统一压缩表示的缩放定律

摘要

规模法则通过基于模型规模、计算量和数据量的可预测性能扩展，塑造了机器学习领域的最新进展。与此同时，人工智能计算成本的上升催生了模型压缩技术，特别是量化和稀疏化，这些技术旨在缓解大规模训练和推理带来的高昂计算需求。本文探讨了规模法则与压缩格式之间的相互作用，研究了一个统一的规模框架是否能在训练过程中，针对如稀疏、标量量化、稀疏量化乃至向量量化等多种压缩表示形式，准确预测模型性能。我们的主要贡献包括验证了一个通用的规模法则公式，并展示了它不仅适用于单一压缩类型，还能跨压缩类型组合应用。基于此，我们的核心发现是从理论和实证两方面证明，存在一个基于表示拟合随机高斯数据能力的简单“容量”度量，该度量能够稳健地预测多种压缩表示下的参数效率。在实践层面，我们扩展了该公式，以直接比较不同压缩格式的精度潜力，并推导出在稀疏量化格式上训练的更好算法。

English

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model compression techniques, notably quantization and sparsification, which have emerged to mitigate the steep computational demands associated with large-scale training and inference. This paper investigates the interplay between scaling laws and compression formats, exploring whether a unified scaling framework can accurately predict model performance when training occurs over various compressed representations, such as sparse, scalar-quantized, sparse-quantized or even vector-quantized formats. Our key contributions include validating a general scaling law formulation and showing that it is applicable both individually but also composably across compression types. Based on this, our main finding is demonstrating both theoretically and empirically that there exists a simple "capacity" metric -- based on the representation's ability to fit random Gaussian data -- which can robustly predict parameter efficiency across multiple compressed representations. On the practical side, we extend our formulation to directly compare the accuracy potential of different compressed formats, and to derive better algorithms for training over sparse-quantized formats.

统一压缩表示的缩放定律

Unified Scaling Laws for Compressed Representations

摘要

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