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Rethinking Softmax with Cross-Entropy

Neural Network Classifier as Mutual Information Estimator

PWC PWC

MI EstimatorPC SoftmaxInfoCAMCreditsLicence

InfoCAM-Procedure

Overview

In the paper, we show the connection between mutual information and softmax classifier through variational form of mutual information. The connection explains the rational behind softmax cross-entropy from information-theoretic perspective, which brings a new insight to understand the classifiers. We utilise the connection between classification and mutual information to improve the weakly-supervised object localisation task. To this end, we propose a new way to compute the classification activation map, which is based on the difference between PMIs.

This repository includes all the experimental implementation.

MI Estimator

In the paper, we prove that classification neural networks that optimise their weights to minimise the softmax cross-entropy are equivalent to the ones that maximise mutual information between inputs and labels with the balanced datasets. This repository includes the implementation for evaluating the effectiveness of classification mutual information estimator via synthetic datasets. We also show the balanced dataset assumption can be relaxed by modifying the traditional softmax to the Probability-Correct (PC) softmax. This repository also contains implementation for evaluating mutual information with PC-softmax on the synthetic dataset.

PC Softmax

We modify the traditional softmax to the Probability-Correct (PC) softmax. This repository contains implementation for demonstrating PC-softmax can improve a large margin than the traditional softmax for the average of the per-class classification accuracy. We experiment on two datasets: MNIST and CUB-200-2011. In terms of the accuracy value merely, we achieve a new state-of-art of the micro classification accuracy (ours: 89.73; previous: 89.6) on CUB-200-2011.

InfoCAM

We propose infoCAM: Informative Class Activation Map, which highlights regions of the input image that are the most relevant to a given label based on differences in information. The activation map helps localise the target object in an image. We in this repository show the effectiveness of the informative-theoretic approach than the traditional CAM.

InfoCAM

Credits

This repository uses the following implementations:

Licence

CC-BY-4.0

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Full implementation of the paper "Rethinking Softmax with Cross-Entropy: Neural Network Classifier as Mutual Information Estimator".

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