Paper:
While deep neural networks have shown outstanding results in a wide range of applications, learning from a very limited number of examples is still a challenging task. Despite the difficulties of the few-shot learning, metric-learning techniques showed the potential of the neural networks for this task. While these methods perform well, they don't provide satisfactory results. In this work, the idea of metric-learning is extended with Support Vector Machines (SVM) working mechanism, which is well known for generalization capabilities on a small dataset. Furthermore, this paper presents an end-to-end learning framework for training adaptive kernel SVMs, which eliminates the problem of choosing a correct kernel and good features for SVMs. Next, the one-shot learning problem is redefined for audio signals. Then the model was tested on vision task (using Omniglot dataset) and speech task (using TIMIT dataset) as well. Actually, the algorithm using Omniglot dataset improved accuracy from 98.1% to 98.5% on the one-shot classification task and from 98.9% to 99.3% on the few-shot classification task.

Review:
Make SVM great again with Siamese kernel for few-shot learning 
** PAPER SUMMARY **
The author proposes to combine siamase networks with an SVM for pair classification. The proposed approach is evaluated on few shot learning tasks, on omniglot and timit.  
** REVIEW SUMMARY **
The paper is readable but it could be more fluent. It lacks a few references and important technical aspects are not discussed. It contains a few errors. Empirical contribution seems inflated on omniglot as the authors omit other papers reporting better results. Overall, the contribution is modest at best.
** DETAILED REVIEW **
On mistakes, it is wrong to say that an SVM is a parameterless classifier. It is wrong to cite (Boser et al 92) for the soft-margin SVM. I think slack variables come from (Cortes et al 95). "consistent" has a specific definition in machine learning https://en.wikipedia.org/wiki/Consistent_estimator , you must use a different word in 3.2. You mention that a non linear SVM need a similarity measure, it actually need a positive definite kernel which has a specific definition, https://en.wikipedia.org/wiki/Positive-definite_kernel .
On incompleteness, it is not obvious how the classifier is used at test time. Could you explain how classes are predicted given a test problem? The setup of the experiments on TIMIT is extremely unclear. What are the class you are interested in? How many classes and examples does the testing problems have? 
On clarity, I do not understand why you talk again about non-linear SVM in the last paragraph of 3.2. since you mention at the end of page 4 that you will only rely on linear SVMs for computational reasons. You need to mention explicitely somewhere that (w,\theta) are optimized jointly. The sentence "this paper investigates only the one versus rest approach" is confusing, as you have only two classes from the SVM perspective i.e. pairs (x1,x2) where both examples come from the same class and pairs (x1,x2) where they come from different class. So you use a binary SVM, not one versus rest. You need to find a better justification for using L2-SVM than "L2-SVM loss variant is considered to be the best by the author of the paper", did you try classical SVM and found them performing worse? Also could you motivate your choice for L1 norm as opposed to L2 in Eq 3?
On empirical evaluation, I already mentioned that it impossible to understand what the classification problem on TIMIT is. I suspect it might be speaker identification. So I will focus on the omniglot experiments. 
Few-Shot Learning Through an Information Retrieval Lens, Eleni Triantafillou, Richard Zemel, Raquel Urtasun, NIPS 2017 [arxiv July'17]
and the reference therein give a few more recent baselines than your table. Some of the results are better than your approach. I am not sure why you do not evaluate on mini-imagenet as well as most work on few shot learning generally do. This dataset offers a clearer experimental setup than your TIMIT setting and has abundant published baseline results. Also, most work typically use omniglot as a proof of concept and consider mini-imagenet as a more challenging set.