Discussion

2.5.1 Overall Performance

In terms of its primary goal of testing whether interval timing could occur within a general model of animal learning, this project was quite successful. The timing performance of the model was very good, equivalent to many of our dedicated timing models. By successfully simulating the performance of animals on an FI schedule, a PI schedule, and a gap schedule, the model demonstrates substantial interval timing abilities. In terms of design, the model met all of the criteria. It maintained its learning abilities while timing, and the changes required for timing were small and there is the possibility that they could be made even smaller with further research. The model was robust in its response to different parameter values, especially the number of nodes required for timing.

While the primary goal of this project was to explore whether interval timing could happen at all within a general learning model, the model created to answer that question can now serve with our other existing models of interval timing. It cannot replace them, but it should provide a unique perspective and comparison for them. Its success raises new theoretical questions that can be pursued through other models and methods.

2.5.2 Difficulties

The principal problem with this general learning model is its failure to scale perfectly. It does scale across a single order of magnitude, but three orders of magnitude are required for the model to approximate the sort of scaling observed in animals. There are two ways to handle this failure to scale. First, it can be taken as a temporary technical setback. It is possible that a general learning model can learn to scale its timing function properly and just has not done so in this case due to problems in the implementation. There are other learning algorithms, and it may simply be a question of hitting upon the right one. This possibility (extant in every computer model) makes it very hard to theorize from the model's inability. As it stands, this model does not scale properly, but that is not to say that a very close cousin could not scale perfectly.

Alternately, this scaling failure could be an inherent limitation of non-clock-based timing systems. If this is so, then it provides us with an interesting theory of the evolutionary pressures that spurred the development of the clock system. If interval timing can be done by any neural system but scaling cannot, then scaling becomes the primary goal of the clock system.

2.5.3 Future Research

This work is intended as a narrowly focused test of a theoretical position, and so the model created to test the position has not been exhaustively explored. There remain a wide variety of extensions that can be made to the model and other animal experiments that can be simulated. One potential line of research is to bring the model closer to the archetypical neural network model. It should be possible to use the recurrent network techniques to maintain interval timing performance while restoring the all-or-nothing property. The output would no longer be a smooth curve, but averaged response rates could produce something similar. This would not provide the network with any new abilities, but it would help generalize these findings. The more different types of neural networks that can produce these kinds of timing results, the more likely that these results will apply to the quite different neural networks in the animal brain.

The integration of learning and interval timing in this model enables it to predict the results of experiments that involve both learning and timing. We can predict novel experiments in which the clock does not simply gather time linearly. For example, subjects might be trained using a PI procedure. During some of the food trials, a tone is presented at a random point during the trial, signaling that the computer controlling the experiment has halved the amount of time that has elapsed so far in the trial. Food will be presented as normal, but will take longer than it would have on a normal food trial. This procedure requires a mental operation unlike any other existing interval timing procedure, a precise manipulation of the animal's or the model's current stored duration.

Because our interval timing models are strictly timing models, they do not do well when faced with experiments where timing is only one of the cognitive abilities required. With this model, it is possible to begin integrating interval timing with other areas of research such as attention, which has also been explored using neural networks. An additional line of research would be to explore to what degree other general learning models can describe interval timing behavior. Backpropagation is not the most biologically plausible learning mechanism, and artificial neural networks are not necessarily the most accurate models of the mental processes of real animals. These issues do not impact the basic claim of this work — that it is possible for a general learning process to time. A next step could be to come as close as possible to proving that the general learning processes used by real animals can also produce interval timing behavior. Of course, we do not have certain knowledge of the precise learning mechanisms of the mind, but there are models that are more similar to what we do know of those mechanisms. Also, replicating these results with several different types of systems would strengthen the hypothesis that any sufficiently general learning mechanism can time, something suggested but not proven by the success of this project.

An example of alternative systems would be to use neural networks trained via genetic algorithms. In this method, a population of artificial neural networks with identical architecture but different weights would be created, and then this population would be made to evolve to better predict the reinforcement interval. Each individual set of weights would be tested to determine how well it predicted the interval and then assigned a fitness value. Those individuals would then have a better chance of passing their weights on to the next generation, modified by mutation and recombination. As each generation is tested and then bred, the individuals gradually become more adapted to predicting the reinforcer.

This learning mechanism has several advantages compared to the backpropaga-tion algorithm used above, such as the ability to explore multiple types of solutions simultaneously. However, this line of research would not be intended to discover which learning mechanism is most effective, but rather to determine the key aspects necessary for a given learning mechanism to be capable of timing. Similar testing could be done on a wide variety of learning mechanisms.

