vertical federated learning

**Vertical Federated Learning** is a **federated learning setting where different participants hold different features (columns) for the same set of samples** — unlike horizontal FL (same features, different samples), vertical FL handles the case where each party has a different view of the same entities. **Vertical FL Architecture** - **Feature Partition**: Party A has features $X_A$, Party B has features $X_B$, for the same sample IDs. - **Label Holder**: Typically one party holds the labels — the others contribute features. - **Split Learning**: The model is split at a cut layer — each party computes their part, shares only intermediate representations. - **Entity Alignment**: Requires matching entities across parties using Private Set Intersection (PSI). **Why It Matters** - **Complementary Data**: In semiconductor manufacturing, metrology data (one system) + process data (another system) for the same wafers. - **Data Silos**: Different departments or companies hold different feature types for the same entities. - **Privacy**: Each party only sees their own features — no raw feature sharing. **Vertical FL** is **learning from different views** — combining complementary features from multiple parties without exposing any party's raw data.