On Approximate Interpretation

Another seminar that I went to in the McGill Psychology department in 2005 was given by Iris van Rooij, a young researcher in cognitive science with a background in computer science. Her talk focused on looking at the issue of computational complexity within cognitive science and her thesis went something like this:

When psychologists describe humans as performing some task, they need to bear in mind that humans must have the cognitive resources to do so.

This is not particularly controversial. My earlier posts argued that humans DON’T have the cognitive resources to compute or understand the implications of the average of 800 large decision trees.

However, the example she gave was was quite different. Her example was the categorization problem. That is, one of the things cognitive scientists think we do is to automatically categorize the world — to decide that some things are chairs and others plants and yet others pacifiers-with-mustaches-drawn-on. Moreover, we don’t just classify the world, we also work out what the classes (and possibly subclasses are) and we do so at a very young age. There is, after all, no evolutionary reason that we should be born knowing what a chair is, or a pacifier-with-mustaches, either.

van Rooij’s problem with this was that the classification problem is NP-hard. This takes a bit of unpacking. Imagine the problem that we have a set of objects, and have some measure that quantifies how similar each pair of objects is. We now want to sort them into a set of classes where the elements of any class are closer to each other than they are to elements of any other class. It turns out that this problem, if you want to get it exactly right, takes computational effort that grows very quickly as the number of objects you are dealing with increases. For even a few hundred objects the amount of time required to produce a categorization on the sort of laptop that I run will end up measured in years, and humans are certainly not much faster at most computation.** Thus, said van Rooij, we cannot reasonably say that humans are solving the categorization problem.

Now the natural response is that “Well obviously we’re not carrying out this form of mathematical idealization.” In fact, when computers are required to do something like this they use a set of heuristic approaches that don’t exactly solve the problem, but hopefully come somewhere close. van Rooij reply would be (actually was) “Then you should describe what humans are actually doing.” Now this is fair enough as it goes, but I still thought “Surely the description that this is the sort of problem we’re trying to solve still has value.”

This is a specific case of saying “the world behaves approximately like this”, or even “my model behaves approximately like this”. From a scientific perspective, the initial proposition “Humans carry out categorization” opens the way to exploring how we do so, or try to do so. So dismissing this approximate description because it isn’t computationally feasible that we exactly solve a mathematical idealization just prevents psychologists from using a good launching pad. With any such claim, they will almost certainly discover that the statements are naive and humans more error-prone than the claim implies.

But it also opens the question of what description of what humans do would suffice? We could certainly go down to voltages traveling between neurons in the brain, but this is unlikely to be particularly helpful for us “understanding” what is going on (even if that level of detail were experimentally, or computationally, feasible). After all, most of the experiments involving this task involve visual stimuli, at least, so various visual processing systems are involved, as well as memory, spacial processing (since we mostly think of grouping objects into piles) and who knows what else. It’s also not clear how specific all of this will be to the individual human. However, it is likely that any other description is only going to be approximate, even if it is now computationally feasible in a technical sense.

I think the higher level description of “they’re sorting the world into categories” is valuable, even knowing that it’s not exactly right, because it allows scientists to conceptualize the questions they’re asking, or to employ this task for other experiments. Of course, this is a very “science by interpretation” framework; a devotee of the ML viewpoint would presumably say that you should just predict what they will do and plug that into whatever you need it for.

By the same token, an approximate description of what the 800 bagged decision trees are doing is often enough to provide humans will some notion of what they need to think about, at least until we have computers to also plan our experiments for us. Of course any approximation has to come with caveates about where it works and when the narrative it gives you leads you in the wrong direction. It’s perfectly reasonable to say “humans categorize the world” if you are interested in using this task as some form of distraction for subjects while studying something else. It may too simplistic if the categories they come up with is part of what you are going to look at. Cognitive scientists are forced to start from the broad over-simplified statement and work out experimentally how it needs to be made more complicated. When looking at an ML model, we can see all of it directly and I’ll spend a post (in a little bit) on how that gets done.

Next, however, are models for dynamics and the distinction between being mechanistic and being interpretable.

**¬†¬†Quantum computers don’t face the same hurdles, but while there are quantum effects in biology, I don’t think we can claim it in the brain.

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