  It has been an open question in deep learning if fault-tolerant computation
is possible: can arbitrarily reliable computation be achieved using only
unreliable neurons? In the grid cells of the mammalian cortex, analog error
correction codes have been observed to protect states against neural spiking
noise, but their role in information processing is unclear. Here, we use these
biological error correction codes to develop a universal fault-tolerant neural
network that achieves reliable computation if the faultiness of each neuron
lies below a sharp threshold; remarkably, we find that noisy biological neurons
fall below this threshold. The discovery of a phase transition from faulty to
fault-tolerant neural computation suggests a mechanism for reliable computation
in the cortex and opens a path towards understanding noisy analog systems
relevant to artificial intelligence and neuromorphic computing.
