  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.
