Interpolation is a much narrower construct then generalization. LLMs are fundamentally much closer to curve fitting (where interpolation is king) then they are to hypothesis testing (where samples are used to describe populations), though they certainly do something akin to the latter to.
The bias I am talking about is not a bias in the training data, but bias in the curve fitting, probably because of mal-adjusted weights, parameters, etc. And since there are billions of them, I am very skeptical they can all be adjusted correctly.
As for bias, I don’t see the distinction you are making. Biases in the training data produce biases in the weights. That’s where the biases come from: over-fitting (or sometimes, correct fitting) of the training data. You don’t end up with biases at random.
As for bias, sampling bias is only one many types of biases. I mean the UNIX program YES(1) has a bias towards outputting the string y despite not sampling any data. You can very easily and deliberately program a bias into everything you like. I am writing a kanji learning program using SSR and I deliberately bias new cards towards the end of the review queue to help users with long review queues empty it quicker. There is no data which causes that bias, just program it in there.
I don‘t know enough about diffusion models to know how biases can arise, but with unsupervised learning (even though sampling bias is indeed very common) you can get a bias because you are using wrong, mal-adjusted, to many parameters, etc. even the way your data interacts during training can cause a bias, heck even by random one of your parameters hits an unfortunate local maxima yielding a mal-adjusted weight, which may cause bias in your output.
I'm not particularly well-versed in LLMs, but isn't there a step in there somewhere (latent space?) where you effectively interpolate in some high-dimensional space?
The LLM uses attention and some other tricks (attention, it turns out, is not all you need) to build a probabilistic model of what the next token will be, which it then sampled. This is much more powerful than interpolation.
It’s a subtle distinction, but I think an important one in this case, because if it was interpolation then genuine creativity would not be possible. But the attention mechanism results in model building in latent space, which then affects the next token distribution.
My reasons to subscribing to the latter camp is that when you have a distribution and you fit things according to that distribution (even when the fitting is stochastic; and even when the distribution belongs in billions of dimensions) you are doing curve fitting.
I think the one extreme would be a random walk, which is obviously not curve fitting, but if you draw from any other distribution then the uniform distribution, say the normal distribution, you are fitting that distribution (actually, I take that back, the original random walk is fitting the uniform distribution).
Note I am talking about inference, not training. Training can be done using all sorts of algorithms, some include priors (distributions) and would be curve fitting, but only compute the posteriors (also distributions). I think the popular stochastic linear descent does something like this, so it would be curve-fitting, but the older evolutionary algorithm just random walks it and is not fitting any curve (except the uniform distribution). What matters to me is that the training arrives at a distribution, which is described by a weight matrix, and what inference is doing is fitting to that distribution (i.e. the curve).
Except in the most technical sense that any function constrained to meet certain input output values is an interpolation. But that is not the smooth interpolation that seems to be implied here.