the g is considered as a matrix with i-j entries as [ e_i(p) . e_j(p)], the standard inner product of i-th and j-th local basis, with non-negative determinant, whose inverse is mentioned here.

The the term "scaling" refers to the scaling of the theorem itself, not to solving the problem of z_i=0. Scaling of the theorem is referred to how the performance or behavior of the theorem changes as certain parameters vary. The issue of z_i=0 arises because it implies that the labeling function associated with z_i​ has an accuracy of 0.5, meaning it's essentially guessing randomly. This situation can be problematic because it doesn't provide any useful information for training the model. However, the scaling of the theorem, in this context, doesn't directly solve the problem of z_i=0. Instead, it helps in understanding how the theorem's performance changes as the parameters, such as z_i, vary. By understanding this scaling behavior, we can assess the impact of such cases where z_i=0 on the overall performance of the weakly supervised learning approach, and potentially devise strategies to mitigate its effects. The effective rank provides insight into the complexity of the sample data. It indicates how much information is contained in the covariance matrix relative to its size. A higher effective rank suggests that the data is less noisy and contains more meaningful information. If the effective rank is high, it implies that the data contains a significant amount of useful information relative to its size. In this case, the theorem may scale favorably, meaning that the model's performance improves as more weakly supervised data is provided. In structured learning tasks, where relationships between data points are important (e.g., in graph-based models), understanding the effective rank helps in determining the appropriate learning rates. By accounting for the complexity of the data through the effective rank, it becomes possible to optimize the learning process and achieve better performance on structured learning tasks.

Unfortunately not. The code underwent a big refactor for public release and the UI wasn't kept in sync. You can find the code though with tutorials at: github.com/HazyResearch/babble

In the same way it deals with improving and changing taxonomic opinion and classification: by the year of the "opinion" expressed in the source. The "experts" are mostly me and the contributors to the Paleobiology Database (paleobiodb.org), but this number will be growing soon....

The data can't be copyrighted, only the articles. There's probably a bigger problem with non-machine readable articles (Nature?)

Marko Bosscher Yep, but just how many articles does this include?

Jon Tennant I believe that depending on the arrangements made by PDD they may have access to all of Elsevier's catalogue except for papers published under restrictive OA license.