Oxford scholars debate the power law linking RL compute to AI task horizons

Oxford philosopher Toby Ord, together with economists Basil Halperin and Ramez Naam, held a series of exchanges about METR's AI time-horizon scaling curve, focusing on whether the curve follows a power law and whether compute growth can explain the rapid lengthening of observed task durations.

Confirmed

• Toby Ord noted that the relevant paper buries the key power-law exponent in a footnote: 0.454. Holding data, algorithms, and other factors constant, compute would need to scale roughly 100x for a model's task time horizon to extend 10x. This exponent is also used as an upper-bound reference for algorithmic progress.
• Ord offered an estimate: in 2025, RL post-training compute grows about 10x every 4-5 months, while new pretraining may have largely stalled; the RL exponent is about 0.3, meaning each 10x in RL compute doubles task duration.
• That 0.3 exponent is roughly twice what the rough rule of thumb "RL exponent is 1/3 of pretraining's" would imply, suggesting returns on RL post-training compute may be higher than simple extrapolation suggests.
• Responding to the objection that "RL scaling has a log problem," Basil Halperin derived that time horizon is most likely still a power law in RL compute, citing the Whitfill-Snodin-Becker paper (empirical + theoretical model); 100x pretraining compute is roughly equivalent to about 1,000,000x RL compute.
• Ord added: the Whitfill-Snodin-Becker paper also presents, after its figures, a version adjusted for Chinchilla-optimal-equivalent training compute, with a better power-law fit—the shared-slope R² improves from 0.906 (the post does not give the specific improved value).

Unconfirmed

• Ord questioned whether compute growth is fast enough to support METR's observed findings: early on, pretraining compute grew only about 5x per 12 months, and slower later; if the task-duration doubling time shortened from 7 months to 4 months and this is attributed entirely to compute, then pre-2024 training compute would need to quadruple roughly every 4 months—inconsistent with historical growth rates.
• Ord also pointed out that the measured curve may be just a "snapshot in time" (compute varying while algorithms/data quality stay fixed), whereas the historical frontier improved all three simultaneously, which affects the paper's headline conclusion; whether pretraining compute gains suffice to support the new power-law conclusion remains disputed.

Why it matters

This exchange bears directly on whether extrapolations of "when AI task durations reach human-workday scale" are credible: if the power-law exponent really is 0.454 and compute growth slows, compute scaling alone cannot sustain the current pace of time-horizon extension—implying either that algorithmic progress is being underestimated, or that future scaling will slow markedly.

2026-11-09 ~ 2026-11-09 · 10 related posts

• [source] Halperin derives time horizon = RL compute^(γ/3), so RL scaling may still be power law — BasilHalperin · 2026-11-09
• Toby Ord: RL scaling likely power law in capabilities, citing horizon-compute paper — tobyordoxford · 2026-11-09
• Toby Ord: Chinchilla-optimal adjustment makes the compute-horizon power law fit even better — tobyordoxford · 2026-11-09
• [source] Toby Ord digs out key exponent: ~100x compute buys only 10x longer AI task horizons — tobyordoxford · 2026-11-09
• Buried footnote reveals exponent 0.454: ~100x compute buys only 10x longer AI task horizons — tobyordoxford · 2026-11-09
• Toby Ord: METR's 4-month doubling implies training compute must 4x every 4 months — tobyordoxford · 2026-11-09
• Toby Ord: pretraining compute growth can't explain METR task-length doubling gains — tobyordoxford · 2026-11-09
• Toby Ord: frontier pre-training compute gains can't explain new power-law claims — tobyordoxford · 2026-11-09
• [source] RL compute scaling: 10x more RL compute may double task horizons, exponent ~0.3 — tobyordoxford · 2026-11-09
• RL scaling exponent ~0.3 is twice what the rule-of-thumb predicts — tobyordoxford · 2026-11-09