Paper:
Meta-learning is an exciting and powerful paradigm that aims to improve the effectiveness of current learning systems. By formulating the learning process as an optimization problem, a model can learn how to learn while requiring significantly less data or experience than traditional approaches. Gradient-based meta-learning methods aims to do just that, however recent work have shown that the effectiveness of these approaches are primarily due to feature reuse and very little has to do with priming the system for rapid learning (learning to make effective weight updates on unseen data distributions). This work introduces Nodal Optimization for Recurrent Meta-Learning (NORML), a novel meta-learning framework where an LSTM-based meta-learner performs neuron-wise optimization on a learner for efficient task learning. Crucially, the number of meta-learner parameters needed in NORML, increases linearly relative to the number of learner parameters. Allowing NORML to potentially scale to learner networks with very large numbers of parameters. While NORML also benefits from feature reuse it is shown experimentally that the meta-learner LSTM learns to make effective weight updates using information from previous data-points and update steps.

Review:
This paper proposes a meta-learner that learns how to make parameter updates for a model on a new few-shot learning task. The proposed meta-learner is an LSTM that proposes at each time-step, a point-wise multiplier for the gradient of the hidden units and for the hidden units of the learner neural network, which are then used to compute a gradient update for the hidden-layer weights of the learner network. By not directly producing a learning rate for the gradient, the meta-learner’s parameters are only proportional to the square of the number of hidden units in the network rather than the square of the number of weights of the network. Experiments are performed on few-shot learning benchmarks. The first experiment is on Mini-ImageNet. The authors build upon the method of Sun et al, where they pre-train the network on the meta-training data and then do meta-training where the convolutional network weights are frozen and only the fully-connected layer is updated on few-shot learning tasks using their meta-learner LSTM. The other experiment is on Omniglot 20-way classification, where they consider a network with only full-connected layers and show that their meta-learner LSTM performs better than MAML.
The closest previous work to this paper is by Ravi & Larochelle, who also propose a meta-learner LSTM. The submission states about this work that “A challenge of this approach is that if you want to optimize tens of thousands of parameters, you would have a massive hidden state and input size, and will therefore require an enormous number of parameters for the meta-learner…In Andrychowicz at al. an alternative approach is introduced that avoids the aforementioned scaling problem by individually optimizing each parameter using a separate LSTM…” I don’t believe this is true.
As stated in the work by Ravi & Larochelle, “Because we want our meta-learner to produce updates for deep neural networks, which consist of tens of thousands of parameters, to prevent an explosion of meta-learner parameters we need to employ some sort of parameter sharing. Thus as in Andrychowicz et al. (2016), we share parameters across the coordinates of the learner gradient. This means each coordinate has its own hidden and cell state values but the LSTM parameters are the same across all coordinates.” Thus, Ravi & Larochelle employ something similar to Andrychowicz at al., meaning that the number of parameters in the LSTM meta-learner there is actually a constant relative to the size of the learner network. 
Thus, the paper’s contribution relative to Ravi & Larochelle is to propose a LSTM meta-learner with more parameters relative to the learner model. Firstly, I think this comparison should be stated and explained clearly in the paper. Additionally, in order to prove the benefit of such an approach, I think a comparison to the work of Ravi & Larochelle with the exact experimental settings used in the submission (pre-training the convolutional network and only using the meta-learner LSTM to tune the last fully-connected layer) would be helpful in order to validate the usefulness of the extra set of parameters in their proposed meta-learner LSTM.
The submission also states that “In many cases it is preferred to have an inner loop that consists of multiple sequential updates. However the inner loop’s computational graph can become quite large if too many steps are taken. This often results in exploding and vanishing gradients since the outer loop still needs to differentiate through the entire inner loop (Aravind Rajeswaran (2019), Antoniou et al. (2018)). This limits MAML to domains where a small amount of update steps are sufficient for learning. The LSTM-based meta-learner proposed in this work, allow gradients to effectively flow through a large number of update steps. NORML can therefore be applied to a wide array of domains.” I think this statement should be validated if it is stated. Can it be shown that when making a lot of inner-loop updates, the LSTM meta-learner performs better than MAML because of overcoming the stated issues with differentiation through a long inner loop? The experiments done in the paper involve very few inner loop steps and so I don’t believe the claim is supported.
Lastly, the experimental results are not very convincing. Though the authors say they modify the method proposed in Sun et al, the results from Sun et al. are not shown in the paper. Sun et al actually seem to achieve better results than the submission with the same 1-shot and better 5-shot accuracy. Was there a reason these results are not shown in the submission? Additionally, for the Omniglot experiment, is there any reason why it was not performed with the typical convolutional network architecture? Since the original MAML results on 20-way Omniglot are with a convolutional network, using the convolutional network would make the results more meaningful relative to previous work and show that the method is more broadly applicable to convolutional networks.
I believe there are several issues with the paper as stated above. Because of these issues, it is hard to evaluate whether the idea proposed is of significant benefit.
References
Andrychowicz et al. Learning to learn by gradient descent by gradient descent. NIPS 2016.
Ravi & Larochelle. Optimization as a Model for Few-Shot Learning. ICLR 2017.
Sun et al. Meta-transfer learning for few-shot learning.