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<p>Softmax is the default choice for normalizing classification outputs in deep learning, yet it suffers from numerical overflow and the tendency to produce overconfident predictions. Despite its wide adoption, these limitations remain underexplored, leaving a gap for more stable alternatives. This study introduces LogSoft, a drop-in replacement for Softmax in which the exponential term used for probability normalization is replaced by the Softplus function, yielding a smoother and more stable output distribution. LogSoft maintains the probabilistic interpretation of Softmax while improving numerical stability, ensuring bounded gradients, and promoting smoother optimization. Extensive experiments on three medicinal plant leaf datasets (MLD, Flavia, IMLI) using five state-of-the-art CNN architectures (ResNet50, InceptionV3, MobileNet, DenseNet121, EfficientNetB0) demonstrate that LogSoft consistently improves generalization, reduces overfitting, and yields more balanced probability distributions. These findings establish LogSoft as a theoretically grounded and practically advantageous alternative to Softmax, particularly valuable in applications requiring numerical stability and calibrated predictions.</p>

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LogSoft: A stable and calibrated drop-in alternative to Softmax

  • 期刊论文

  • 发表日期：

    2026年6月16日

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  • Anjali,
  • Jolly Puri,
  • M. K. Sharma,
  • Rajendra Kumar Sharma

摘要

Softmax is the default choice for normalizing classification outputs in deep learning, yet it suffers from numerical overflow and the tendency to produce overconfident predictions. Despite its wide adoption, these limitations remain underexplored, leaving a gap for more stable alternatives. This study introduces LogSoft, a drop-in replacement for Softmax in which the exponential term used for probability normalization is replaced by the Softplus function, yielding a smoother and more stable output distribution. LogSoft maintains the probabilistic interpretation of Softmax while improving numerical stability, ensuring bounded gradients, and promoting smoother optimization. Extensive experiments on three medicinal plant leaf datasets (MLD, Flavia, IMLI) using five state-of-the-art CNN architectures (ResNet50, InceptionV3, MobileNet, DenseNet121, EfficientNetB0) demonstrate that LogSoft consistently improves generalization, reduces overfitting, and yields more balanced probability distributions. These findings establish LogSoft as a theoretically grounded and practically advantageous alternative to Softmax, particularly valuable in applications requiring numerical stability and calibrated predictions.