arXiv:2605.22341v1 Announce Type: new Abstract: Hard-label classification is usually trained with smooth surrogate losses, most prominently softmax cross-entropy. We isolate an asymptotic mechanism by which this mismatch between smooth surrogate and discrete labels produces power-law learning curves in an online teacher-student model. After subtracting the mean logit, the thermodynamic-limit dynamics close in centered variables: a growing centered student-teacher alignment $D$ and the residual student variance $\Delta$. At late times, examples away from teacher decision boundaries are already
The paper investigates the fundamental learning mechanisms in online softmax classification, a core component of modern AI systems, driven by continued academic exploration into neural network dynamics.
Understanding the asymptotic mechanisms behind learning curves in AI models can lead to more efficient and explainable training processes, impacting the development of advanced AI applications.
This theoretical work provides deeper insight into the power-law learning curves observed in hard-label classification, potentially improving future algorithmic design and optimization.
- · AI algorithm developers
- · Machine learning researchers
- · AI infrastructure providers
- · Inefficient AI training methods
Improved understanding of deep learning training dynamics for softmax classifiers.
Development of new algorithms that exploit this understanding to achieve faster and more robust AI model convergence.
Reduced computational costs and accelerated deployment of high-performing AI systems across various industries.
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