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.