Understanding the Mechanics of SPIGOT: Surrogate Gradients for Latent Structure Learning

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.Comment: EMNLP 202

Learning Binary Decision Trees by Argmin Differentiation

We address the problem of learning binary decision trees that partition data for some downstream task. We propose to learn discrete parameters (i.e., for tree traversals and node pruning) and continuous parameters (i.e., for tree split functions and prediction functions) simultaneously using argmin differentiation. We do so by sparsely relaxing a mixed-integer program for the discrete parameters, to allow gradients to pass through the program to continuous parameters. We derive customized algorithms to efficiently compute the forward and backward passes. This means that our tree learning procedure can be used as an (implicit) layer in arbitrary deep networks, and can be optimized with arbitrary loss functions. We demonstrate that our approach produces binary trees that are competitive with existing single tree and ensemble approaches, in both supervised and unsupervised settings. Further, apart from greedy approaches (which do not have competitive accuracies), our method is faster to train than all other tree-learning baselines we compare with. The code for reproducing the results is available at https://github.com/vzantedeschi/LatentTrees