

“Hyperbolic model fits METR capabilities estimate worse than exponential model” by gjm
Aug 20, 2025
A fascinating critique of hyperbolic versus exponential models sheds light on technological progress. The discussion dives into the mathematical intricacies behind each approach, revealing notable differences in their effectiveness. Charts and graphs illustrate how these models performed with historical data from 2019 to 2026. The conclusion urges caution against overestimating future growth based on flawed extrapolations. Insightful remarks emphasize the importance of clear data interpretation and recognizing the pitfalls in predictive modeling.
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Models Compared For METR Data
- Valentin2026 compared hyperbolic and exponential families when fitting META's time-horizon data.
- The hyperbolic family allows a finite-time singularity controlled by parameters A, T1, and Q.
Code Availability And Suspicious Fits
- GJM recounts that Valentin provided both data and code for his fits and showed hyperbolic fits looked better.
- GJM examined the code and found suspicious differences in fitting methods between models.
Different Fit Methods Bias Comparison
- Valentin fit the exponential by least squares on log(data) while fitting the hyperbolic by nonlinear least squares on raw data.
- Fitting logs emphasizes small values and penalizes large-value errors less, biasing comparisons.