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

Oriented object detection predicts orientation in addition to object location and bounding box. Precisely predicting orientation remains challenging due to angular periodicity, which introduces boundary discontinuity issues and symmetry…

Neural networks have been able to achieve groundbreaking accuracy at tasks conventionally considered only doable by humans. Using stochastic gradient descent, optimization in many dimensions is made possible, albeit at a relatively high…

The identification of boosted heavy particles such as top quarks or vector bosons is one of the key problems arising in experimental studies at the Large Hadron Collider. In this article, we introduce LundNet, a novel jet tagging method…

Traditional network embedding primarily focuses on learning a continuous vector representation for each node, preserving network structure and/or node content information, such that off-the-shelf machine learning algorithms can be easily…

This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…

Modern sensing and metrology systems now stream terabytes of heterogeneous, high-dimensional (HD) data profiles, images, and dense point clouds, whose natural representation is multi-way tensors. Understanding such data requires regression…

Large-scale neuroimaging studies have been collecting brain images of study individuals, which take the form of two-dimensional, three-dimensional, or higher dimensional arrays, also known as tensors. Addressing scientific questions arising…

Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…

Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…

In this paper we generalize the 1-bit matrix completion problem to higher order tensors. We prove that when $r=O(1)$ a bounded rank-$r$, order-$d$ tensor $T$ in $\mathbb{R}^{N} \times \mathbb{R}^{N} \times \cdots \times \mathbb{R}^{N}$ can…

This paper presents SO-Net, a permutation invariant architecture for deep learning with orderless point clouds. The SO-Net models the spatial distribution of point cloud by building a Self-Organizing Map (SOM). Based on the SOM, SO-Net…

We study symmetry-enriched topological order in two-dimensional tensor network states by using graded matrix product operator algebras to represent symmetry induced domain walls. A close connection to the theory of graded unitary fusion…

A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is…

Branch-and-bound approaches in integer programming require ordering portions of the space to explore next, a problem known as node comparison. We propose a new siamese graph neural network model to tackle this problem, where the nodes are…

The joint entity and relation extraction task aims to extract all relational triples from a sentence. In essence, the relational triples contained in a sentence are unordered. However, previous seq2seq based models require to convert the…

Symmetric objects are common in daily life and industry, yet their inherent orientation ambiguities that impede the training of deep learning networks for pose estimation are rarely discussed in the literature. To cope with these…

This paper introduces a 3D shape generative model based on deep neural networks. A new image-like (i.e., tensor) data representation for genus-zero 3D shapes is devised. It is based on the observation that complicated shapes can be well…

Suppose we are given an $n$-dimensional order-3 symmetric tensor $T \in (\mathbb{R}^n)^{\otimes 3}$ that is the sum of $r$ random rank-1 terms. The problem of recovering the rank-1 components is possible in principle when $r \lesssim n^2$…

For any positive integer $k$, there exist neural networks with $\Theta(k^3)$ layers, $\Theta(1)$ nodes per layer, and $\Theta(1)$ distinct parameters which can not be approximated by networks with $\mathcal{O}(k)$ layers unless they are…

Jets from boosted heavy particles have a typical angular scale which can be used to distinguish them from QCD jets. We introduce a machine learning strategy for jet substructure analysis using a spectral function on the angular scale. The…