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maths

Truth is not a direction: a Tarski attack on LLM probes

Abel Jansma

A diagonal attack for LLM truth probes shows why no probe on a language model’s embedding space can pin down truth. A linear dream Modern LLMs famously encode input texts as vectors in some embedding space. One of the most satisfying discoveries about LLMs is that many natural concepts,...

A Möbius inversion theorem for modules and vector spaces

Abel Jansma

In a previous post, I proposed to study complex systems through a mereological lens by applying the Möbius inversion theorem. This has become my favourite theorem by now, because I think it allows you to do integration and differentiation on observables in complex systems where this was not...

Möbius Functions on Powerset Antichains

Abel Jansma

UPDATE: I have now found an explicit formula for the Möbius function on the redundancy lattice. This will appear in a preprint soon. I calculated the full Möbius function on the lattice of powerset antichains of 2, 3, and 4 variables. As far as I can tell, these results have not been shared...

Introducing: Stator

Abel Jansma

In my PhD thesis, I developed a method and software package to infer interactions and cell states from gene expression data. Both the software and the research are now published! The software is called Stator, and comprises the Stator Nextflow pipeline, as well as a bespoke Shiny app developed by...