Lattice Vector Quantization for Neural Networks
From First Principles to Efficient Inference
Preface
This book develops lattice vector quantization for neural networks from first principles. It is written for machine-learning researchers, systems researchers, graduate students, and engineers who want to understand both the mathematics and the implementation path to efficient inference.
The central principle is simple: introduce mathematics only when it solves a concrete engineering problem. Modular arithmetic, cosets, lattices, quotient groups, Reed-Muller codes, and Barnes-Wall lattices appear because quantization forces them to appear.
The running example uses dimension d = 4, the D4 lattice, hierarchy radix q = 2, hierarchy depth M = 4, an eight-value weight vector, and an eight-value activation vector. The same example is revisited throughout the book until it becomes a complete Hierarchical Nested Lattice Quantization (HNLQ) and lookup-table inference pipeline.
Standard lattice background will be grounded in references such as Conway and Sloane (1999) and connected to quantization and coding viewpoints such as Forney (1988).