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The Curvature Rate {\lambda}: A Scalar Measure of Input-Space Sharpness in Neural Networks

arXiv — cs.LG•Tuesday, November 4, 2025 at 5:00:00 AM
PositiveArtificial Intelligence

The Curvature Rate {\lambda}: A Scalar Measure of Input-Space Sharpness in Neural Networks

A new study introduces the curvature rate, a scalar measure of input-space sharpness in neural networks, which could significantly enhance our understanding of how these systems generalize and respond to input changes. This innovation addresses the limitations of existing sharpness metrics that are often complex and hard to interpret, making it easier for researchers to analyze neural network performance. By focusing on input space rather than parameter space, this approach promises to improve the robustness and reliability of neural networks, which is crucial for their application in various fields.
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