I'm often asked about the differences and similarities between Simplex' and Timaeus' research agendas. The question is natural enough. Both focus on a 'fundamental science' approach to AI alignment. Both organizations base their research agendas on sophisticated mathematical frameworks handed down from a bearded ur-figure (Sumio Watanabe, James Crutchfield).

We may posit the following correspondence

Dan Murfet + Jesse Hoogland : Developmental Interpretability : Singular Learning Theory : Sumio Watanabe

<->

Adam Shai + Paul Riechers : Belief-state Geometry: Computational Mechanics : James Crutchfield

SLT vs CompMech

Round One. Fight!

Weights vs Activations

DevInterp & SLT is about weight space. Belief-state geometry is more about studying activation space.

Activation space is what is already being studied in MechInterp & most 'mainstream' approaches to interpretability. It is concrete and present to the senses. Weight space is much larger, more abstract, harder to measure and sample.

Training vs Inference

SLT is about training. CompMech is about inference.

Both study Bayesian posteriors and updating. For SLT that is the Bayesian posterior on weight space - hence relevant for training. The Belief-State Geometry agenda studies the Mixed State Presentation from CompMech which describes an [idealized] version of in-context learning [...]

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Outline:

(00:55) SLT vs CompMech

(01:02) Weights vs Activations

(01:30) Training vs Inference

(02:19) IID vs non-IID Data

(02:40) Parameterization vs Invariant structure

(03:25) Asymptotic vs Exact

(03:43) Mechanism vs Behaviourial

(04:04) Bottom-up vs Top-down interpretability

(05:10) Physics vs Math?

(05:46) Conclusion

The original text contained 2 footnotes which were omitted from this narration.

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First published:
October 1st, 2026

Source:
https://www.lesswrong.com/posts/Fs4inpM72PeH4hsAv/simplex-vs-timaeus-round-one

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Narrated by TYPE III AUDIO.

“Simplex vs Timaeus: Round One” by Alexander Gietelink Oldenziel

LessWrong (30+ Karma)

“Simplex vs Timaeus: Round One” by Alexander Gietelink Oldenziel