Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions

Combining neural networks with discrete probability distributions and combinatorial optimisation is difficult because discrete choices interrupt ordinary gradient-based learning.

Implicit Maximum Likelihood Estimation provides a general framework for backpropagating through these choices. It requires only the ability to compute the most probable discrete state and avoids problem-specific smooth relaxations.

The framework connects several implicit-differentiation techniques, introduces noise distributions for perturb-and-MAP inference, and performs competitively with or better than specialised relaxation-based methods across multiple tasks.

Paper: https://proceedings.neurips.cc/paper/2021/hash/7a430339c10c642c4b2251756fd1b484-Abstract.html