IC-453Hidden representation trajectories in trained LLMs exhibit considerable linearity (mean LSS 4.25) compared to 6.54 at initialization, and linearity increases with training
Murdock Aubry, Haoming Meng, Anton Sugolov, Vardan Papyan
The line-shape score (LSS) measures how close a token's trajectory through the layers is to a straight line. Across 1,200 prompts from the Open LLM Leaderboard datasets, trained LLMs show a mean LSS of 4.25, compared to 6.54 for randomly initialized models. The low variation across benchmark prompts indicates robustness. In Pythia 12B, LSS decreases (linearity increases) as a function of training checkpoint, and this improvement is visible at multiple depths (layers 5, 15, 30). The paper notes this aligns with behaviour previously observed in ResNets.
Evidence
correlational
Key metric
mean LSS 4.25 (trained) vs 6.54 (initialization), computed on 1,200 prompts; LSS decreases with training checkpoints in Pythia 12B
Caveat
LSS values for LLMs (4.25) are higher than for ResNets (2.0-3.0), attributed to varying trajectory length and hidden dimension; the comparison across architectures is not directly comparable.