In this work, we analyze the relation between reparametrizations of gradient flow and the induced implicit bias in linear models, which encompass various basic 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 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 which are closely connected to $\ell_p$- or trigonometric regularizers.

翻译：本文分析了线性模型中梯度流重参数化与诱导隐式偏差之间的关系，该类模型涵盖了多种基本回归任务。我们特别致力于理解模型参数（重参数化、损失函数和链接函数）对梯度流收敛行为的影响。研究结果给出了隐式偏差可被清晰描述且梯度流收敛性有保障的条件。此外，我们展示了如何利用这些见解设计重参数化函数，从而产生与$\ell_p$范数或三角函数正则化器密切相关的特定隐式偏差。