Deep neural nets do not learn only from examples! They encode strong inductive
biases in their carefully hand-engineered and hand-tuned architectures, hence
for example CNNs are used for image recognition and LSTMs for sequence
learning etc. Without these biases deep neural nets would not be able to
generalise as well as they do (in the sense of local generalisation but not
global generalisation as meant by François Chollet [1]).

The biggest advances in deep neural nets have come from the discovery and use
of good inductive biases: training with gradient descent, backpropagation,
more hidden layers, the "constant error carousel", convolutional layers, ReLu
over sigmoid, attention, etc, etc. One could say that deep neural nets are all
about good inductive bias.

It's interesting that you bring up the ARC dataset. The paper that introduced
it (also from Chollet) [2] makes a strong claim about the necessity of
"knowledge priors" for a system to be considered intelligent. These are
described at length in section III.1.2 "Core knowledge priors" and are exactly
a set of strong inductive biases that the author of the paper considers
necessary for a machine learning system to solve the ARC tasks and that
consist of such problem-specific biases as object cohesion, object
persistence, object influence via contact, etc. It is exactly such "knowledge
priors" that are encoded as background knowledge in ILP systems.

Indeed, in the ARC challenge on Kaggle, the best-performing systems (i.e. the
ones that solved the most tasks) were crude approximations of the ILP
approach: a library of hand-crafted functions and a brute-force search
procedure to combine them. I note also that attempts to use deep learning to
solve the challenge didn't go anywhere.

Humans also have strong inductive biases that help us solve such problems. But
I'm not the best placed to discuss all this - I'm not a cognitive scientist.

In the end, what you are asking for is magick: a learner that learns only from
examples, without any preconceived notions about how to learn from those
examples, or what to learn from them. There is no such machine learning
system.

>> Doesn't matter, since the programmer gives that information. As you admit,
Louise cannot check for arbitrary programs.

I don't understand what you mean "check for arbitrary programs". I can give
Louise zero BK and metarules and ask it to generate all Prolog programs, say.
Prolog is a Turing complete language so that would give me the set of all
programs computable by a Universal Turing Machine (it would take a while). But
what would that achieve?

At this point I'm not sure I understand what your remaining objections are
against the approach I showed you. For the purpose of learning arbitrary
programs it works better than anything else. Of course it's not magick.
Perhaps you should take my suggestion to think about the problem a bit more
carefully, if you're really intersted in it. Or are you? I mean, if you
consider AI solved, e.g. by GPT-3, then I can see how you wouldn't be
interested in thinking any further about the issue.

_________________

[1] https://blog.keras.io/the-limitations-of-deep-learning.html

[2] https://arxiv.org/abs/1911.01547

P.S. To clarify, I'm keeping this discussion up for your sake, albeit eagerly.
You have expressed some strongly held, but incorrect opinions that it seems to
me you have acquired by consulting inexpert sources, probably because you have
a day job that has nothing to do with AI and doesn't leave you enough time to
study the matter properly. My day job is to study AI and I feel that such a
privilege is only justified if I spend time and effort to help others improve
their knowledge on the subject. I'm guessing that on your part, you're more
interested in "winning" the conversation, but please try to gain something
from our interaction, otherwise all the time we both spent at it would be to
waste. When this is over, try to dig out and read some authoritative sources.
I would advise you on which ones - but you'd probably resist my recommendation
anyway, so you're on your own there.