Michał P. Karpowicz

activity

20232026

most citedOn the Fundamental Impossibility of Hallucination Control in Large Language Models

2 citations · 2 across the 3 of their papers we have counts for

collaborators

4 papers

math.NA2026

Generalized Inverses of Matrix Products: From Fundamental Subspaces to Randomized Decompositions

Michał P. Karpowicz, Gilbert Strang

We investigate the Moore-Penrose pseudoinverse and generalized inverse of a matrix product $A = C R$ to establish a unifying framework for generalized and randomized matrix inverses.…

stat.ML2025★ 2 cited

On the Fundamental Impossibility of Hallucination Control in Large Language Models

Michał P. Karpowicz

Large language models hallucinate. This paper shows when that is unavoidable and what we can do about it. We model inference as an auction of ideas, in which a model's components,…

math.NA2023

The Pseudoinverse of $A = C R$ is $A^{+} = R^{+} C^{+}$ (?)

Michał P. Karpowicz, Gilbert Strang

This paper gives three formulas for the pseudoinverse of a matrix product $A = C R$ . The first is sometimes correct, the second is always correct, and the third is almost never corr…

math.NA2023

The secret life of matrix factorizations: how matrix decompositions reveal and keep secrets of linear equations and what we can do about it

Michał P. Karpowicz

This paper explores the relationship between matrix factorizations and linear matrix equations. It shows that every matrix factorization defines two hidden projectors, one for the…

Generalized Inverses of Matrix Products: From Fundamental Subspaces to Randomized Decompositions

On the Fundamental Impossibility of Hallucination Control in Large Language Models

The Pseudoinverse of A=CR is A+=R+C+ (?)

The secret life of matrix factorizations: how matrix decompositions reveal and keep secrets of linear equations and what we can do about it

The Pseudoinverse of $A = C R$ is $A^{+} = R^{+} C^{+}$ (?)