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  • Review Article
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State-dependent computations: spatiotemporal processing in cortical networks

Key Points

  • All forms of sensory processing require sense to be made of the complex spatiotemporal patterns of action potentials that are generated in our sensory organs by external stimuli.

  • Any general model of cortical processing must account for the brain's ability to process both the spatial and the temporal features of stimuli, and thus must account for spatiotemporal processing in general.

  • State-dependent classes of neural network models propose that the temporal information is inherently encoded in the state of the network.

  • The internal state can be divided into the active state, which reflects ongoing neural activity that interacts with incoming external inputs, and the hidden state, which reflects neural properties that change in time even when a network is silent (for example, short-term synaptic plasticity).

  • In vivo electrophysiological recordings show that the neural population response of a network is strongly influenced by preceding activity, and thus that networks behave in a state-dependent manner.

  • A prediction that emerges from the proposed framework is that the neural network response to a given stimulus encodes not only the current stimulus, but also previous stimuli.

Abstract

A conspicuous ability of the brain is to seamlessly assimilate and process spatial and temporal features of sensory stimuli. This ability is indispensable for the recognition of natural stimuli. Yet, a general computational framework for processing spatiotemporal stimuli remains elusive. Recent theoretical and experimental work suggests that spatiotemporal processing emerges from the interaction between incoming stimuli and the internal dynamic state of neural networks, including not only their ongoing spiking activity but also their 'hidden' neuronal states, such as short-term synaptic plasticity.

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Figure 1: Trajectories of active and hidden states.
Figure 2: Active and hidden network states.
Figure 3: Discrimination of complex spatiotemporal patterns.
Figure 4: Population activity from the cat visual cortex encodes both the current and previous stimuli.

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Acknowledgements

We would like to thank D. Nikolić and W. Singer for providing the experimental data shown in figure 4. We would also like to thank S. Haeusler and S. Klampfl for help with data analysis and figures. For providing helpful comment on earlier versions of this manuscript we would like to thank T. Carvalho, L. Dobrunz, S. Haeusler, M. Kilgard, S. Klampfl, D. Nikolić, F. Sommer and T. Zador. D.V.B.'s work is supported by the National Institute of Mental Health (MH60163). The work by W.M. on this article was partially supported by the research project FACETS of the European Union, and the Austrian Science Fund FWF projects P17229-N04 and S9102-N04.

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Correspondence to Dean V. Buonomano.

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Glossary

Perceptron

A simple linear neuron model that computes a weighted sum of its inputs, and outputs 1 if the weighted sum is larger than some threshold, and 0 otherwise. Weights and thresholds can be learned by the perceptron learning rule.

Multi-layer perceptron

A feedforward network of units, the computational function of which is similar to that of a perceptron, except that a smooth function (instead of a threshold) is applied to the weighted sum of inputs at each unit. Weights and thresholds can be learned by the back-propagation learning rule.

Integrate-and-fire neuron

A simple model of a spiking neuron. It integrates synaptic inputs with a passive membrane time constant. Whenever the resulting membrane voltage reaches a firing threshold, it generates an output spike.

Retinotopy

A spatial arrangement in which neighbouring visual neurons have receptive fields that cover neighbouring (although partly overlapping) areas of the visual field.

Somatotopy

A spatial arrangement in which neighbouring sensory neurons respond to the stimulation of neighbouring receptors in the skin.

Membrane time constant

A physical measure that reflects the time it takes the voltage of a neuron to achieve 63% of its final value for a steady-state current pulse.

Liquid-state machine

A class of computational model that is characterized by one or several read-outs applied to some generic dynamical system, such as a recurrent network of spiking neurons. Whereas the dynamical system contributes generic computational operations, such as fading memory and nonlinear combinations of features that are independent of concrete computational tasks, each read-out can be trained to extract different pieces of the information that is accumulated in the dynamical system.

Echo-state network

A class of artificial neural network model that is based on recurrent connections between analogue units, in which the connection weights are random but appropriately scaled to generate stable internal dynamics. These models can encode temporal information as a result of the active state but do not have hidden states.

State-dependent network

A class of model that is based on the characteristics described in this Review. The state-dependent network model proposes that cortical networks are inherently capable of encoding time and processing spatiotemporal stimuli as a result of the state-dependent properties imposed by ongoing activity (the active state) and as a result of time-dependent neural properties (the hidden states).

Reservoir computing

A general term used primarily in machine learning to refer to models that rely on mapping stimuli onto a high-dimensional space in a nonlinear fashion. Such models include echo-state machines, liquid-state machines and state-dependent networks.

Linear discriminator

A type of classifier that can be computed by a perceptron.

Synaptic weights

The strength of synaptic connections between neurons.

Learning rule

A rule that governs the relationship between patterns of pre- and postsynaptic activity and long-term changes in synaptic strength. For example, spike timing-dependent plasticity.

Recurrent network

A network in which any neuron can be directly or indirectly connected to any other — the flow of activity from any one initial neuron can propagate through the network and return to its starting point. By contrast, in a feedforward network information cannot return to the point of origin.

Spike timing-dependent plasticity

(STDP). Traditionally, a form of synaptic plasticity in which the order of the pre- and postsynaptic spikes determines whether synaptic potentiation (pre- and then postsynaptic spikes) or depression (post- and then presynaptic spikes) ensues.

Invariant pattern classification

The discrimination of patterns in a manner that is invariant across some transformation. For example, recognition of the same word spoken at different speeds or by different speakers.

Chaos

In theoretical work this term is applied only to deterministic dynamical systems without external inputs, and characterizes extreme sensitivity to initial conditions. In neuroscience it is also applied more informally to systems that receive ongoing external inputs (and that are subject to noise and hence are not deterministic), and characterizes neuronal systems with a trajectory of neural states that is strongly dependent on noise and less dependent on external stimuli.

Hyperplane

A hyperplane is a generalization of the concept of a plane in a three-dimensional space to d-dimensional spaces for arbitrary values of the dimension d. A hyperplane in d dimensions splits the d-dimensional space into two half spaces.

Attractor

The state of a dynamical system to which the system converges over time, or the state that 'attracts' neighbouring states.

Sparse code

A neural code in which only a small percentage of neurons is active at any given point in time.

Psychophysics

Studies based on perceptual decisions regarding the physical characteristics of stimuli, such as the intensity or duration of sensory stimuli.

Tonotopy

A spatial arrangement in which tones that are close to each other in terms of frequency are represented in neighbouring auditory neurons.

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Buonomano, D., Maass, W. State-dependent computations: spatiotemporal processing in cortical networks. Nat Rev Neurosci 10, 113–125 (2009). https://doi.org/10.1038/nrn2558

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