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

TL;DR

This paper introduces a neural network-based method for input similarity evaluation that reduces representation size and computation time by using orthogonal weight initialization and modified normalization, with minimal information loss.

Contribution

It proposes a novel neural representation technique leveraging random projection principles, orthogonal weights, and modified normalization to improve similarity tasks.

Findings

Achieves competitive similarity results on MNIST and physical datasets.

Reduces vector size and computation time compared to gradient-based methods.

Provides a lower bound estimate for hidden layer size using orthogonal matrices.

Abstract

In this paper, we propose a novel approach for implicit data representation to evaluate similarity of input data using a trained neural network. In contrast to the previous approach, which uses gradients for representation, we utilize only the outputs from the last hidden layer of a neural network and do not use a backward step. The proposed technique explicitly takes into account the initial task and significantly reduces the size of the vector representation, as well as the computation time. The key point is minimization of information loss between layers. Generally, a neural network discards information that is not related to the problem, which makes the last hidden layer representation useless for input similarity task. In this work, we consider two main causes of information loss: correlation between neurons and insufficient size of the last hidden layer. To reduce the correlation between neurons we use orthogonal weight initialization for each layer and modify the loss function to ensure orthogonality of the weights during training. Moreover, we show that activation functions can potentially increase correlation. To solve this problem, we apply modified Batch-Normalization with Dropout. Using orthogonal weight matrices allow us to consider such neural networks as an application of the Random Projection method and get a lower bound estimate for the size of the last hidden layer. We perform experiments on MNIST and physical examination datasets. In both experiments, initially, we split a set of labels into two disjoint subsets to train a neural network for binary classification problem, and then use this model to measure similarity between input data and define hidden classes. Our experimental results show that the proposed approach achieves competitive results on the input similarity task while reducing both computation time and the size of the input representation.