Power Law Trends in Speedrunning and Machine Learning
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We find that improvements in speedrunning world records follow a power law pattern. Using this observation, we answer an outstanding question from previous work: How do we improve on the baseline of predicting no improvement when forecasting speedrunning world records out to some time horizon, such as one month? Using a random effects model, we improve on this baseline for relative mean square error made on predicting out-of-sample world record improvements as the comparison metric at a p < 10^-5 significance level. The same set-up improves even on the ex-post best exponential moving average forecasts at a p = 0.15 significance level while having access to substantially fewer data points. We demonstrate the effectiveness of this approach by applying it to Machine Learning benchmarks and achieving forecasts that exceed a baseline. Finally, we interpret the resulting model to suggest that 1) ML benchmarks are far from saturation and 2) sudden large improvements in Machine Learning are unlikely but cannot be ruled out.
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