  Latent structure models are a powerful tool for modeling language data: they
can mitigate the error propagation and annotation bottleneck in pipeline
systems, while simultaneously uncovering linguistic insights about the data.
One challenge with end-to-end training of these models is the argmax operation,
which has null gradient. In this paper, we focus on surrogate gradients, a
popular strategy to deal with this problem. We explore latent structure
learning through the angle of pulling back the downstream learning objective.
In this paradigm, we discover a principled motivation for both the
straight-through estimator (STE) as well as the recently-proposed SPIGOT - a
variant of STE for structured models. Our perspective leads to new algorithms
in the same family. We empirically compare the known and the novel pulled-back
estimators against the popular alternatives, yielding new insight for
practitioners and revealing intriguing failure cases.
