Paper:
Meta-learning for few-shot learning involves a meta-learner that acquires shared knowledge from a set of prior tasks to improve the performance of a base-learner on new tasks with a small amount of data. Kernels are commonly used in machine learning due to their strong nonlinear learning capacity, which have not yet been fully investigated in the meta-learning scenario for few-shot learning. In this work, we explore kernel approximation with random Fourier features in the meta-learning framework for few-shot learning. We propose learning adapative kernels by meta variational random features (MetaVRF), which is formulated as a variational inference problem. To explore shared knowledge across diverse tasks, our MetaVRF deploys an LSTM inference network to generate informative features, which can establish kernels of highly representational power with low spectral sampling rates, while also being able to quickly adapt to specific tasks for improved performance. We evaluate MetaVRF on a variety of few-shot learning tasks for both regression and classification. Experimental results demonstrate that our MetaVRF can deliver much better or competitive performance than recent meta-learning algorithms.

Review:
This paper proposes a meta-learning framework for learning adaptive kernels using a meta-learner. For representing kernels, the paper learns a variational posterior for the kernel features, by maximizing the Evidence lower Bound. Furthermore, to plug the kernel learning into the meta-learning framework, they let the variational feature posterior to condition on the current support set for adapting and to use a modified LSTM network for accumulating information. Empirically, they compare the proposed MetaVRF with multiple baselines in the standard fewshot classification benchmarks and demonstrate superior performance. They also illustrate that their adaptively-learnt Fourier feature outperforms the standard variational Fourier features.
Strengths, 
1, The idea of learning kernels in meta-learning is interesting. In fact, learning a kernel is equivalent to learning a distance between objects. If a reasonable distance between objects can be learnt, using the corresponding kernel should be able to achieve superior performance even if the kernel doesn't adapt in each episode. 
2, The proposed method achieves competitive performances. In particular, Figure 5 shows how the performance changes when the test-shot and test-way are varied. It seems surprising that the MetaVRF achieves >90% accuracy for 100-way test when trained on only 5-way 5-shot.
Weakness,
1, The notations in the paper are not well presented. (a) In eq(2), the formula $alpha^t=\Lambda(\Phi^t(x), y)$ is not exact, cuz $\alpha^t$ should depend on the whole support set $S^t$ while $(x,y)$ is only one instance in $S^t$.  (b) In eq(11), the variational posterior $q(w | S^t, w^{1:t-1})$ is not exact either. Because $w^{1:t-1}$ are random variables, they cannot be observed and cannot be conditioned on. Similar issues also exist in the caption of Figure 1.
2, The paper doesn't introduce what is the likelihood $log p(y| x, S, w)$. It is unclear how the kernel regression is adopted in classification. 
3, The meta-prior $p(w| x, S)$ depends on the feature of the query point, which doesn't seem to be a common practice in variational inference. It would be beneficial if the authors could explain this and probably validate it empirically.
4, The motivations of the modified LSTM should be clarified more. Does the paper remove h_t in LSTM for removing short-term memory ? Why $\hat{c}_t$ only depends on $e^t$ instead of $[e^t, c^{t-1}]$ ? 
5, The paper compares with multiple competitive baselines. However, the settings for the baselines should be better presented. For example, it is strange that the numbers of SNAIL are different with the numbers in their paper. And SNAIL on Omniglot is not reported. Furthermore, another competitive method TADAM (Oreshkin et. al., 2019) should also be compared with.