2.5.4 Theoretical Implications

Perhaps the most powerful idea about interval timing presented by this model is how simple it is. Timing can be accomplished with only three nodes, without any special architecture or processes. This implies that interval timing could potentially be found in any animal with a nervous system, unlike more complex models that require the evolutionary development of special-purpose mechanisms. Interval timing has so far been demonstrated in a variety of mammals and birds, and has recently been shown in fish as well (e.g., Talton et al., 1999). This author is also aware of an unpublished study involving the successful training of crabs under an FI schedule. If this model is correct in predicting that interval timing can happen with very few neurons, there is no reason why insects and other organisms with simpler nervous systems could not produce basic timing behavior.

The true difficulty in exploring this idea will be creating the experimental technology necessary to test such things in insects and other small organisms. Presenting the stimuli in a salient manner, providing rewards of an appropriate size and type, and measuring responses are all nontrivial problems in any new species. As always, it is important to distinguish between the failure of the procedure to accurately measure the animal's capabilities and the absence of those capabilities.

The ability of a generalized neural network to time also suggests that interval timing may be ubiquitous within the brain. If any three neurons hooked end to end can time, then we can reasonably expect that any or all subsystems within the brain can time independently if necessary. Areas of the brain dedicated to visual processing may time visual stimuli; auditory areas, auditory stimuli; and so on (see Penney, this volume).

The best comparison for this ubiquitous timing might be our current paradigms for memory. We no longer think of memories as being kept in a single storehouse, but as associated with the areas involved with the processing, such as memory for faces being stored in the face recognition areas. There are discrete areas of the brain that, if damaged, create global effects on memory, but these are thought of as routing depots rather than storehouses. Similarly, there may be discrete brain areas that are globally involved in timing but are not clocks. A search for a central clock may be futile, but that does not mean that all interval timing functions are perfectly distributed. What we have been looking at as central clocks may in fact be central processing areas for timing related information.

The comparison to memory also raises the idea that there may be qualitatively different types of timing within interval timing. It is commonly understood that interval and circadian timing are distinct, but there may be multiple mechanisms contributing to interval timing in animals. We can distinguish implicit and explicit forms of memory, and there is the fascinating possibility that there may be implicit and explicit varieties of interval timing. Implicit timing would be similar to that shown here, requiring no special architecture, but perhaps limited in scale. Explicit timing would rely on a dedicated clock mechanism that is the focus of the vast majority of research in this field (see Meck, this volume). Each would serve different needs, and it might be possible to damage explicit timing while preserving implicit timing, through precisely targeted lesions or genetic manipulation. This is, of course, pure speculation, but one of the primary purposes of behavioral models is to suggest speculative lines of research that can later be followed up with physiological experiments.

This idea of ubiquitous timing may also predict that the total number of intervals that can be timed simultaneously is very large (see MacDonald and Meck, this volume; Meck and Church, 1984; Pang and McAuley, this volume). The smaller the capacity required to time, the more timing that can be done with a given capacity (for discussions of attentional allocation and timing, see Buhusi, this volume; Fortin, this volume). Our typical research paradigms involve simplifying the experiments as much as possible in order to make analysis of the results clearer. This has meant presenting the subjects with as few intervals as are strictly necessary for the experiment, and to the best of my knowledge, no attempt has been made to explore how many separate intervals animals are capable of tracking simultaneously — although Meck (1987) has shown that three signals of different modalities (auditory, tactile, and visual) can be timed simultaneously. Such experiments would have to be carefully designed to avoid running into other cognitive limitations and therefore incorrectly determining a maximum number of intervals that is too low.

If we carry forth the idea of implicit and explicit timing, it may be that the implicit mechanisms can time an unlimited number of stimuli, while the explicit timing mechanisms can only handle a much smaller number of intervals — perhaps even the classic 7 ± 2. It would make sense that implicit timing abilities, drawing only on properties inherent in every neuron, would be essentially unlimited. But the explicit timing areas, being discrete and therefore of fixed capacity, would only be able to time a smaller number of simultaneous events.

This project has successfully achieved its goals. It has shown that interval timing can occur within a general learning model, requiring only minor, common changes. It has also provided a number of theoretical insights and potential lines of research. Most importantly, it offers a new way to look at one of the most fundamental principles of interval timing theory: the internal clock.

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