A measure of complexity of large language models (LLMs) is the number of “parameters” they use. GPT-1 had on the order of 100 million parameters; the recently released GPT-4 used in ChatGPT has on the order of 1 trillion parameters — a ten-thousand-fold increase. I’m not an AI researcher, but I think we can look at human children to see why scaling the number of parameters will likely lead to diminishing returns on intelligence.
Firstly, we need to distinguish between being “intelligent” and being “knowledgeable”. Being “intelligent” refers to the ability to apply reason and thinking to bear on a problem. Being “knowledgeable” refers to the possession of information. A novice intelligent chess player can figure out what move to play based on thinking and planning about the moves on the board. A player who is knowledgeable about chess might know about certain strategies or heuristics that can help them make moves without having to reason about all possible outcomes.
The more parameters an LLM contains, the more potential for knowledge it has. It’s a matter of information entropy: a tiny LLM may not have the space (or at least it’s not important enough) to store the word “Toronto” let alone any concepts associated with that word. However, as the number of parameters increases, there are opportunities for more connections to be formed between “Toronto” and new constructs in the LLM like “Canada”, “transit”, and “CN Tower”. An even larger model might learn things like “Toronto”, “transit”, “Toronto Transit Commission”, “TTC”, “510”, “Spadina”, “Streetcar”, and “Chinatown” are all related concepts.
Similarly, a tiny model might have been trained on lots of examples such that the most probable completion of the string 1 + 1 = is 2. With a much larger model, it might learn that 123 + 456 = 579. There are probably far fewer examples of that string in the wild, so unless parameters are being devoted to that, the LLM may not learn that fact.
And then there’s the whole, well, language thing. An LLM “knows” things like the plural form of words: goat/goats, desk/desks, cup/cups. I’m not an expert here, but I suspect it simply “memorizes” the plural forms and hence irregular words like mouse/mice, knife/knives, and moose/moose pose no additional effort on the LLM.
In the first example above about Toronto transit, things like route numbers for cities don’t follow universal rules. You just have to know them. All else equal, if you want your LLM to know this information without having to look it up, you need a bigger model (or one that devotes more of its parameters to the topic). There’s no two ways about it. Bigger models win.
When it comes to arithmetic, things are different. We memorize our single-digit addition tables and then we learn rules on how to add multi-digit numbers rather than memorize multi-digit additions. As a kid, my parents made sure I knew my 1-times- multiplication tables through to my 9-times table before I started grade school — and how to do multi-digit multiplication through summing values. I spent time in school in Australia and that’s where I was “formally” taught multiplication. But in Australia, I guess due to the legacy of the imperial measurement system, we were expected to know our times tables up to our 12-times table. I decided, at this point, that brute computation was going to serve me better than brute memorization. Sure, if I memorized 6 x 12 = 72, I could do that faster than if I had to do the multiplication out by hand, but I could do it the “long” way quickly enough, thus saving the effort of memorizing this. Besides, that would also let me solve 6 x 13 = 78 just as easily.
Now, I don’t profess to know enough about LLMs to make any kind of knowledgeable claims, but I do know that it’s impossible to memorize every single possible pair of additions that can be done if for no other reason that there’s an infinite number of them. So at some point, maybe an LLM will learn or read about (and “understand”) the pattern thus allowing them to make arbitrary arithmetic computations without having to resort to writing programs and without devoting an unboundedly large amount of parameters to the subject.
Similarly, there’s a “feature” in humans that is sometimes apparent in children known as over-regularization. Up until this point, all our language features are new to them. Plurals, conjugations… everything. Everything to be memorized. But then… aha! There’s a pattern to all of this! Desk/desks, so crab/crabs and knife/knifes. And goose/geese, so moose/meese!1 When I first learned about this, it was kind of mind-blowing that some of us would go through this consolidation period where we temporarily regressed while we “compressed” our knowledge using intelligence.
At some point, I would love to dig more into how LLMs get trained and whether our current techniques can lead to this sort of learning/compression. Regardless of whether it’s possible at this moment, I’d be curious as to what the crossover point is (for a given corpus) where the kind of “understanding” required to generalize a rule becomes cheaper than memorization. For example, if I never had to multiply anything beyond 12 x 12, perhaps it would have been worth my effort to just memorize those 144 multiplication values rather than the 81 required for up to the 9-times tables and then learning how to do the remaining multiplications manually.
What I’d be really fascinated to find out is that learning patterns and rules is an emergent property of LLMs. It probably wouldn’t be too surprising to learn that language patterns like pluralization and conjugation are “compressed” by LLMs in an emergent way due to the amount of entropy we have, at least in English. If we found that to hold true for arithmetic, at what size does that happen at and what other features that we often ascribe to intelligence are inevitable as the size of the model grows?
- For those of you who aren’t necessarily the most fluent in English, yes, it’s weird, but the correct plural of knife in English is knives and the correct plural of moose is moose. ↩︎