Title: Thinking Deeper With Recurrent Networks: Logical Extrapolation Without Overthinking. Abstract: Classical machine learning systems perform best when they are trained and tested on the same distribution, and they lack a mechanism to increase model power after training is complete. In contrast, recent work has observed that recurrent networks can exhibit logical extrapolation; models trained only on small/simple problem instances can extend their abilities to solve large/complex instances at test time simply by performing more recurrent iterations.  While preliminary results on these ``thinking systems'' are promising, existing recurrent systems, when iterated many times, often collapse rather than improve their performance.  This ``overthinking'' phenomenon has prevented thinking systems from scaling to particularly large and complex problems. In this paper, we design a recall architecture that keeps an explicit copy of the problem instance in memory so that it cannot be forgotten.  We also propose an incremental training routine that prevents the model from learning behaviors that are specific to iteration number and instead pushes it to learn behaviors that can be repeated indefinitely. Together, these design choices encourage models to converge to a steady state solution rather than deteriorate when many iterations are used. These innovations help to tackle the overthinking problem and boost deep thinking behavior on each of the benchmark tasks proposed by  Schwarzschild et al. (2021a).