chains, such as proteins and nucleic…
Learning invariant representations from images is one of the hardest challenges facing computer vision. Spatial pooling is widely used to create invariance to spatial shifting, but it is restricted to convolutional models. In this paper, we…
We study the typical properties of polynomial Support Vector Machines within a Statistical Mechanics approach that allows us to analyze the effect of different normalizations of the features. If the normalization is adecuately chosen, there…
This article focuses on automatically generating polynomial equations that are inductive loop invariants of computer programs. We propose a new algorithm for this task, which is based on polynomial interpolation. Though the proposed…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
We study a new biholomorphic invariant of holomorphic maps between domains in different dimensions based on generic initial ideals. We start with the standard generic monomial ideals to find invariants for rational maps of spheres and…
We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…
Effective recognition of spatial patterns and learning their hierarchy is crucial in modern spatial data analysis. Volumetric data applications seek techniques ensuring invariance not only to shifts but also to pattern rotations. While…
Extracting discriminative local features that are invariant to imaging variations is an integral part of establishing correspondences between images. In this work, we introduce a self-supervised learning framework to extract discriminative…
We describe new results and algorithms for two different, but related, problems which deal with circulant matrices: learning shift-invariant components from training data and calculating the shift (or alignment) between two given signals.…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
In this contribution, we show how to incorporate prior knowledge to a deep neural network architecture in a principled manner. We enforce feature space invariances using a novel layer based on invariant integration. This allows us to…
In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic…
Achieving invariance to nuisance transformations is a fundamental challenge in the construction of robust and reliable vision systems. Existing approaches to invariance scale exponentially with the dimension of the family of…
Polarization measurements provide a detailed method to test the Standard Model and to search for new physics. Most previous studies depend on pre-selected coordinates, which blurs the significance of the results. The construction of two…
In this paper, we utilize hyperspheres and regular $n$-simplexes and propose an approach to learning deep features equivariant under the transformations of $n$D reflections and rotations, encompassed by the powerful group of O$(n)$. Namely,…