# Quantification and Analysis of Layer-wise and Pixel-wise Information Discarding

## TL;DR

This paper introduces entropy-based metrics to quantify how input information is progressively discarded across layers in deep neural networks, providing new insights into their information processing and performance.

## Contribution

It proposes novel, fair metrics for layer-wise and pixel-wise information analysis, offering a new perspective beyond existing attribution methods.

## Key findings

- Metrics effectively analyze information discarding in DNNs
- Strong connection between information loss and network performance
- Applicable to various classic DNN architectures

## Abstract

This paper presents a method to explain how the information of each input variable is gradually discarded during the forward propagation in a deep neural network (DNN), which provides new perspectives to explain DNNs. We define two types of entropy-based metrics, i.e. (1) the discarding of pixel-wise information used in the forward propagation, and (2) the uncertainty of the input reconstruction, to measure input information contained by a specific layer from two perspectives. Unlike previous attribution metrics, the proposed metrics ensure the fairness of comparisons between different layers of different DNNs. We can use these metrics to analyze the efficiency of information processing in DNNs, which exhibits strong connections to the performance of DNNs. We analyze information discarding in a pixel-wise manner, which is different from the information bottleneck theory measuring feature information w.r.t. the sample distribution. Experiments have shown the effectiveness of our metrics in analyzing classic DNNs and explaining existing deep-learning techniques.