arXiv:2605. 24316v2 Announce Type: replace Abstract: Scaling laws provide compact descriptions of how prediction error varies with compute, model size, and data, but existing theory mainly treats single-sample SGD or full data reuse, leaving the role of mini-batching unclear.
arXiv:2605. 24316v3 Announce Type: replace Abstract: Mini-batching is central to large-scale optimization, yet its role in statistical scaling laws remains limited.
arXiv:2602. 02431v2 Announce Type: replace-cross Abstract: It is folklore that reusing training data more than once can improve the statistical efficiency of gradient-based learning.
The paper presents empirical scaling laws for autoregressive language models, linking prediction loss to model size, data size, and compute, and investigates their theoretical basis using a teacher–student linear RNN framework. In this tractable setting, a stable latent linear RNN generates trajectories while a sketched linear recurrent student is trained via full‑batch WSD gradient descent on next‑token prediction. The study derives explicit approximation, optimization, and statistical scaling laws that depend on the sketch dimension, number of trajectories, and trajectory length, revealing how different power‑law exponents for innovation and initialization covariances affect the rates and crossovers between regimes.
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:2602. 03001v2 Announce Type: replace-cross Abstract: To maximize hardware utilization, modern machine learning systems typically employ large constant or manually tuned batch size schedules, relying on heuristics that are brittle and costly to tune.
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 a capacity exponent. The authors then analyze risk dynamics, optimize final‑step risk under a fixed data budget, and present a three‑regime batch‑size phase diagram that highlights Polyak’s ability to enlarge the critical batch size and Nesterov’s superior data efficiency in the large‑batch regime.
arXiv:2610. 00436v1 Announce Type: new Abstract: Online batch selection fine-tunes a language model on the most useful part of each candidate batch.
arXiv:2606. 19179v1 Announce Type: cross Abstract: Stochastic momentum methods such as heavy ball (HB), Nesterov momentum, and variants of Accelerated SGD (ASGD) [Kidambi et al.
arXiv:2606. 15832v1 Announce Type: new Abstract: Empirical risk minimization on massive datasets naturally exhibits a nested double finite-sum structure, where $N=nm$ total samples are logically or physically partitioned into $n$ blocks of size $m$ (e.
arXiv:2608. 07922v1 Announce Type: new Abstract: Adaptive learning needs both a state that preserves what observations imply and opportunities to act on that state.
arXiv:2608. 03197v1 Announce Type: new Abstract: Sharpness-Aware Minimization (SAM) improves generalization by seeking parameters whose loss is robust to local adversarial perturbations, but the quantitative mechanism underlying its implicit bias toward flat minima remains unclear.
arXiv:2603. 10485v3 Announce Type: replace-cross Abstract: In this work, we study the convergence properties of the Dual Space Preconditioned Gradient Descent, encompassing optimizers such as Normalized Gradient Descent and Gradient Clipping.