Calibrating Latent Traveling Waves Controls Memory Retrieval in Recurrent Networks

Traveling waves have been linked to working-memory transport in the brain and in recurrent neural networks (RNNs), although their causal role in RNN computation remains unclear. We test whether the phase velocity of a learned latent wave determines when an RNN outputs a stored sequence. Using a task requiring the networks to output memorized inputs after $N$ steps, we scale the complex phases of the learned recurrent dynamics by $N/(N+2)$ and preserve their eigenvectors and eigenvalue magnitudes. Four controls reverse every other phase change while preserving either absolute phase displacement or the recurrent edit's Frobenius norm. Phase scaling produces higher output accuracy than every control in every network. Across five delays and three training procedures, phase scaling exceeds the strongest control in mean output accuracy by more than $0.10$ in 13 of 15 conditions. The difference is smaller than $0.10$ in the other two conditions, both at $N = 4$. In every network, phase scaling moves the peak in output accuracy from $N$ to the predicted delay $N + 2$. Predicted and observed delays therefore agree with $R^2 = 1.0$ and zero mean absolute error.