Estimating Local Learning Coefficients to Probe Loss Landscape Robustness

The project studies the robustness of the loss landscape by estimating the LLC, a basic approach in singular learning theory. The project is well executed. It would have been interesting to see more investigations of trends, e.g. plotting the LLC and loss delta vs. training step, and to report measures of uncertainty. The report is missing the abstract, but is otherwise clear.

Innovation & Originality: The project aims to investigate how LLC estimates correlate with loss landscape robustness. This is a great first step and sensible thing to do to build familiarity with tooling around LLC estimation. With that being said, the project neither uses existing methods in novel settings, nor do they design new methods.

Technical Rigor & Feasibility: The authors estimate loss landscape robustness by adding a single noise tensor to each checkpoint and measuring the resulting change in validation loss. I understand this to be deriving an estimate from a sample size of one. Apriori, one should expect this to be a fairly high variance estimate, which is in accordance with the results reported in figure 1 . An alternative approach could have been to uniformly sample an epsilon ball around each checkpoint and report the average change in validation loss. I expect this to have shown a tighter fit.

Although I'm not an expert in this area, I understand LLC to estimation to include a fair amount of hyperparameter tuning. I don't have a sense of whether their chosen set is reasonable, but I assume they did not run any sort of sweeps to calibrate their hyperparameters. If the authors would like to learn more about this technique, I would encourage them to read up on the relevant literature (such as Appendix F of https://arxiv.org/abs/2501.17745) and engage in the DevInterp Discord.

AI Safety Relevance: I expect loss landscape analysis to be an important piece of the puzzle of building out a firm foundation for AI Safety science.

One way to look at the addition of pure Gaussian noise is as an infinite-temperature limit of the local learning coefficient (in which case the gradient term vanishes, and the equilibrium distribution is just samples drawn from a Gaussian shell centered at the original weights). I think this is a very interesting limit to study. In the cases where it is predictive of the LLC, we don't have to do the expensive SGMCMC thing, we can just add random noise! But as you also see, they're not generally perfectly correlated.

I'd be interested in seeing a deeper investigation into how these estimates vary with temperature, and with the radius of the Gaussian shell. Understanding the role of these hyperparameters is absolutely key if we want to develop interpretability methodologies on top of them, and we still know relatively little.