A network model of behavioural performance in a rule learning task

Abstract

Humans demonstrate differences in performance on cognitive rule learning tasks which could involve differences in properties of neural circuits. An example model is presented to show how gating of the spread of neural activity could underlie rule learning and the generalization of rules to previously unseen stimuli. This model uses the activity of gating units to regulate the pattern of connectivity between neurons responding to sensory input and subsequent gating units or output units. This model allows analysis of network parameters that could contribute to differences in cognitive rule learning. These network parameters include differences in the parameters of synaptic modification and presynaptic inhibition of synaptic transmission that could be regulated by neuromodulatory influences on neural circuits. Neuromodulatory receptors play an important role in cognitive function, as demonstrated by the fact that drugs that block cholinergic muscarinic receptors can cause cognitive impairments. In discussions of the links between neuromodulatory systems and biologically based traits, the issue of mechanisms through which these linkages are realized is often missing. This model demonstrates potential roles of neural circuit parameters regulated by acetylcholine in learning context-dependent rules, and demonstrates the potential contribution of variation in neural circuit properties and neuromodulatory function to individual differences in cognitive function.This article is part of the theme issue 'Diverse perspectives on diversity: multi-disciplinary approaches to taxonomies of individual differences'.

Keywords: acetylcholine; muscarinic receptors; neocortex; rule learning.

Figure 1.

(a) Diagram of the behavioural task. Participants learn associations between four items A,B,C,D and two other items X,Y. The association rules change with spatial quadrant, but pairs of quadrants have the same associations (e.g. 1 and 4, 2 and 3), allowing participants to extract a common higher order rule. For example, item A followed by item X in quadrant 1 requires a Go response to be correct. There are 16 Go pairings and 16 NoGo pairings. (b) Task with probe stimuli testing generalization. The task is the same as A, except that in each quadrant, about half of the cue combinations are not shown during training (indicated by the question mark ‘?’). All examples of A and C are shown, but only a single example for B and D are shown. After training, simulations are presented with the missing cue and have to infer the correct paired associate (X, Y) from experience in the equivalent quadrant.

Figure 2.

Network structure. (a) The activity array used in simulations. Units are assigned to the first items A,B,C,D, second items X,Y, locations 1,2,3,4 and gates 1,2,3,4,5,6,7 and output Go, NoGo. (b) The network connectivity of gating in the model. Gate 1 regulates gated weights G_ij1 between first patterns A,B,C or D and gates 2,3,4,5. Black squares indicate strengthened connections in a specific example of function also shown in figure 3. Gates 2,3,4,5 then regulate gated weights G_ij2, G_ij3, G_ij4, G_ij5 between second patterns X or Y and gates 6 or 7. Gates 6 or 7 then regulate gated weights G_ij6 and G_ij7 between location inputs 1,2,3 or 4 and outputs Go (G) or NoGo (N). (c) The same network connectivity as in b, but shown with circles representing units and lines (instead of matrices) representing weights. Filled circles represent active units for the examples described in the main text. (d) Example of a network without gating units or gated weights. Synapses between neurons representing patterns are strengthening with Hebbian modification only. This results in overlap for the association of pattern A with pattern X in location 1 versus pattern C with pattern X in location 1. The need for two different outputs cannot be accommodated in this structure.

Figure 3.

Simulation of task after training. (a) On each trial, the full network was presented with a sequence of binary patterns with active units (black rectangles) representing one item from A,B,C,D (top row, ‘C’) followed by one item from X,Y (second row, ‘X’) followed by one of 4 location cues (third row, ‘Loc3’). Each trial started with activity in gate 1 (index 11), and after learning cue C activates gate 5 (index 15), cue X activates gate 7 (index 17), and Loc3 activates the Go response via weights shown in part b. These network weights were previously strengthened when the network was rewarded for a correct Go response or NoGo based on the combinations shown in figure 1. The network learned to correctly respond to all combinations. (b) After learning, gate 1 has a weight matrix G_ij1 with four strong weights (black squares) linking the four first cues to specific gates, so input ‘C’ in column 3 activates output row corresponding to gate 5 (index 15). The grey scale values represent the random initial weights that were not modified due to the absence of pre- or post-synaptic activity. Darker grey represents stronger weights. (c) The next four gates link the second cue to a different set of gates. In this example, active gate 5 (index 15) allows input X to activate gate 7. (d) The next two gates link the location context to a correct response. In this example, active gate 7 (index 17) allows Loc3 to activate Go. (e) Left: Performance of a single network over 3000 training trials, showing relatively rapid increase in performance from random (50%) to 100% correct around trial 800. Right: Performance change averaged over 20 networks, showing that all networks converge over time to 100% correct responses on all 32 trial types.

Figure 4.

More examples of neural networks trained on task. (a) A different example, after different training. In this case, gate 1 (index 11) links input cue ‘A’ to gate 3 (index 13). Gate 3 links cue ‘Y’ to gate 7 (index 17). Gate 7 links ‘Loc2’ to Go response which is correct. (b) Performance of the network for different levels of noise (0.0 to 1.0) when trained on all 32 combinations. The network does not perform well with zero noise, because it does not explore enough gating patterns, but does perform well for noise of 0.1 and 0.2. Higher levels of noise cause a decrease in correct steady state responding. (c) Example of generalization from average across 20 networks, showing that when presented with only 18 of the 32 combinations, the networks attain about 75% performance. Then on the last 400 trials, most of the networks (19 out of 20) can correctly generalize to 100% correct responses when presented with all 32 pattern combinations (without further learning). (d) With noise set to zero, the average performance of 20 networks does not learn the rules and remains at 50% performance and does not generalize, indicating sensitivity to specific network parameters. (e) Performance of the network for different numbers of gating units, showing that insufficient numbers prevent good performance. Best performance is attained first with seven units, which allows four gating units to be activated by the four input items A,B,C,D. (f) With purely Hebbian connectivity without gating units and gated weights, a network cannot learn to attain better than 50% performance, due to incompatible responses that must be routed through the same neuron.