The brain's secret? Local balance!

Imagine a brain made of thousands of neurons talking to each other. Some say 'let's go forward', others 'stop here'. If these messages weren't balanced, the system would crash. Researchers discovered that local balance between excitatory and inhibitory signals is crucial for regulating the behavior of these networks. In randomly connected neuron networks, local balance doesn't change the network structure, but deeply transforms its dynamics. If neurons respond strongly, balance keeps the system stable. If the response is weak or clashes, the network falls into chaos. This effect disappears with symmetric mathematical functions. Local balance acts as a brake on feedback that would otherwise make activity grow infinitely. This discovery opens new paths to understand how the brain maintains order amid chaos.

Random recurrent neural networks are mathematical models simulating interactions between units. Local balance means that, for each neuron, the weighted sum of incoming signals approaches zero. This doesn't alter the eigenvalues of the connectivity matrix, maintaining linear network stability. However, it introduces significant nonlinear effects. When the activation function is linear or superlinear (e.g., ReLU), local balance suppresses exponential growth of the network state, stabilizing it. With sublinear or saturating functions (e.g., sigmoid), balance induces dynamic chaos instead. This phenomenon disappears for odd activation functions (f(-x) = -f(x)), commonly used in theoretical studies. The key effect is suppression of internally generated feedback input. Local balance reduces effective self-connection, limiting signal amplification. For saturating functions, the effective dimension of dynamics varies non-monotonically with balance degree, showing complex behavior. This unifying mechanism reveals local balance as an overlooked control parameter in realistic disordered networks.