Autonomous Expertise Formation in Transformer Systems: The Davies Threshold and Post-Threshold Token Compression
Year: 2026
Type: preprint
Abstract: This paper identifies a structural flaw in all deployed AI systems: they allocate identical computational resources to a mastered task on its millionth execution as on the first. I define the Davies Threshold, the precise deployment depth at which a transformer transitions from exploratory to expert computation, and derive the Post-Threshold Token Efficiency Law showing that minimum token requirements fall exponentially after threshold crossing. I then derive the four-stage physical mechanism of expert condensation: Activation Manifold Collapse, Residual Stream Contraction, Attention Head Crystallisation, and Logit Sharpening. The result is a system that produces expert-quality outputs from one to three tokens with near-certain accuracy. The theory predicts a 600,000-fold reduction in inference compute for mastered task classes with full biological correspondence to human expertise formation.
Source: OSF Preprints (OSF Preprints)
Author: Kalori, Davies
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161591390
Cites:
Cited by:
Related to: