In neural computation, the essential information is generally encoded into the neurons via their spiking configurations, activation values or (attractor) dynamics. The synapses and their associated plasticity mechanisms are, by contrast, mainly used to process this information and implement the crucial learning features. Here, we propose a novel Turing complete paradigm of neural computation where the essential information is encoded into discrete synaptic states, and the updating of this information achieved via synaptic plasticity mechanisms. More specifically, we prove that any 2-counter machine-and hence any Turing machine-can be simulated by a rational-weighted recurrent neural network employing spike-timing-dependent plasticity (STDP) rules. The computational states and counter values of the machine are encoded into discrete synaptic strengths. The transitions between those synaptic weights are then achieved via STDP. These considerations show that a Turing complete synaptic-based paradigm of neural computation is theoretically possible and potentially exploitable. They support the idea that synapses are not only crucially involved in information processing and learning features, but also in the encoding of essential information. This approach represents a paradigm shift in the field of neural computation.

Laboratory of Mathematical Economics and Applied Microeconomics University Paris 2 Panthéon Assas 75005 Paris France Institute of Computer Science Czech Academy of Sciences 18207 Prague 8 Czech Republic

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