Explain how you would approach setting the input and recurrent weights to enable the network to learn a rich set of temporal dependencies in this specific application, given that stability near the edge is critical for representing complex histories.

Set the input and recurrent weights so that the dynamical system is near the edge of stability. This can be achieved by ensuring that the eigenvalues of the Jacobian of the state-to-state transition function are close to 1, indicating a balance between complexity and simplicity in the temporal dependencies captured by the network.