Forethought Paper Defines Compute Extrapolation as Test-Time Scaling Beyond Training Limits

Details

Test-time scaling is divided into two types: standard scaling bounded by the maximum per-task compute used in training, and compute extrapolation, which allows performance gains at test-time compute levels exceeding that training maximum.
Compute extrapolation is defined as continued performance improvement when test-time compute reaches 10x or 1000x the 99th percentile of per-task training compute, with key metrics being the ceiling (maximum effective multiplier) and slope (rate of improvement beyond the training limit).
Evidence from open-weight models like Delethink shows performance continuing to rise past 4x the maximum training compute (24k tokens) up to 128k tokens, while closed models like Anthropic's Opus 4.6 and OpenAI's GPT-5.1-Codex-Max show signs of extrapolation through improved efficiency and context management.
The phenomenon shifts competitive spending from training to test-time compute, potentially making dangerous capability evaluations prohibitively expensive as arbitrary test-time compute may be required for verification.
Multi-agent scaling is proposed as a method to extend the ceiling and slope of compute extrapolation, as hierarchical agent structures may generalize better than single-agent chain-of-thought in time-constrained scenarios.

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