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In this paper, we propose a novel approach for implicit data representationto evaluate similarity of input data using a trained neural network. Incontrast to the previous approach, which uses gradients for representation, weutilize only the outputs from the last hidden layer of a neural network and donot use a backward step. The proposed technique explicitly takes into accountthe initial task and significantly reduces the size of the vectorrepresentation, as well as the computation time. The key point is minimizationof information loss between layers. Generally, a neural network discardsinformation that is not related to the problem, which makes the last hiddenlayer representation useless for input similarity task. In this work, weconsider two main causes of information loss: correlation between neurons andinsufficient size of the last hidden layer. To reduce the correlation betweenneurons we use orthogonal weight initialization for each layer and modify theloss function to ensure orthogonality of the weights during training. Moreover,we show that activation functions can potentially increase correlation. Tosolve this problem, we apply modified Batch-Normalization with Dropout. Usingorthogonal weight matrices allow us to consider such neural networks as anapplication of the Random Projection method and get a lower bound estimate forthe size of the last hidden layer. We perform experiments on MNIST and physicalexamination datasets. In both experiments, initially, we split a set of labelsinto two disjoint subsets to train a neural network for binary classificationproblem, and then use this model to measure similarity between input data anddefine hidden classes. Our experimental results show that the proposed approachachieves competitive results on the input similarity task while reducing bothcomputation time and the size of the input representation.

Neural Random Projection: From the Initial Task To the Input Similarity Problem