Routing Transformer is an efficient transformer that uses online k-means clustering to route tokens into clusters — computing attention only within each cluster, reducing complexity from $O(N^2)$ to $O(N^{1.5})$ while maintaining content-dependent sparsity.

How Does Routing Transformer Work?

• Cluster Centroids: Maintain $k$ learnable centroid vectors.
• Route: Assign each token to its nearest centroid (online k-means).
• Attend: Compute full attention only within each cluster.
• Update Centroids: Update centroids using exponential moving average of assigned tokens.
• Paper: Roy et al. (2021).

Why It Matters

• Content-Aware: Tokens that are semantically similar get clustered together and can attend to each other.
• Learned Routing: The routing is learned end-to-end, unlike LSH (Reformer) which uses random projections.
• Flexible: The number and size of clusters adapt to the input distribution.

Routing Transformer is attention with learned traffic control — routing semantically similar tokens together for efficient, content-aware sparse attention.