The Flow has not summarised this story yet — read it at arXiv Machine Learning.
arXiv:2606. 29519v1 Announce Type: new Abstract: Long-range learning is hard for recurrent networks trained with stochastic gradient descent, because the influence of a past input fades with the lag $\ell$, and if it fades too fast the dependence cannot be learned from finite data.
The paper derives an exact discrete‑time law that captures how learning‑rate schedules and weight decay interact in scale‑invariant neural networks, showing that a single scalar quantity governs the effective step size. It demonstrates that the balance point between contraction and expansion is intrinsically unstable, leading to recurrent dynamics when using constant learning rates with weight decay. The authors extend this analysis to various optimizers and datasets, confirming the law’s precision and showing that performance peaks sharply at the predicted boundary.
Long-range learning is hard for recurrent networks trained with stochastic gradient descent, because the influence of a past input fades with the lag $\ell$, and if it fades too fast the dependence cannot be learned from finite data. This fade is captured by an envelope $f(\ell)$.
arXiv:2607. 10959v1 Announce Type: new Abstract: Standard learning rate schedules such as cosine annealing are tied to a fixed training horizon, limiting their ability to accommodate post hoc horizon extension.
The paper investigates how momentum methods affect large‑batch training in a one‑pass setting using power‑law kernel regression. It derives critical learning rates for SGD, Polyak, and Nesterov, and shows how these rates depend on batch size, momentum, and model capacity. The authors provide scaling laws for risk dynamics, a three‑regime batch‑size phase diagram, and demonstrate that Polyak increases the critical batch size while Nesterov improves data efficiency in the large‑batch regime.
arXiv:2607. 23967v1 Announce Type: new Abstract: Delayed generalization, or grokking, remains poorly understood despite extensive empirical study.