The code in your notebook does its hyperbolic fitting by (nonlinear) least squares on the original data, but its exponential fitting by (linear) least squares on the log of the original data.
This means (1) that your exponential fit will look worse “on the right” where the numbers are larger than an actual least-squares fit of an exponential, and (2) it will have worse mean squared error (on the original data) than an actual least-squares fit of an exponential.
When I do an exponential fit using the same machinery as you used for your hyperbolic fit, I get this graph
and a “total error” of 0.107 versus 0.141 for the q=2 hyperbolic fit.
[EDITED to add:] The specific exponential I get, in case anyone wants to check, is horizon = exp b (t-t0) where b = 1.8421 and t0 is 2025-02-27.
[EDITED to add:] I’ve strong-downvoted the post, not because I think there’s anything very terrible about making the mistake I believe you made, but because at first glance it looks like evidence for something important and I think it isn’t in fact evidence for that important thing and I don’t want people to be misled.
Thanks for checking, confirming, and editing accordingly. I reiterate that despite my criticisms of the content, this is what epistemic virtue looks like: write things in such a way that others can check them, and correct appropriately if they turn out to have been wrong.
(Strong-downvote undone since with the corrections at the top the OP is no longer likely to mislead anyone much.)
The code in your notebook does its hyperbolic fitting by (nonlinear) least squares on the original data, but its exponential fitting by (linear) least squares on the log of the original data.
This means (1) that your exponential fit will look worse “on the right” where the numbers are larger than an actual least-squares fit of an exponential, and (2) it will have worse mean squared error (on the original data) than an actual least-squares fit of an exponential.
When I do an exponential fit using the same machinery as you used for your hyperbolic fit, I get this graph
and a “total error” of 0.107 versus 0.141 for the q=2 hyperbolic fit.
[EDITED to add:] The specific exponential I get, in case anyone wants to check, is horizon = exp b (t-t0) where b = 1.8421 and t0 is 2025-02-27.
[EDITED to add:] I’ve strong-downvoted the post, not because I think there’s anything very terrible about making the mistake I believe you made, but because at first glance it looks like evidence for something important and I think it isn’t in fact evidence for that important thing and I don’t want people to be misled.
[EDITED again to add:] Full post at https://www.lesswrong.com/posts/ZEuDH2W3XdRaTwpjD/hyperbolic-model-fits-metr-capabilities-estimate-worse-than
Thank you very much for catching the mistake! I checked, you are completely right.
Thanks for checking, confirming, and editing accordingly. I reiterate that despite my criticisms of the content, this is what epistemic virtue looks like: write things in such a way that others can check them, and correct appropriately if they turn out to have been wrong.
(Strong-downvote undone since with the corrections at the top the OP is no longer likely to mislead anyone much.)