This perspective enable a more direct comprehension of how the learning trajectory influences generalization error.

This perspective enable a more direct comprehension of how the learning trajectory influences generalization error.

Recently, there has been a marked increase in interest regarding the generalization capabilities of unregularized gradient-based learning methods.

Modern distributed training of machine learning models often suffers from high communication overhead for synchronizing stochastic gradients and model parameters.

In general, this has a cubic cost in dataset size and is sensitive to conditioning.

Riemannian setting is a highly challenging affair.

As training data become larger, distributed training has been broadly adopted in machine learning tasks.

In Table 1, we compare our agnostic learning results. Our results in this setting come from Theorem 3.3. We note that the sample complexity for Diakonikolas et al. To prove Lemma 3.5, we use the following result of Y ehudai and Shamir [35]. We first consider the case when σ satisfies Assumption 3.1.