We describe how to go about fitting a BNSL to yield best extrapolation in the last paragraph of Appendix Section A.6 "Experimental details of fitting BNSL and determining the number of breaks" of the paper:
https://arxiv.org/pdf/2210.14891.pdf#page=13
Sigmoids don't accurately extrapolate the scaling behavior(s) of the performance of artificial neural networks.
Use a Broken Neural Scaling Law (BNSL) in order to obtain accurate extrapolations:
https://arxiv.org/abs/2210.14891
https://arxiv.org/pdf/2210.14891.pdf
The setting was adversarial training and adversarial evaluation. During training, PGD attacker of 30 iterations is used to construct adversarial examples used for training. During testing, the evaluation test set is an adversarial test set that is constructed via PGD attacker of 20 iterations.
Experimental data of y-axis is obtained from Table 7 of https://arxiv.org/abs/1906.03787; experimental data of x-axis is obtained from Figure 7 of https://arxiv.org/abs/1906.03787.
"However, to the best of our knowledge there are no quantitative scaling laws for robustness yet."
For scaling laws for adversarial robustness, see appendix A.15 of openreview.net/pdf?id=sckjveqlCZ#page=22
One other goal / theme of mechanistic interpretability research imo:
twitter.com/norabelrose/status/1588571609128108033
Sections 3.1 and 6.6 titled "Ossification" of "Scaling Laws for Transfer" paper (https://arxiv.org/abs/2102.01293) show that current training of current DNNs exhibits high path dependence.
Read Section 6 titled “The Limit of the Predictability of Scaling Behavior” in this paper:
https://arxiv.org/abs/2210.14891