ADAPTIVE POSTERIOR LEARNING: FEW-SHOT LEARNING WITH A SURPRISE-BASED MEMORY MODULE
The ability to generalize quickly from few observations is crucial for intelligent systems. In this paper we introduce APL, an algorithm that approximates probability distributions by remembering the most surprising observations it has encountered. These past observations are recalled from an external memory module and processed by a decoder network that can combine information from different memory slots to generalize beyond direct recall. We show this algorithm can perform as well as state of the art baselines on few-shot classification benchmarks with a smaller memory footprint. In addition, its memory compression allows it to scale to thousands of unknown labels. Finally, we introduce a meta-learning reasoning task which is more challenging than direct classification. In this setting, APL is able to generalize with fewer than one example per class via deductive reasoning.
Summary: the authors propose a new algorithm, APL, for a few-shot and a life-long learning based on an external memory module. APL uses a surprise-based signal to determine which data points to store in memory and an attention mechanism to the most relevant points for prediction. The authors evaluate APL on a few-shot classification task on Omniglot dataset and on a number analogy task.
Quality: the authors consider interesting approach to life-long learning and I really liked the idea of a surprise-based signal to choose the data to store. However, I am not convinced by the learning setting that authors study. While a digit-symbol task from the introduction is interesting to study the properties of APL, I fail to see any real world analogy where it is useful. The same happens in a few-shot omniglot classification. The authors decided to shuffle the labels within episodes that, I guess, is supposed to represent different tasks in a typical life-long learning scenario. Again, it maybe interesting to study the behaviour of the algorithm, but I don't see any practical relevance here. It would make more sense to study the algorithm in a life-long learning setting, for example, considered in [1] and [2].
Clarity: the paper is well-written in general. I failed to decode the meaning behind the paragraph under Figure 3 on page 4 and would advise the authors to re-write it. The same goes to the first paragraph on page 3.
Originality: the paper builds on the prior work of Kaiser et al., 2017 and Santoro et al., 2016, but the proposed modifications are novel to my best knowledge.
Significance: below average: the paper combines interesting ideas that potentially can be used in different learning contexts and with other algorithms, however, the evaluation does not show the benefit in an obvious way.
Other comments: 
* throughout the whole paper it is not clear if the embeddings are learned or not. I suppose they are, but what then happens to the ones in memory? If they are not, like in ImageNet example, where do they come from?
* the hyperparameter \sigma: the authors claim "the value of \sigma seems to not matter too much". Matter for what? It's great if the performance is stable for a wide range of \sigma, but it seems like it should have a great influence over the memory footprint of APL. I feel this is an important point that needs more attention.
* it would be interesting to see how APL performs with a simple majority vote instead the decoder layer. This would count for an ablation study and could emphasize the role of the decoder.
* Figure 4, b) plots are completely unreadable on black-and-white print, the authors might like to address that
* In conclusion, the first claim about state-of-the-art accuracy with smaller memory footprint: I don't think that the results of the paper justify this claim.
[1] Yoon et al, Lifelong Learning with Dynamically Expandable Networks, ICLR 2017
[2] Rebuffi et al,  iCaRL: Incremental Classifier and Representation Learning, CVPR 2017
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After authors response:
Thanks to the authors for a detailed response. The introduction led me to believe that the paper solves a different task from what it actually does. I still like the algorithm and, given that the scope of the paper is limited to a few-shot learning, I tend to change my evaluation and recommend to accept the paper. It was a good idea to change the title to avoid possible confusion by other readers. The introduction is still misleading though. It creates the impression that APL solves a more general problem where it would be good enough to limit the discussion to a few-shot learning setting and explain it in greater detail for an unfamiliar reader. Some details also seem to be missing, e.g. I didn't get that the memory is flushed after each episode and could not find where this is mentioned in the paper.