- Bichan Wu (@bichanw.bsky.social) & I wrote a tutorial paper on Reduced Rank Regression (RRR) — the statistical method underlying "communication subspaces" from Semedo et al 2019 — aimed at neuroscientists. arxiv.org/abs/2512.12467
- Part of our motivation was our own difficulty understanding RRR and its mathematical origins (e.g., Why is this an eigenvector problem?). We thought others might benefit from a simple derivation and some figures and comparisons to build intuition.Dec 17, 2025 02:06
- We also derive some useful (known) extensions, such as adding a ridge penalty ("ridge RRR") and non-spherical noise (accounting for correlated response noise), both of which preserve a closed-form solution.
- We introduce metrics for quantifying the degree of alignment between the communication subspace and the dominant modes of input and output population activity. (e.g., Are the dominant modes of the input population the same ones driving communication?)
- We'd be grateful for any comments about points we overlooked, additional citations, as well as any corrections, clarifications, or suggestions for improvement! 🙏
