Abstract:Scaling laws predict loss from compute but not how capabilities interact. We measure the coupling between reasoning and truthfulness across 63 base models from 16 families and find a regime change invisible to loss curves: below a family-dependent critical scale $N_c$, capabilities anticorrelate; above it, they cooperate. $N_c \approx 3.5$B parameters [2.9B, 13.4B] (bootstrap 95\% CI), but model size is not the only variable that determines phase. Architecture, data curation, and training recipe each shift $N_c$ independently: curated training eliminated the coupling dip between Qwen generations (0.025 $\to$ 0.830 at matched scale), Gemma-4 at 4B achieves coupling 0.871, characteristic of 13B+ standard-trained models, through distillation and architectural innovation, and Phi at 1B matches web-trained coupling at 10B through data curation alone. Width normalization eliminates the anticorrelation across all tested families, supporting an output-projection bottleneck. Internally, 38 of 40 models show zero competing attention heads. A sparse-regression ODE cross-predicts held-out Llama-2 at 5.6\% error. The diagnostic requires no model internals -- only public benchmark scores across a model family. The cooperative regime extends to the frontier ($r = +0.72$, 34 models, 10 labs). A proof-of-concept intervention confirms the bottleneck is exploitable: adding a single truth-direction vector at the identified layer corrects 60\% of misaligned outputs in the tax phase with zero retraining -- a surgical, per-inference correction that requires no weight modification. Code, data, an open-source steering CLI for any open-weight model, and an interactive dashboard for phase diagnosis are released: this https URL.
| Comments: | 15 pages, 8 figures, 2 tables. Companion paper: "The Growing Pains of Frontier Models: When Leaderboards Stop Separating and What to Measure Next." ( this https URL). Code: this https URL. Dashboard: this https URL |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL) |
| Cite as: | arXiv:2605.18838 [cs.LG] |
| (or arXiv:2605.18838v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.18838 arXiv-issued DOI via DataCite |
From: Adil Amin [view email]
[v1]
Wed, 13 May 2026 03:14:09 UTC (1,736 KB)
[v2]
Sat, 23 May 2026 21:02:16 UTC (1,737 KB)
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