  We provide a unified framework, applicable to a general family of convex
losses and across binary and multiclass settings in the overparameterized
regime, to approximately characterize the implicit bias of gradient descent in
closed form. Specifically, we show that the implicit bias is approximated (but
not exactly equal to) the minimum-norm interpolation in high dimensions, which
arises from training on the squared loss. In contrast to prior work which was
tailored to exponentially-tailed losses and used the intermediate
support-vector-machine formulation, our framework directly builds on the
primal-dual analysis of Ji and Telgarsky (2021), allowing us to provide new
approximate equivalences for general convex losses through a novel sensitivity
analysis. Our framework also recovers existing exact equivalence results for
exponentially-tailed losses across binary and multiclass settings. Finally, we
provide evidence for the tightness of our techniques, which we use to
demonstrate the effect of certain loss functions designed for
out-of-distribution problems on the closed-form solution.
