This course develops a principled, unified foundation for representation learning  through the lens of spectral decomposition. Starting from the sufficiency of spectral representations for downstream tasks, we systematically build a framework that connects classical component analysis methods (PCA, CCA, Laplacian Embedding) to modern self-supervised learning algorithms (SimCLR, BYOL, CLIP, DINO) and extends to applications in reinforcement learning, causal inference, and controllable generation.

    The course follows the theoretical backbone of "Spectral Ghost in Representation Learning" (Dai, Li & Schuurmans, 2026), supplemented by the RL-specific treatment in "Spectral Representation-based Reinforcement Learning" (Gao, Sun, Li, Schuurmans &  Dai, 2026).