A key challenge for neural modeling is to explain how a continuous stream of multimodal input from a rapidly changing environment can be processed by stereotypical recurrent circuits of integrate-and-fire neurons in real time. We propose a new computational model for real-time computing on time-varying input that provides an alternative to paradigms based on Turing machines or attractor neural networks. It does not require a task-dependent construction of neural circuits. Instead, it is based on principles of high-dimensional dynamical systems in combination with statistical learning theory and can be implemented on generic evolved or found recurrent circuitry. It is shown that the inherent transient dynamics of the high-dimensional dynamical system formed by a sufficiently large and heterogeneous neural circuit may serve as universal analog fading memory. Readout neurons can learn to extract in real time from the current state of such recurrent neural circuit information about current and past inputs that may be needed for diverse tasks. Stable internal states are not required for giving a stable output, since transient internal states can be transformed by readout neurons into stable target outputs due to the high dimensionality of the dynamical system. Our approach is based on a rigorous computational model, the liquid state machine, that, unlike Turing machines, does not require sequential transitions between well-defined discrete internal states. It is supported, as the Turing machine is, by rigorous mathematical results that predict universal computational power under idealized conditions, but for the biologically more realistic scenario of real-time processing of time-varying inputs. Our approach provides new perspectives for the interpretation of neural coding, the design of experiments and data analysis in neurophysiology, and the solution of problems in robotics and neurotechnology.

The precise times of occurrence of individual pre- and postsynaptic action potentials are known to play a key role in the modification of synaptic efficacy. Based on stimulation protocols of two synaptically connected neurons, we infer an algorithm that reproduces the experimental data by modifying the probability of vesicle discharge as a function of the relative timing of spikes in the pre- and postsynaptic neurons. The primary feature of this algorithm is an asymmetry with respect to the direction of synaptic modification depending on whether the presynaptic spikes precede or follow the postsynaptic spike. Specifically, if the presynaptic spike occurs up to 50 ms before the postsynaptic spike, the probability of vesicle discharge is upregulated, while the probability of vesicle discharge is downregulated if the presynaptic spike occurs up to 50 ms after the postsynaptic spike. When neurons fire irregularly with Poisson spike trains at constant mean firing rates, the probability of vesicle discharge converges toward a characteristic value determined by the preand postsynaptic firing rates. On the other hand, if the mean rates of the Poisson spike trains slowly change with time, our algorithm predicts modifications in the probability of release that generalize Hebbian and Bienenstock-Cooper-Munro rules. We conclude that the proposed spike- based synaptic learning algorithm provides a general framework for regulating neurotransmitter release probability.

Transmission across neocortical synapses depends on the frequency of presynaptic activity (Thomson & Deuchars, 1994). Interpyramidal synapses in layer V exhibit fast depression of synaptic transmission, while other types of synapses exhibit facilitation of transmission. To study the role of dynamic synapses in network computation, we propose a unified phenomenological model that allows computation of the postsynaptic current generated by both types of synapses when driven by an arbitrary pattern of action potential (AP) activity in a presynaptic population. Using this formalism, we analyze different regimes of synaptic transmission and demonstrate that dynamic synapses transmit different aspects of the presynaptic activity depending on the average presynaptic frequency. The model also allows for derivation of mean-field equations, which govern the activity of large, interconnected networks. We show that the dynamics of synaptic transmission results in complex sets of regular and irregular regimes of network activity.