Mathematical models in natural language processing

Mathematical Models in Natural Language Processing: Foundations, Embedding, and Probabilistic Approaches is a comprehensive guide that explores the mathematical principles underlying modern Natural Language Processing (NLP). Designed for students, researchers, educators, and industry practitioners, this book bridges the gap between theoretical mathematics and practical language technologies.

Natural Language Processing has become one of the most influential areas of Artificial Intelligence, powering applications such as machine translation, search engines, virtual assistants, sentiment analysis, recommendation systems, and large language models. While many resources focus on implementation and software tools, relatively few explain the mathematical foundations that make these systems possible.

This book addresses that need by providing a structured exploration of vector spaces, linear algebra, probability theory, statistical language modeling, embeddings, matrix factorization, probabilistic models, optimization techniques, and neural representation learning.

Readers will gain a deep understanding of how words, sentences, and documents can be represented mathematically, how statistical and probabilistic models process language, and how modern embedding techniques such as Word2Vec, GloVe, FastText, ELMo, and BERT revolutionized language understanding.

The book further explores hidden Markov models, probabilistic context-free grammars, topic modeling, variational inference, and the mathematical foundations of neural language models. Advanced topics include contextual embeddings, representation learning, multilingual NLP, information retrieval, machine translation, and the probabilistic interpretation of large language models such as GPT and LLaMA.

Written with a balance of mathematical rigor and practical intuition, this book enables readers to move beyond using NLP libraries as black boxes and develop a deeper understanding of the principles that drive modern language technologies.

Whether you are preparing for academic research, graduate studies, machine learning careers, or advanced NLP development, this book provides the theoretical foundation necessary for mastering modern language intelligence systems.