There's a lot to unpack here. I agree that a large part of creating AGI is building in the right priors ("learning priors" is a bit of an oxymoron imo, since a prior is exactly the part you don't learn, but it makes sense that a posterior for a pre-trained model is a prior for a fine-tuned model).

Invariance and equivariance are a great example. Expressed mathematically, using symbols, it makes no sense to say a model is more or less equivariant - it either is or it isn't. If you explicitly build equivariance into a model (and apparently it's not as straightforward as e.g. just using convolutions), then this is really what you get. For example, the handwriting model from my blogpost has real translational equivariance (because the location of a character is sampled).

If you instead learn the equivariance, you will only ever learn a shortcut - something that works on training and test data, but not universally, as the paper from the twitter thread shows. Just like the networks that can solve the LEGO task for 6 variables don't generalize to any number of variables, learning "equivariance" on one dataset (even if it's a huge one) doesn't guarantee equivariance on another. A neural network can't represent an algorithm like "for all variables, do x", or constraints like "f(g(x)) = g(f(x)), for all x" - you can't represent universal quantifiers using finite dimensional vectors.

That being said, you can definitely learn some useful priors by training very large networks on very large data. An architecture like the Transformer allows for some very general-purpose priors, like "do something for pairs of tokens 4 tokens apart".