Your Language Model Cannot Say Certain Sentences. The Reason Is the Rank of a Matrix. Let Us Prove It With Tiny Numbers, By Hand.

Last Updated on June 22, 2026 by Editorial Team Author(s): Dr Swarneendu AI Originally published on Towards AI. There are next-word predictions your model is mathematically forbidden from making. Not unlikely. Forbidden, the way a piano with too few keys cannot play a note that lies past its keyboard. The proof needs nothing but small whole numbers and patience. We will do every step on paper. Summary of the article Read the full blog for free on Medium. Join thousands of data leaders on the AI newsletter. Join over 80,000 subscribers and keep up to date with the latest developments in AI. From research to projects and ideas. If you are building an AI startup, an AI-related product, or a service, we invite you to consider becoming a sponsor. Published via Towards AI