Regularizing cross entropy loss via minimum entropy and K-L divergence
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866916580006297600 |
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| author | Ibraheem, Abdulrahman Oladipupo |
| author_facet | Ibraheem, Abdulrahman Oladipupo |
| contents | I introduce two novel loss functions for classification in deep learning. The two loss functions extend standard cross entropy loss by regularizing it with minimum entropy and Kullback-Leibler (K-L) divergence terms. The first of the two novel loss functions is termed mixed entropy loss (MIX-ENT for short), while the second one is termed minimum entropy regularized cross-entropy loss (MIN-ENT for short). The MIX-ENT function introduces a regularizer that can be shown to be equivalent to the sum of a minimum entropy term and a K-L divergence term. However, it should be noted that the K-L divergence term here is different from that in the standard cross-entropy loss function, in the sense that it swaps the roles of the target probability and the hypothesis probability. The MIN-ENT function simply adds a minimum entropy regularizer to the standard cross entropy loss function. In both MIX-ENT and MIN-ENT, the minimum entropy regularizer minimizes the entropy of the hypothesis probability distribution which is output by the neural network. Experiments on the EMNIST-Letters dataset shows that my implementation of MIX-ENT and MIN-ENT lets the VGG model climb from its previous 3rd position on the paperswithcode leaderboard to reach the 2nd position on the leaderboard, outperforming the Spinal-VGG model in so doing. Specifically, using standard cross-entropy, VGG achieves 95.86% while Spinal-VGG achieves 95.88% classification accuracies, whereas using VGG (without Spinal-VGG) our MIN-ENT achieved 95.933%, while our MIX-ENT achieved 95.927% accuracies. The pre-trained models for both MIX-ENT and MIN-ENT are at https://github.com/rahmanoladi/minimum entropy project. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13709 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularizing cross entropy loss via minimum entropy and K-L divergence Ibraheem, Abdulrahman Oladipupo Computer Vision and Pattern Recognition Machine Learning I introduce two novel loss functions for classification in deep learning. The two loss functions extend standard cross entropy loss by regularizing it with minimum entropy and Kullback-Leibler (K-L) divergence terms. The first of the two novel loss functions is termed mixed entropy loss (MIX-ENT for short), while the second one is termed minimum entropy regularized cross-entropy loss (MIN-ENT for short). The MIX-ENT function introduces a regularizer that can be shown to be equivalent to the sum of a minimum entropy term and a K-L divergence term. However, it should be noted that the K-L divergence term here is different from that in the standard cross-entropy loss function, in the sense that it swaps the roles of the target probability and the hypothesis probability. The MIN-ENT function simply adds a minimum entropy regularizer to the standard cross entropy loss function. In both MIX-ENT and MIN-ENT, the minimum entropy regularizer minimizes the entropy of the hypothesis probability distribution which is output by the neural network. Experiments on the EMNIST-Letters dataset shows that my implementation of MIX-ENT and MIN-ENT lets the VGG model climb from its previous 3rd position on the paperswithcode leaderboard to reach the 2nd position on the leaderboard, outperforming the Spinal-VGG model in so doing. Specifically, using standard cross-entropy, VGG achieves 95.86% while Spinal-VGG achieves 95.88% classification accuracies, whereas using VGG (without Spinal-VGG) our MIN-ENT achieved 95.933%, while our MIX-ENT achieved 95.927% accuracies. The pre-trained models for both MIX-ENT and MIN-ENT are at https://github.com/rahmanoladi/minimum entropy project. |
| title | Regularizing cross entropy loss via minimum entropy and K-L divergence |
| topic | Computer Vision and Pattern Recognition Machine Learning |
| url | https://arxiv.org/abs/2501.13709 |