Hard Way, The Only Way: Provable Merits of Training on Hardest Examples

The paper presents a high‑dimensional theory of learning with data pruning via weighted empirical risk minimization. It analyzes pruning along a one‑dimensional subspace and derives limiting test‑error curves as input dimension and sample size grow with a fixed ratio. The authors show that, in the high‑sample regime, the optimal strategy is to keep only the 2N hardest examples, achieving a Bayes‑optimal error scaling of order N/P instead of the usual sqrt(N/P).

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• efficiency