Papers › Rethinking Softmax with Cross-Entropy: Neural Network Classifier as Mutual Information...
Rethinking Softmax with Cross-Entropy: Neural Network Classifier as Mutual Information Estimator
Zhenyue Qin, Dongwoo Kim, Tom Gedeon
Mutual information is widely applied to learn latent representations of observations, whilst its implication in classification neural networks remain to be better explained. We show that optimising the parameters of classification neural networks with softmax cross-entropy is equivalent to maximising the mutual information between inputs and labels under the balanced data assumption. Through experiments on synthetic and real datasets, we show that softmax cross-entropy can estimate mutual information approximately. When applied to image classification, this relation helps approximate the point-wise mutual information between an input image and a label without modifying the network structure. To this end, 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 input image. Through experiments on the semi-supervised object localisation task with two real-world datasets, we evaluate the effectiveness of our information-theoretic approach.
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Code
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Fine-Grained Image Classification | Imbalanced CUB-200-2011 | PC-Softmax | Accuracy | 89.73 | #1 of 1 | Archive leaderboard | report |
| Fine-Grained Image Classification | Imbalanced CUB-200-2011 | PC-Softmax | Average Per-Class Accuracy | 87.69 | #1 of 1 | Archive leaderboard | report |
| Image Classification | Imbalanced CUB-200-2011 | PC-Softmax | Accuracy | 89.73 | #2 of 2 | Archive leaderboard | report |
| Image Classification | Imbalanced CUB-200-2011 | PC-Softmax | Average Per-Class Accuracy | 87.69 | #2 of 2 | Archive leaderboard | report |
| Weakly-Supervised Object Localization | CUB-200-2011 | InfoCAM | Top-1 Error Rate | 54.17 | #10 of 10 | Archive leaderboard | report |
| Weakly-Supervised Object Localization | CUB-200-2011 | InfoCAM | Top-1 Localization Accuracy | 55.83 | #10 of 10 | Archive leaderboard | report |
| Weakly-Supervised Object Localization | Tiny ImageNet | InfoCAM | Top-1 Localization Accuracy | 43.34 | #1 of 3 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Methods
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