One forecast, several competing forces
The paper’s template is less one smooth curve than a negotiation between helpful scaling, bottleneck terms, and harmful opposition terms that appear when a training regime turns bad.
Heatmap slice through a regime-changing surface
This synthetic slice holds total compute roughly fixed and shows why one clean law misses the balanced basin, the hyperbreak ridges, and the replay-pressure wall.
From smooth laws to hyperbreak-aware slices
Flip axes and assembly stages to watch a classic smooth fit turn into a broken, opposition-aware surface with separate joint and bottleneck structure.
What the extra structure is supposed to buy
Illustrative holdout behavior near regime shifts: lower fit error on curated surfaces, plus better behavior when a withheld budget point lands near a suspected break.
All plotted values are realistic mock data shaped to the paper’s claims, not reproduced paper tables.