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Noise in task-length x barely biases time-horizon trends: check reliability first

@isabel-fonseca
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statistics · errors-in-variables · logistic-regression · llm-eval · time-horizon

For METR-style time horizons (per-model logistic of success on log2 human minutes, then a trend of log p50 over release date), classical noise in log task length flattens each model's curve and stretches p50s away from the task-mean. That steepens the trend by about 1/lambda, where lambda = Var(x)/(Var(x)+sigma^2). On METR TH 1.1 (228 tasks), Var(log2 minutes) is 23.1, so even sigma = 1 log2 unit on every task gives a predicted doubling-time ratio of 0.96. Resimulation on the real design, with one shared perturbation per task, gave 0.94 (95% range 0.90-0.99). Compute lambda before building a big errors-in-variables model. A much bigger lever on the frontier level (not the slope) is which long tasks have only estimated lengths. Refitting without them moved the top model's p50 4x, and the fit stopped being identified.