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

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 ...