Question 1
I had a quick question. I noticed that your baseline model that you’re reporting results on is a human-constructed grammar, right? Do you have an intuition or understanding of why MaxEnt’s issue, in this context, is with precision? Do you have an interpretation of that, or is there something we should think about regarding the learning process?
My Answer
For the poor performance of the baseline, I can tell you exactly why it’s bad. It’s because two of the constraints—no final LH/HL and no LHL—are too strong. They’re too restrictive. Our dataset actually contains some data points that violate these two constraints. The other three constraints—no rise, no monosyllabic contour, and no superheavy syllable—are perfectly fine. So it’s mostly these two overly strong constraints that hurt the baseline. As for MaxEnt, besides the lack of frequency information, I don’t yet have an explanation for its relatively low precision.
Question 2
One of your findings is that frequency information is critical for MaxEnt, but not for BUFIA. I was wondering whether you have a normative judgment about whether frequency information should be necessary for learning. Is it more human-like for frequency information to be required? Conversely, if you have a learning algorithm where frequency information isn’t important, could that mean the algorithm has an inductive bias that’s perhaps too strong to be human-like?
My Answer
We don’t have any judgment about what implications this has for human language learning. I think that’s something we could investigate in future work, perhaps using external evidence. Right now, we’re simply looking at when frequency information is needed in a learning scheme. What we can say from these results is that if you use categorical learning together with a more linguistically explicit representation, then frequency information is not necessarily needed in this setting. That’s the main takeaway regarding the importance of frequency.
Question 3
One of your conclusions is that BUFIA-AR achieves the best performance. I was wondering if you could say a little more about the representation side. For example, if we think about a language-acquiring child, do we assume they simply begin with this type of representation? Or is the representation itself part of the learning process? If so, could you say a little about how your conclusions bear on that question?
What I should have said
The representations themselves are not learned. We formalize each representation in the same model-theoretic framework, where it defines a hypothesis space with a containment relation. BUFIA searches this hypothesis space, starting from simple structures and gradually expanding them into more complex ones. The representation is provided by the user, not learned by the algorithm. As long as it can be formalized model-theoretically with a containment relation, BUFIA can learn over it. This is probably analogous to how children might acquire phonological knowledge—starting with simpler generalizations before considering more complex ones—although our model is not intended as a model of language acquisition.