arXiv:2507.12224cs.LG2025-07被引 19

优化器不仅影响训练速度,还决定模型最终解的质量和特性。

Optimizers Qualitatively Alter Solutions And We Should Leverage This

  • 优化器通过引入归纳偏置,改变模型的表达能力
  • 现有优化器会隐式塑造解的性质,而不仅是加速收敛
  • 应设计新优化器来主动引导期望的模型特性

由于深度神经网络(DNNs)的非线性特性,仅依赖局部信息的优化器(如SGD)无法保证收敛到唯一的全局最小值。早期因此对DNN可行性存在质疑。但过去几十年的发展表明,足够大的DNN在标准训练协议下展现出稳定优化动态,并收敛到高性能解。这一成功使研究者倾向于将凸优化作为学习的思维模型,关注训练效率(如迭代次数、计算量或时钟时间)。然而我们主张,除了收敛速度,优化器还深刻影响解的定性特征——即其内在归纳偏置与有效表达能力。因此,优化器可被用作显式编码学习目标的工具。我们呼吁深入理解现有优化器的偏差,并设计新优化器以主动诱导期望的解特性,而非仅以收敛速度评判。这有助于提升对学习过程如何塑造模型结果的理解,并强化优化器设计作为与架构、数据并列的关键杠杆。

原文摘要 · Abstract (English)

Due to the nonlinear nature of Deep Neural Networks (DNNs), one can not guarantee convergence to a unique global minimum of the loss when using optimizers relying only on local information, such as SGD. Indeed, this was a primary source of skepticism regarding the feasibility of DNNs in the early days of the field. The past decades of progress in deep learning have revealed this skepticism to be misplaced, and a large body of empirical evidence shows that sufficiently large DNNs following standard training protocols exhibit well-behaved optimization dynamics that converge to performant solutions. This success has biased the community to use convex optimization as a mental model for learning, leading to a focus on training efficiency, either in terms of required iteration, FLOPs or wall-clock time, when improving optimizers. We argue that, while this perspective has proven extremely fruitful, another perspective specific to DNNs has received considerably less attention: the optimizer not only influences the rate of convergence, but also the qualitative properties of the learned solutions. Restated, the optimizer can and will encode inductive biases and change the effective expressivity of a given class of models. Furthermore, we believe the optimizer can be an effective way of encoding desiderata in the learning process. We contend that the community should aim at understanding the biases of already existing methods, as well as aim to build new optimizers with the explicit intent of inducing certain properties of the solution, rather than solely judging them based on their convergence rates. We hope our arguments will inspire research to improve our understanding of how the learning process can impact the type of solution we converge to, and lead to a greater recognition of optimizers design as a critical lever that complements the roles of architecture and data in shaping model outcomes.

优化器归纳偏置模型特性

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