Avi Schwarzschild, Eitan Borgnia, Arjun Gupta, Furong Huang, Uzi Vishkin, Micah Goldblum, Tom Goldstein
Deep neural networks are powerful machines for visual pattern recognition, but reasoning tasks that are easy for humans may still be difficult for neural models. Humans possess the ability to extrapolate reasoning strategies learned on simple problems to solve harder examples, often by thinking for longer. For example, a person who has learned to solve small mazes can easily extend the very same search techniques to solve much larger mazes by spending more time. In computers, this behavior is often achieved through the use of algorithms, which scale to arbitrarily hard problem instances at the cost of more computation. In contrast, the sequential computing budget of feed-forward neural networks is limited by their depth, and networks trained on simple problems have no way of extending their reasoning to accommodate harder problems. In this work, we show that recurrent networks trained to solve simple problems with few recurrent steps can indeed solve much more complex problems simply by performing additional recurrences during inference. We demonstrate this algorithmic behavior of recurrent networks on prefix sum computation, mazes, and chess. In all three domains, networks trained on simple problem instances are able to extend their reasoning abilities at test time simply by "thinking for longer."