Defining T-Schemas via the Parametric Encoding of Second Order Languages in AI Models

Sat, 15 Feb 2025 00:00:00 +0800

TL;DR

The article argues that AI models cannot verify truth from purely within their own formal system (Tarski’s undefinability of truth), so scaling models and data that are entirely human-produced caps their intelligence near - or below - the humans who produced the training and benchmark data.
Two workarounds are proposed: reality-testing against an ungamable external metric the model can act on and observe the results of (echoing the site’s other work on disk space or crypto-wallet balances as reward signals), and building an internal metalanguage - a T-schema - against which future claims can be judged, the way Newton derived formulae from Kepler’s data.
The piece argues that recent evidence about “grokking” - the phenomenon where models suddenly generalise well after being trained far past the point of overfitting - shows models doing exactly this: building an internal higher-order abstraction rather than only memorising.
It cites the Grokfast team’s finding that memorisation and generalisation correspond to distinct fast and slow frequencies in weight updates, and a separate study showing that removing a cluster of training data sharply reduces generalisation while adding a few examples back restores it.
Further cited evidence links grokking to the model discovering a lower-rank encoding solution - achieving more with fewer effective features - which the piece reads as evidence of an internal abstraction layer.
It closes with the company’s own plan: train diffusion models, which reportedly show grokking-like behaviour throughout training and outperform on compositional and coding tasks, on data generated by its own “Generalising Agents,” as a route toward independent knowledge generation.

Key Takeaways

Grokking on Eigenform Articles

Defining T-Schemas via the Parametric Encoding of Second Order Languages in AI Models