Before revision:  Functional network models often employ rate units that are continuously coupled by analog signals. Is there a benefit of discrete signaling? By a unified mean-field theory we show that large random networks of rate and binary units have identical second order statistics. Yet their stimulus processing properties are radically different: We discover a chaotic sub-manifold in binary networks that does not exist in rate models. Its dimensionality increases with time after stimulus onset and reaches a fixed point depending on the synaptic coupling strength. Low dimensional stimuli are transiently expanded into higher-dimensional representations within this manifold. High noise resilience persists not only near the edge of chaos, but throughout the chaotic regime. In rate models of spiking activity, the effective spiking noise suppresses chaos, severely impairing classification performance.
After revision:  Even if the timings of the individual events are strongly chaotic (microscopic chaos), the rate of events might still be non-chaotic or at the edge of what is known as rate chaos. Such edge-of-chaos dynamics are beneficial to the computational power of neuronal networks. We analyze both types of chaotic dynamics in densely connected networks of asynchronous binary neurons, by developing and applying a model-independent field theory for neuronal networks. We find a strongly size-dependent transition to microscopic chaos. We then expose the conceptual difficulty at the heart of the effective spiking noise suppresses chaos, severely impairing classification performance.