Related papers: Machine-Learning Kronecker Coefficients
We study the remarkable Saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups S_n contain all irreducibles as their constituents. Our main result is that they contain representations…
Despite all the impressive advances of recurrent neural networks, sequential data is still in need of better modelling. Truncated backpropagation through time (TBPTT), the learning algorithm most widely used in practice, suffers from the…
Processing qubit Hamiltonians derived from electronic-structure problems can become classically prohibitive because many downstream manipulations still rely on dense operator constructions whose cost grows exponentially with qubit number.…
We study the supersymmetric ground states of the Kronecker model of quiver quantum mechanics. This is the simplest quiver with two gauge groups and bifundamental matter fields, and appears universally in four-dimensional N=2 systems. The…
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…
Binary Neural Network (BNN) represents convolution weights with 1-bit values, which enhances the efficiency of storage and computation. This paper is motivated by a previously revealed phenomenon that the binary kernels in successful BNNs…
For any three element set of positive integers, $\{a,b,n\}$, with $a<b<n$, $n$ sufficiently large and $\gcd(a,b)=1$, we find the least $\alpha$ such that given any real numbers $t_1$, $t_2$, $t_3$, there is a real number $x$ such that…
The Clebsch--Gordan coefficients of the Kronecker products of the irreducible representations of the Quaternion Group Q8, of the Generalized Quaternion Groups Q16 and Q32, and of the factor group (Q32 X Q32)/{(1,1),(-1,-1)} are computed as…
Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…
Brundan and Kleshchev introduced graded decomposition numbers for representations of cyclotomic Hecke algebras of type $A$, which include group algebras of symmetric groups. Graded decomposition numbers are certain Laurent polynomials,…
Two geometric spaces are in the same topological class if they are related by certain geometric deformations. We propose machine learning methods that automate learning of topological invariance and apply it in the context of knot theory,…
K-nearest neighbors (KNN) is one of the earliest and most established algorithms in machine learning. For regression tasks, KNN averages the targets within a neighborhood which poses a number of challenges: the neighborhood definition is…
We present a way of computing Kronecker coefficients that uses a new family of rational convex polytopes, called column-row polytopes. We give several different formulas for the computation. They are alternating sums of numbers of integer…
Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in…
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…
The performance of a neural network for a given task is largely determined by the initial calibration of the network parameters. Yet, it has been shown that the calibration, also referred to as training, is generally NP-complete. This…
The paper discusses the limitations of deep learning models in identifying and utilizing features that remain invariant under a bijective transformation on the data entries, which we refer to as combinatorial patterns. We argue that the…
In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…
Random graph models are playing an increasingly important role in various fields ranging from social networks, telecommunication systems, to physiologic and biological networks. Within this landscape, the random Kronecker graph model,…
Invariance has recently proven to be a powerful inductive bias in machine learning models. One such class of predictive or generative models are tensor networks. We introduce a new numerical algorithm to construct a basis of tensors that…