Primate errors in transitive ‘inference’: a two-tier learning model

Abstract

Transitive performance (TP) is a learning-based behaviour exhibited by a wide range of species, where if a subject has been taught to prefer A when presented with the pair AB but to prefer B when presented with the pair BC, then the subject will also prefer A when presented with the novel pair AC. Most explanations of TP assume that subjects recognize and learn an underlying sequence from observing the training pairs. However, data from squirrel monkeys (Saimiri sciureus) and young children contradict this, showing that when three different items (a triad) are drawn from the sequence, subjects’ performance degrades systematically (McGonigle and Chalmers, Nature 267:694–696, 1977; Chalmers and McGonigle, Journal of Experimental Child Psychology 37:355–377, 1984; Harris and McGonigle, The Quarterly Journal of Experimental Psychology 47B:319–348, 1994). We present here the two-tier model, the first learning model of TP which accounts for this systematic performance degradation. Our model assumes primate TP is based on a general-purpose task learning system rather than a special-purpose sequence-learning system. It supports the hypothesis of Heckers et al. (Hippocampus 14:153–162, 2004) that TP is an expression of two separate general learning elements: one for associating actions and contexts, another for prioritising associations when more than one context is present. The two-tier model also provides explanations for why phased training is important for helping subjects learn the initial training pairs and why some subjects fail to do so. It also supports the Harris and McGonigle (The Quarterly Journal of Experimental Psychology 47B:319–348, 1994) explanation of why, once the training pairs have been acquired, subjects perform transitive choice automatically on two-item diads, but not when exposed to triads from the same sequence.

Appendices

Appendix A: the binary sampling model

In one of the earliest responses to Bryant and Trabasso (1971), McGonigle and Chalmers (1977) not only demonstrated non-human animal learning of TP, but also proposed a model to account for the errors the animals made. Their subjects were squirrel monkeys (Saimiri sciureus). Like human children, these monkeys tend to score only around 90% on the pair $BD$. To explain this, McGonigle and Chalmers proposed the binary-sampling theory. This theory assumes that:

• Subjects consider not only the items visible, but also items that might be expected to be visible. That is, they take into account elements associated with the current stimulus, especially intervening stimuli associated with both.

• Subjects consider only two of these possible elements, choosing the pair at random. If they were trained on that pair, they perform as trained; otherwise they perform at chance, unless one of the items is an end item, A or E, in which case they perform by selecting or avoiding the item, respectively.

• If the subject chooses an item that is only expected, not actually present, it obviously cannot act on that selection (e.g. grasp the item). However, selection reinforces consideration of that item, which makes it likely the next pair the animal considers includes one of the higher-valued of the items displayed.

Thus for the pair $BD$, this model assumes an equal chance the monkey will focus on $BC$, $CD$, or $BD$. Either established training pair results in the monkey selecting B, while the pair $BD$ results in an even (therefore 17%) chance of either element being chosen. This predicts that the subjects would select B about 83% of the time, which is near to the average actual performance of 85%.

The binary-sampling theory can be viewed as a naive probabilistic model—it incorporates the concept of expectation, but not in a full-fledged probabilistic framework. It proved controversial both because of lack of parsimony (or explanation) for the ‘imagining’ the extra items, and for apparently contradicting the SDE, since further-apart pairs may require more operations (though see McGonigle and Chalmers 1992). What is significant to the present model is that it motivated McGonigle and Chalmers to generate a data set showing the results of testing monkeys (and later children Chalmers and McGonigle 1984) on triads of three items. The binary-sampling theory predicts that for the triad $BCD$ there is a 17% chance D will be chosen (half of the times $BD$ is attended to), a 33% chance C will be chosen (all of the times $CD$ is attended to) and a 50% chance of B (all of $BC$ plus half of $BD$). Any model using a fully sequential representation, or indeed true TP, would of course predict 0, 0 and 100%. In fact, the monkeys showed 3, 36 and 61%, respectively. Six-year-old human children showed a similar pattern on triad results (Chalmers and McGonigle 1984). While this is a fairly good match, the Harris (1988) production-rule model provides a significantly better one.

Appendix B: details of the simulation

The ALife agents were written in the Common Lisp Object System (CLOS) (Steele 1990), a standard programming language frequently used for artificial intelligence. The code was developed under the Behavior Oriented Design methodology, developed by one of the authors (Bryson 2001), and implemented on top of a graphical software development environment for CLOS called LispWorks (Xanalys 2001).⁹

The artificial intelligence (AI) program that runs the simulations controls not only the learning agents but also the operation of the test apparatus including the recording of results. The program is modular, and the knowledge in the modules representing different real-world agents (the subjects, apparatus and operator) is kept isolated from the other agents’ knowledge. That is, although the testing-apparatus modules contain knowledge about the correct solution of the experiment, the test subject has no direct access to this knowledge except as evidenced by the reward.

On each trial, the testing agent (the apparatus) generates an n-gram (either diad or triad) as appropriate to the current phase of the experiment and places its element in the test-board. The learning agent (the subject) then selects one of the options by transferring it from the test-board to its hand. The apparatus determines whether the subject has chosen correctly and provides reinforcement with either a ‘peanut or a ‘buzzer token. The apparatus also records the trial results, and ends the trial by clearing the testing area.

When the subject is presented with the test-board it selects an object as described (see Fig. 1). When the subject receives reinforcement, it applies the learning rule in Eq. (1) based on its current variable state (its expectations), its current context (the contents of the test board and its hand, and the rules to which it is attending) and the presence or absence of the ‘peanut reward.’

In Experiments 1 and 2, an indefinite number of trials were run until the simulation was terminated by the human experimenter. In Experiment 3, the apparatus was enhanced to run the training and testing procedure shown in Table 1.