Local connectivity balance shapes population dynamics in random recurrent networks

What the math gives to ML

The paper identifies local excitatory-inhibitory balance as a dynamical control parameter that is invisible to the usual connectivity spectrum but strongly changes recurrent-state behavior through suppression of self-generated feedback. This suggests a practical initialization and regularization strategy for RNNs and state-space sequence models: control each neuron's incoming row sum independently of global spectral radius, rather than relying only on spectral normalization. The effect should be especially measurable with saturating or sub-linear non-odd activations, where the paper predicts that balance can change growth, chaos, and effective dynamical dimension. A small-scale ablation over balance strength and activation type can directly test whether balanced recurrent networks train more stably or retain richer dynamics.