相关论文: Optimal Scaling Needs Optimal Norm

A central question in modern deep learning is how to design optimizers whose behavior remains stable as the network width $w$ increases. We address this question by interpreting several widely used neural-network optimizers, including…

Large foundation models are typically trained on data from multiple domains, with the data mixture--the proportion of each domain used--playing a critical role in model performance. The standard approach to selecting this mixture relies on…

Optimal configuration of the learning rate (LR) is a fundamental yet formidable challenge in large-scale pre-training. Given the stringent trade-off between training costs and model performance, the pivotal question is whether the optimal…

Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…

This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…

Large Language Models (LLMs) have demonstrated remarkable capabilities, yet their scalability raises a critical question: Have we reached the scaling ceiling? This paper addresses this pivotal question by developing a unified theoretical…

In recent years, the state-of-the-art in deep learning has been dominated by very large models that have been pre-trained on vast amounts of data. The paradigm is very simple: investing more computational resources (optimally) leads to…

Diffusion models have achieved remarkable success in generative modeling. Despite more stable training, the loss of diffusion models is not indicative of absolute data-fitting quality, since its optimal value is typically not zero but…

Machine learning algorithms typically assume that the training and test samples come from the same distributions, i.e., in-distribution. However, in open-world scenarios, streaming big data can be Out-Of-Distribution (OOD), rendering these…

As large language models (LLMs) continue to scale in size, the computational overhead has become a major bottleneck for task-specific fine-tuning. While low-rank adaptation (LoRA) effectively curtails this cost by confining the weight…

A common pursuit in modern statistical learning is to attain satisfactory generalization out of the source data distribution (OOD). In theory, the challenge remains unsolved even under the canonical setting of covariate shift for the linear…

Scaling laws are useful guides for derisking expensive training runs, as they predict performance of large models using cheaper, small-scale experiments. However, there remain gaps between current scaling studies and how language models are…

Training compute is increasingly outpacing the availability of high-quality data. This shifts the central challenge from optimal compute allocation to extracting maximum value from limited data. The widely adopted Chinchilla scaling law…

We study the compute-optimal trade-off between model and training data set sizes for large neural networks. Our result suggests a linear relation similar to that supported by the empirical analysis of chinchilla. While that work studies…

Learning to generalise from limited data is a fundamental challenge for both artificial and biological systems. A common strategy is to extract reusable structure from abundant unlabelled data, enabling efficient adaptation to new tasks…

We study the implicit regularization of optimization methods for linear models interpolating the training data in the under-parametrized and over-parametrized regimes. Since it is difficult to determine whether an optimizer converges to…

Scaling LLMs requires tremendous computational resources, and recent advances in AI have gone hand in hand with massive amounts of capital expenditure. While it is established that scaling up LLMs reliably increases model quality…

Several recently introduced deep learning optimizers utilizing matrix-level preconditioning have shown promising speedups relative to the current dominant optimizer AdamW, particularly in relatively small-scale experiments. However, efforts…

Training a single model on multiple input domains and/or output tasks allows for compressing information from multiple sources into a unified backbone hence improves model efficiency. It also enables potential positive knowledge transfer…

Adam has been at the core of large-scale training for almost a decade, yet a simple empirical fact remains unaccounted for: both validation scores and the qualitative behaviour of the training runs improve when the momentum parameters…