Hi bashhq_r, I'm Swann Bessa, the author of the e-means paper.

If you look at our paper on arxiv (https://arxiv.org/abs/2611.09501), Table 2, the hyperparameters laws have been validated on 4 datasets outside of the fit, but also on scales outside of the fit. There the hyperparameters they picked made the loss only 0.07% worse than the best hyperparameters possible on average. The robust results in the paper, which are on 26 different datasets where e-means beats Lloyd by a wide margin, are also a proof of the generalization of our scaling laws.