Lattice Vector Quantization for Neural Networks

From First Principles to Efficient Inference

Author

Soma Dhavala

Published

July 7, 2026

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).