Related papers: Rethinking SO(3)-equivariance with Bilinear Tensor…

Dense retrieval models use bi-encoder network architectures for learning query and document representations. These representations are often in the form of a vector representation and their similarities are often computed using the dot…

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…

Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…

Neural networks that incorporate geometric relationships respecting SE(3) group transformations (e.g. rotations and translations) are increasingly important in molecular applications, such as molecular property prediction, protein structure…

At the CERN LHC, the task of jet tagging, whose goal is to infer the origin of a jet given a set of final-state particles, is dominated by machine learning methods. Graph neural networks have been used to address this task by treating jets…

We propose a general algorithm to compute all the symmetry classes of any $\mathrm{SO}(3)$ or $\mathrm{O}(3)$ linear representation. This method relies on the introduction of a binary operator between sets of conjugacy classes of closed…

This paper develops a rotation-invariant needlet convolution for rotation group SO(3) to distill multiscale information of spherical signals. The spherical needlet transform is generalized from $\mathbb{S}^2$ onto the SO(3) group, which…

Interpreting the spectral energy distributions (SEDs) of astrophysical objects with physically motivated models is computationally expensive. These models require solving coupled differential equations in high-dimensional parameter spaces,…

We develop techniques for the analysis of SO(2N) invariant couplings which allow a full exhibition of the SU(N) invariant content of the spinor and tensor representations. The technique utilizes a basis consisting of a specific set of…

The ability to perform fast and accurate atomistic simulations is crucial for advancing the chemical sciences. By learning from high-quality data, machine-learned interatomic potentials achieve accuracy on par with ab initio and…

We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different…

This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…

We introduce the $\star_G$ tensor algebra, in which any finite group $G$ defines the multiplication rule, making equivariance an intrinsic algebraic property rather than an architectural constraint. The framework rests on three…

Deep Learning approaches are becoming the go-to methods for data analysis in High Energy Physics (HEP). Nonetheless, most physics-inspired modern architectures are computationally inefficient and lack interpretability. This is especially…

Different neural networks trained on the same dataset often learn similar input-output mappings with very different weights. Is there some correspondence between these neural network solutions? For linear networks, it has been shown that…

What is a good vector representation of an object? We believe that it should be generative in 3D, in the sense that it can produce new 3D objects; as well as be predictable from 2D, in the sense that it can be perceived from 2D images. We…

We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors $\boldsymbol x \in \mathbb R^d$, $r$ hidden units with weights $\{\boldsymbol w_i\}_{1\le…

Using deep neural networks for identifying physics objects at the Large Hadron Collider (LHC) has become a powerful alternative approach in recent years. After successful training of deep neural networks, examining the trained networks not…

Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…

Convolutional neural networks typically consist of many convolutional layers followed by one or more fully connected layers. While convolutional layers map between high-order activation tensors, the fully connected layers operate on…