I’d like to add one more layer to this great explanation.

Usually, this kind of predictions should be made in two steps:

1. calculate the conditional probability of the next word (given the data), for all possible candidate words;

2. choose one word among these candidates.

The choice in step 2. should be determined, in principle, by two factors: (a) the probability of a candidate, and (b) also a cost or gain for making the wrong or right choice if that candidate is chosen. There’s a trade-off between these two factors. For example, a candidate might have low probability, but also be a safe choice, in the sense that if it’s the wrong choice no big problems arise – so it’s the best choice. Or a candidate might have high probability, but terrible consequences if it were the wrong choice – so it’s better to discard it in favour of something less likely but also less risky.

This is all common sense! but it’s at the foundation of the theory behind this (Decision Theory).

The proper calculation of steps 1. and 2. together, according to fundamental rules (probability calculus & decision theory) would be enormously expensive. So expensive that something like chatGPT would be impossible: we’d have to wait for centuries (just a guess: could be decades or millennia) to train it, and then to get an answer. This is why Large Language Models do two approximations, which obviously can have serious drawbacks:

• they use extremely simplified cost/gain figures – in fact, from what I gather, the researchers don’t have any clear idea of what they are;

• they directly combine the simplified cost/gain figures with probabilities;

• They search for the candidate with the highest gain+probability combination, but stopping as soon as they find a relatively high one – at the risk of missing the one that was actually the real maximum.

I think that the theory behind these algorithms can actually be explained in very common-sense term, without too much technobabble, as @TheChurn’s comment showed.

We don’t understand it because no one designed it. We designed how to train a nn, we designed some parts of the structure, but not the individual parts inside. For the largest LLMs there are upwards of 70 billion different parameters. Each being individual numbers they were can tweak. The are just too many of them to understand what any individual one does, and since we just left a optimization algorithm do it’s optimizing we can’t really even know what groups of them do.

We can get around this, we can study it like we do the brain. Instead of looking at what an individual part does, group them together and figure out how they group influences things (AI explanability), or even get a different NN to look at it and generate an explanation (post hoc rationale generation). But that’s not really the same as actually understand what it is actually doing under the hood. What it is doing under the hood is more or less fundamentally unknowable, there is just to much information and it’s not well organized enough for us to be able to understand. Maybe one day we will be able to abstract what is going on in there and organize it in an understandable manner, but not yet.

It’s not it’s biological origins that make it hard to understand the brain, but the complexity. For example, we understand how the heart works pretty well.

While LLMs are nowhere near as complex as a brain, they’re complex enough to make it extremely difficult to understand.

But then there comes the question: if they’re so difficult to understand, how did people make them in the first place?

The way they did it actually bears some similarities to evolution. They created an “empty” model - a large neural network that wasn’t doing anything useful or meaningful. But it depended on billions of parameters, and if you tweak a parameter, its behavior changes slightly.

Then they expended enormous amount of computing power tweaking parameters, each tweak slightly improving its ability to model language. While doing this, they didn’t know what each number meant. They didn’t know how or why each tweak was improving the model. Just that each tweak was making an improvement.

Unlike evolution, each tweak isn’t random. There’s an algorithm called back-propagation that can tell you how to tweak the neural network to make it predict some known data slightly better. But unfortunately it doesn’t tell you anything about the “why” this tweak is good, or “what” each parameter change means. Hence why we don’t understand how LLMs work.

One final clarification: It’s not a complete black box. We do have some understanding of how LLM works, mostly on high level. Kind of like we have some basic understanding of how a brain works. We understand LLMs much better than brains, of course.

From my extremely limited understanding, it’s because of the sheer scale of the data that’s been fed into LLMs, and because of the (admittedly small) possibility that the people working on LLMs never really took the time to understand what sort of connections the LLM was making between all the datapoints it was interacting with and drawing connections between, or at least a deeper understanding of how the math worked; just that it did.

As the scale of the project kept growing and LLM companies just kept throwing ‘more data, more neural networks, more hardware!’ into the mix, the black box became…well, blacker and it kept getting harder to figure out the internal ‘logic’ used by the LLM to predict the next word. Now, the people who’re trying to figure it all out are working with extremely large amounts of data with nothing to go off of.

In short, the people making GPT were somehow smart enough to make it, but not smart enough to understand what they were making.