Input Similarity from the Neural Network Perspective

TL;DR

This paper introduces a neural network-based similarity measure for input examples, enabling better understanding of data density, denoising effects, and improved training efficiency without relying on true labels.

Contribution

It defines and analyzes a neural network perspective of input similarity, and demonstrates its applications in data analysis and training acceleration.

Findings

Neural networks can almost perfectly denoise noisy labels through similarity-based averaging.

The proposed similarity measure quantifies how inputs influence each other in the network's parameter space.

Enforcing similarity during training can speed up learning for certain datasets.

Abstract

We first exhibit a multimodal image registration task, for which a neural network trained on a dataset with noisy labels reaches almost perfect accuracy, far beyond noise variance. This surprising auto-denoising phenomenon can be explained as a noise averaging effect over the labels of similar input examples. This effect theoretically grows with the number of similar examples; the question is then to define and estimate the similarity of examples. We express a proper definition of similarity, from the neural network perspective, i.e. we quantify how undissociable two inputs $A$ and $B$ are, taking a machine learning viewpoint: how much a parameter variation designed to change the output for $A$ would impact the output for $B$ as well? We study the mathematical properties of this similarity measure, and show how to use it on a trained network to estimate sample density, in low complexity, enabling new types of statistical analysis for neural networks. We analyze data by retrieving samples perceived as similar by the network, and are able to quantify the denoising effect without requiring true labels. We also propose, during training, to enforce that examples known to be similar should also be seen as similar by the network, and notice speed-up training effects for certain datasets.