Something I’m wondering, but don’t have the expertise in meta-learning to say confidently (so, epistemic status: speculation, and I’m curious for critiques): extra OOMs of compute could overcome (at least) one big bottleneck in meta-learning, the expense of computing second-order gradients. My understanding is that most methods just ignore these terms or use crude approximations, like this, because they’re so expensive. But at least this paper found some pretty impressive performance gains from using the second-order terms.
Maybe throwing lots of compute at this aspect of meta-learning would help it cross a threshold of viability, like what happened for deep learning in general around 2012. I think meta-learning is a case where we should expect second-order info to be very relevant to optimizing the loss function in question, not just a way of incorporating the loss function’s curvature. In the first paper I linked, the second-order term accounts for how the base learner’s gradients depend on the meta-learner’s parameters. This seems like an important feature of what their meta-learner is trying/supposed to do, i.e., use the meta-learned update rule to guide the base learner—and the performance gains in the second paper are evidence of this. (Not all meta-learners have this structure, though, and MAML apparently doesn’t get much better when you use Hessians. Hence my lack of confidence in this story.)
Something I’m wondering, but don’t have the expertise in meta-learning to say confidently (so, epistemic status: speculation, and I’m curious for critiques): extra OOMs of compute could overcome (at least) one big bottleneck in meta-learning, the expense of computing second-order gradients. My understanding is that most methods just ignore these terms or use crude approximations, like this, because they’re so expensive. But at least this paper found some pretty impressive performance gains from using the second-order terms.
Maybe throwing lots of compute at this aspect of meta-learning would help it cross a threshold of viability, like what happened for deep learning in general around 2012. I think meta-learning is a case where we should expect second-order info to be very relevant to optimizing the loss function in question, not just a way of incorporating the loss function’s curvature. In the first paper I linked, the second-order term accounts for how the base learner’s gradients depend on the meta-learner’s parameters. This seems like an important feature of what their meta-learner is trying/supposed to do, i.e., use the meta-learned update rule to guide the base learner—and the performance gains in the second paper are evidence of this. (Not all meta-learners have this structure, though, and MAML apparently doesn’t get much better when you use Hessians. Hence my lack of confidence in this story.)