In this work, we analyze the relation between reparametrizations of gradient flow and the induced implicit bias on general linear models, which encompass various basic classification and regression tasks. In particular, we aim at understanding the influence of the model parameters - reparametrization, loss, and link function - on the convergence behavior of gradient flow. Our results provide user-friendly conditions under which the implicit bias can be well-described and convergence of the flow is guaranteed. We furthermore show how to use these insights for designing reparametrization functions that lead to specific implicit biases like $\ell_p$- or trigonometric regularizers.

翻译：本文分析了梯度流重参数化与广义线性模型（涵盖多种基本分类与回归任务）中诱导隐式偏差之间的关系。我们特别着眼于理解模型参数（重参数化、损失函数和链接函数）对梯度流收敛行为的影响。研究结果提供了易于使用的条件，使得隐式偏差可被充分描述，且梯度流的收敛性得到保证。此外，我们展示了如何利用这些见解来设计重参数化函数，从而产生特定的隐式偏差，例如$\ell_p$正则化或三角函数正则化。