So there's some arguing over terminology, and then the main technical point seems to be that you can reverse-engineer a training dataset from the "virtual machine" built by training a neural network. The decompilation process doesn't just use the neural network though, if I understand correctly it also uses logs from the final training epoch that include error and weight update data. Does this somehow smuggle the tra…
Beyond the global output and error of each sample from the last epoch, the log also includes the weight update of one single (fully connected) node for each layer. During the compilation phase, the training dataset is projected on a complex vector space that is constituted by both the "model" of the "neural network" and these logs. It's just like projecting a shadow over a bidimensional surface: if you discard the da…
Basically the argument starts with a claim (you can reconstruct the training set of model X from its weights alone) and then shows something totally different. Of course you can reconstruct from the gradient updates plus the weights—that's not interesting, nor does it support the claim.