The Neurodynamics of Cognition: A Tutorial on Computational Cognitive Neuroscience

Abstract

Computational Cognitive Neuroscience (CCN) is a new field that lies at the intersection of computational neuroscience, machine learning, and neural network theory (i.e., connectionism). The ideal CCN model should not make any assumptions that are known to contradict the current neuroscience literature and at the same time provide good accounts of behavior and at least some neuroscience data (e.g., single-neuron activity, fMRI data). Furthermore, once set, the architecture of the CCN network and the models of each individual unit should remain fixed throughout all applications. Because of the greater weight they place on biological accuracy, CCN models differ substantially from traditional neural network models in how each individual unit is modeled, how learning is modeled, and how behavior is generated from the network. A variety of CCN solutions to these three problems are described. A real example of this approach is described, and some advantages and limitations of the CCN approach are discussed.

Figure 1

The leaky integrate-and-fire model (with β = 1/60, γ = 7/60, V_peak = -10, and V_reset = -50). The top panel shows the membrane potential predicted by Eq. 1. In the bottom panel vertical lines have been drawn by hand to simulate spiking.

Figure 2

Spike train produced by the quadratic integrate-and-fire model of Eq. 2 (with β = 11.83, γ = .117, V_r = -60, V_t = -40, V_peak = 35, and V_reset = -50).

Figure 3

Examples of some of the different dynamics that can be modeled with Eq. 3. An electronic version of this figure and reproduction permissions are freely available at www.izhikevich.com.

Figure 4

AMPA and NMDA glutamate receptors (Na⁺ = sodium, Ca²⁺ = calcium, Mg⁺ = magnesium).

Figure 5

The neural architecture of the Ashby and Crossley (2010) model in a task with one response alternative. The thick black arrows represent the information flow. Also shown are activations from trials early and late in training, i.e., before and after the TAN has learned that the environment is rewarding. Initially the stimulus does not cause the TAN to pause, and therefore the MSN does not fire to stimulus presentation. As a result, the firing rate of the premotor unit (pre-SMA/SMA) does not change after stimulus onset. After training, the TAN pauses to the stimulus, which releases the MSN from its tonic inhibition. This allows the MSN to fire to the stimulus, which causes the firing rate in pre-SMA/SMA to increase above baseline (SMA = supplementary motor area, VA = ventral anterior nucleus of the thalamus, VL = ventral lateral nucleus of the thalamus, CM-Pf = centremedian and parafascicular nuclei of the thalamus, GP_i = internal segment of the globus pallidus, MSN = medium spiny neuron, TAN = tonically active neuron).

Figure 6

Patch-clamp recording from the TAN of a rat (top panel; from Reynolds et al., 2004) and simulated responses of the Ashby and Crossley (2010) TAN model (bottom panel) during a patch clamp experiment when positive current is injected into the cell for 100 ms (denoted by the solid gray rectangle).