Foundations of Causal Representation Learning: Identifiability, Optimization, and Generalization

Modern AI systems excel at pattern recognition but fail to understand cause and effect, collapsing under distribution shifts or out-of-distribution scenarios. This monograph presents Causal Representation Learning (CRL)-a unified framework bridging causal inference and deep learning to build AI systems that understand the world, not just mirror it. This book covers theoretical foundations, algorithms, and applications across ten chapters. Beginning with structural causal models and identifiability theory, it progresses through latent variable models, multi-environment learning, interventional methods, and unified optimization frameworks. It explores causal deep generative models (normalizing flows, diffusion processes), causal reinforcement learning, and ethics/fairness. The final chapter outlines open problems including causality in foundation models and neuro-symbolic AI. Key features include: rigorous identifiability proofs under various assumptions; comprehensive causal discovery algorithms; case studies in robotics, healthcare, vision, and NLP; extensive fairness and safety discussions; and practical benchmark guidance. Written for graduate students, researchers, and practitioners, this monograph assumes familiarity with linear algebra, probability, and basic machine learning. Each chapter includes exercises and references to state-of-the-art implementations. Appendices cover graph theory, optimization, and datasets. By integrating causal reasoning into representation learning, this book charts a path toward robust, interpretable, and fair AI systems essential for high-stakes domains. The era of associative AI is ending; the era of causal AI has begun.