Forecasting AI Time Horizon Under Compute Slowdowns

METR's time horizon metric has grown exponentially since 2019, along with compute. However, it is unclear whether compute scaling will persist at current rates through 2030, raising the question of how possible compute slowdowns might impact AI agent capability forecasts. Given a model of time horizon as a function of training compute and algorithms, along with a model of how compute investment spills into algorithmic progress (which, notably, precludes the possibility of a software-only singularity), and the empirical fact that both time horizon and compute have grown at constant rates over 2019--2025, we derive that time horizon growth must be proportional to compute growth. We provide additional, albeit limited, experimental evidence consistent with this theory. We use our model to project time horizon growth under OpenAI's compute projection, finding substantial projected delays in some cases. For example, 1-month time horizons at 80% reliability occur 7 years later than simple trend extrapolation suggests.