DIVERGENT INTERNAL DYNAMICS FOR IDENTICAL BEHAVIOR: TRANSITIONING FROM CHAOS TO PERIODICITY IN RNN RULE LEARNING

Flexible behavior requires neural systems to switch outputs based on implicit rules or contexts. While Recurrent Neural Networks (RNNs) can learn such tasks, it remains unclear whether the internal representations governing these behaviors are merely specific to the training data or reflect a generalized understanding of the underlying rule. We trained an RNN on a reversal learning task where the network had to switch between two output patterns every 10 trials without explicit cues. To evaluate rule internalization, we used an incremental training curriculum, increasing the number of blocks (10-trial segments) the network had to navigate. We then analyzed the latent neural dynamics as the network transitioned from performing only on trained sequences to generalizing across any number of blocks. We identified two distinct internal representations for identical behavioral outputs. In the "specific" phase (trained on 3–5 blocks), the network successfully performed the task but failed to generalize to longer sequences. This state was characterized by chaotic neural activity, where trajectories were sensitive to initial conditions and lacked a stable structure for long-term counting. Conversely, as the network mastered around 10 blocks, it transitioned to a "general" representation characterized by periodic neural activity. In this regime, a specialized population of "counter neurons" emerged, exhibiting structured oscillations. This periodic geometry allowed the network to generalize the reversal rule indefinitely. Our results demonstrate that the same flexible behavior can emerge from fundamentally different dynamical regimes, providing a potential framework for how biological circuits achieve generalizable intelligence.