In my view, the Lottery Ticket Hypothesis is one of the weirder and more mysterious phenomena of the last few years of Machine Learning. We've known for awhile that we can take trained networks and prune them down to a small fraction of their weights (keeping those weights with the highest magnitudes) and maintain test performance using only those learned weights. That seemed somewhat surprising, in that there were a lot of weights that weren't actually necessary to encoding the learned function, but, the thinking went, possibly having many times more weights than that was helpful for training, even if not necessary once a model is trained. The authors of the original Lottery Ticket paper came to the surprising realization that they could take the weights that were pruned to exist in the final network, re-initialize them (and only them) to the values they had during initial training, and perform almost as well as the final pruned model that had all weights active during training. And, performance using the specific weights and their particular initialization values is much higher than training a comparable topology of weights with random initial values. 

This paper out of Facebook AI adds another fascinating experiment to the pile of off evidence around lottery tickets: they test whether lottery tickets transfer *between datasets*, and they find that they often do (at least when the dataset on which the lottery ticket is found is more complex (in terms of in size, input complexity, or number of classes) than the dataset the ticket is being transferred to. Even more interestingly, they find that for sufficiently simple datasets, the "ticket" initialization pattern learned on a more complex dataset actually does *better* than ones learned on the simple dataset itself. They also find that tickets by and large transfer between SGD and Adam, so whatever kind of inductive bias or value they provide is general across optimizers in addition to at least partially general across datasets. 

https://i.imgur.com/H0aPjRN.png

I find this result fun to think about through a few frames. The first is to remember that figuring out heuristics for initializing networks (as a function of their topology) was an important step in getting them to train at all, so while this result may at first seem strange and arcane, in that context it feels less surprising that there are still-better initialization heuristics out there, possibly with some kind of interesting theoretical justification to them, that humans simply haven't been clever enough to formalize yet, and have only discovered empirically through methods like this. 

This result is also interesting in terms of transfer: we've known for awhile that the representations learned on more complex datasets can convey general information back to smaller ones, but it's less easy to think about what information is conveyed by the topology and connectivity of a network. This paper suggests that the information is there, and has prompted me to think more about the slightly mind-bending question of how training models could lead to information compressed in this form, and how this information could be better understood.