Chapter 1
Tensor Fundamentals in Machine Learning and Systems
Far beyond being mere arrays, tensors are the backbone of modern machine learning systems, shaping how data is represented, manipulated, and accelerated for high-throughput model computations. This chapter illuminates the mathematical structures, storage strategies, and practical considerations that define the efficiency and reliability of tensor-centric pipelines. By understanding these foundational components, readers will gain a rare inside view into the delicate interplay between data, algorithms, and system performance that distinguishes high-performance ML applications.
1.1 Mathematical Foundations of Tensors
A tensor can be formally defined as a multilinear map that takes multiple vector and dual vector arguments and produces a scalar, or equivalently, as an element of a tensor product of vector spaces and their duals. Given a finite-dimensional vector space V over a field