Broadcast Product: Shape-aligned Element-wise Multiplication and Beyond

TL;DR

This paper introduces the broadcast product, a new tensor operator that simplifies complex tensor operations and enables novel tensor decompositions for dimensionality reduction.

Contribution

It proposes the broadcast product operator and demonstrates its application in tensor decomposition and shape-aligned element-wise multiplication.

Findings

Simplifies tensor operations in libraries like numpy.

Enables new tensor decomposition methods.

Highlights potential for dimensionality reduction.

Abstract

We propose a new operator defined between two tensors, the broadcast product. The broadcast product calculates the Hadamard product after duplicating elements to align the shapes of the two tensors. Complex tensor operations in libraries like \texttt{numpy} can be succinctly represented as mathematical expressions using the broadcast product. Finally, we propose a novel tensor decomposition using the broadcast product, highlighting its potential applications in dimensionality reduction.