Deep Equilibrium Models For Algorithmic Reasoning

In this blogpost we discuss the idea of teaching neural networks to reach fixed points when reasoning. Specifically, on the algorithmic reasoning benchmark CLRS the current neural networks are told the number of reasoning steps they need. While a quick fix is to add a termination network that predicts when to stop, a much more salient inductive bias is that the neural network shouldn't change it's answer any further once the answer is correct, i.e. it should reach a fixed point. This is supported by denotational semantics, which tells us that while loops that terminate are the minimum fixed points of a function. We implement this idea with the help of deep equilibrium models and discuss several hurdles one encounters along the way. We show on several algorithms from the CLRS benchmark the partial success of this approach and the difficulty in making it work robustly across all algorithms.