Proceedings of the Annual Meeting of the Cognitive Science Society

How do learned strategies generalize to new problems? Children who learn to count can add any two numbers by iteratively updating a running total, even for sums they have not encountered. We trained RNNs with a working-memory readout that tracks the progressive count at every timestep and is fed back to maintain a running total, using problems requiring counts up to 5, and tested generalization on counts up to 9. We demonstrate that such RNNs successfully generalize, with continuous drift dynamics and reaction times scaling linearly with count length. Analyzing internal dynamics, we found two emergent number-line representations: one for rapid retrieval of the starting value, one for slow iterative counting, consistent with graded number representations observed in human parietal cortex. Generalization was strongest when network activity remained within linear regimes visited during training, providing a mechanistic account of both successful generalization and its limits.