Paper:
We propose a novel unsupervised representation learning framework called neighbor-encoder in which domain knowledge can be trivially incorporated into the learning process without modifying the general encoder-decoder architecture. In contrast to autoencoder, which reconstructs the input data, neighbor-encoder reconstructs the input data's neighbors. The proposed neighbor-encoder can be considered as a generalization of autoencoder as the input data can be treated as the nearest neighbor of itself with zero distance. By reformulating the representation learning problem as a neighbor reconstruction problem, domain knowledge can be easily incorporated with appropriate definition of similarity or distance between objects. As such, any existing similarity search algorithms can be easily integrated into our framework. Applications of other algorithms (e.g., association rule mining) in our framework is also possible since the concept of "neighbor" is an abstraction which can be appropriately defined differently in different contexts. We have demonstrated the effectiveness of our framework in various domains, including images, time series, music, etc., with various neighbor definitions. Experimental results show that neighbor-encoder outperforms autoencoder in most scenarios we considered.

Review:
This paper presents a variant of auto-encoder that relaxes the decoder targets to be neighbors of a data point. Different from original auto-encoder, where data point x and the decoder output \hat{x} are forced to be close, the neighbor-encoder encourage the decoder output to be similar to the neighbors of the input data point. By considering the neighbor information, the decoder targets would have smaller intra-class distances, thus larger inter-class distances, which helps to learn better separated latent representation of data in terms of data clusters. The authors conduct experiments on several real but relative small-scale data sets, and demonstrate the improvements of learned latent representations by using neighbors as targets. 
The method of neighbor prediction is a simple and small modification of the original auto-encoder, but seems to provide a way to augment the targets such that intra-class distance of decoder targets can be tightened. Improvements in the conducted experiments seem significant compared to the most basic auto-encoder.
Major issues:
There are some unaddressed theoretical questions. The optimal solution to predict the set of neighbor points in mean-squared metric is to predict the average of those points, which is not well justified as the averaged image can easily fall off the data manifold. This may lead to a more blurry reconstruction when k increases, despite the intra-class targets are tight. It can also in turn harm the latent representation when euclidean neighbors are not actually similar (e.g. images in cifar10/imagenet that are not as simple as 10 digits). This seems to be a defect of the neighbor-encoder method and is not discussed in the paper.
The data sets used in the experiments  are relatively small and simple, larger-scale experiments should be conducted. The fluctuations in Figure 9 and 10 suggest the significant variances in the results. Also, more complicated data/images can decrease the actual similarities of euclidean neighbors, thus affecting the results.
The baselines are weak. Only the most basic auto-encoder is compared, no additional variants or other data augmentation techniques are compared. It is possible other variants improve the basic auto-encoder in similar ways. 
Some results are not very well explained. It seems the performance increases monotonically as the number of neighbors increases (Figure 5, 9, 10). Will this continue or when will the performance decrease? I would expect it to decrease as the far away neighbors will be dissimilar. The authors can either attach the nearest neighbors figures or their statistics, and provide explanations on when and why the performance decrease is expected.
Some notations are confusing and need to be improved. For example, X and Y are actually the same set of images, the separation is a bit confusing; y_i \in y in last paragraph of page 4 is incorrect, should use something like y_i in N(y).