IC-472The degree of emergence metric derived from Pythia's internal structure positively correlates with benchmark performance across training epochs

Xiongye Xiao, Heng Ping, Chenyu Zhou, Defu Cao, Yaxing Li, Yi-Zhuo Zhou, Shixuan Li, Nikos Kanakaris, Paul Bogdan

SourceNeuron-based Multifractal Analysis of Neuron Interaction Dynamics in Large Models

The paper tracks the degree of emergence (a structural metric combining heterogeneity and regularity changes) alongside standard benchmark scores for Pythia 160M, 1.4B, and 2.8B across training epochs. The structural metric rises sharply in the first ~15,000 epochs, then gradually increases to ~40,000 epochs, then stabilizes with fluctuations. This trajectory mirrors the improvement in LAMBADA, PIQA, ARC-Easy, and SCIQ scores. The authors note significant performance oscillations on WSC and LogiQA, suggesting limited utility of those benchmarks.

Evidence
correlational
Key metric
Pythia-1b degree of emergence: 0.00 (epoch 0) → 0.23 (epoch 3000) → 0.65 (epoch 23000) → 0.73 (epoch 53000) → 0.71 (epoch 143000); Pythia-1.4b: 0.00 → 0.30 → 0.54 → 0.65 → 0.68; LAMBADA (1b): 0.00 → 0.33 → 0.53 → 0.58 → 0.62; PIQA (1b): 0.53 → 0.60 → 0.66 → 0.69 → 0.70
Caveat
The authors acknowledge the correlation is restricted to the specific datasets tested and that a more comprehensive evaluation across more datasets is needed. The relationship is correlational, not causal.
Model
Pythia
Datasets
LAMBADA [eval], PIQA [eval], ARC [eval], SciQ / SciQA [eval], Winogrande [eval], LogiQA [eval]
Related findings
IC-471, IC-473
Extraction
automatic-extraction