Learnability and Competition in High-Dimensional Multi-Component ICA
Independent Component Analysis (ICA) is a foundational tool for unsupervised representation learning, yet its high-dimensional theory remains largely limited to single-component recovery. We develop an asymptotically exact mean-field theory for multi-component online ICA, capturing the coupling induced by simultaneous learning and orthogonalization. In the high-dimensional limit, the joint empirical distribution of learned estimates and ground-truth components converges to a deterministic process, yielding a closed ODE system for the overlap matrix between learned directions and true components. This characterization reveals a genuinely multi-component, initialization-driven phase structu...
| Authors | Eser Ilke Genc, Samet Demir, Zafer Dogan |
|---|---|
| Primary category | stat.ML |
| Published | 8 May 2026 |
| Last updated at source | 8 May 2026 |
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