Hard labels sampled from sparse targets mislead rotation invariant algorithms
One of the most common machine learning setups is logistic regression. In many classification models, including neural networks, the final prediction is obtained by applying a logistic link function to a linear score. In binary logistic regression, the feedback can be either soft labels, corresponding to the true conditional probability of the data (as in distillation), or sampled hard labels (taking values $\pm 1$). We point out a fundamental problem that arises even in a particularly favorable setting, where the goal is to learn a noise-free soft target of the form $σ(\mathbf{x}^{\top}\mathbf{w}^{\star})$. In the over-constrained case (i.e. the number of samples $n$ exceeds the input di...
| Authors | Avrajit Ghosh, Bin Yu, Manfred Warmuth et al. |
|---|---|
| Primary category | stat.ML |
| Published | 21 March 2026 |
| Last updated at source | 4 June 2026 |
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