https://youtu.be/wPonuHqbNds?t=1199

Chomsky's apparently erroneous critique of Transformer-based LLMs is
actually correct in the larger sense. His apparent error?

Ask ChatGPT the following:

"What is the grammar diagram for the sentence:
The friends of my brothers are in England."

Contrary to what Chomsky says, it will produce the correct structure and,
indeed, if asked "Who is in England, my brother or their friends?" It will
answer correctly.

The larger sense in which Chomsky is correct is given in the paper "Neural
Networks and the Chomsky Hierarchy".  See, in particular, Figure 1, which
classifies Transformers as at the bottom rung in the Chomsky Hierarchy of
grammars.  The reason for this classification is similar to the reason that
diagram places RNNs just above Transformers despite the fact that
topologically speaking, they are capable of emulating a universal Turing
machine (which is at or next to the top grammar, depending on how strict
one wants to be):

The pragmatic limits on gradient descent training algorithms combined with
that of attempting to represent a UTM's writable store in RNN form.

Transformers can, within the context length they provide, learn grammars
with recursion depth to some extent (much shorter than their context
length) -- but aside from the limited recursion per sentence, there is also
the fact that that number of parameters goes up as the square of the
context length, which makes total document comprehension subject to limits
that natural language understanding is not.

This distinction becomes crucial when the field of AI ethics refuses to
address the IS vs OUGHT distinction head-on and, instead, comes up with all
manner of unprincipled "metrics" that they use to "quantify" properties of
LLMs such as "bias" or "safety" or "toxicity" or "hallucination" or... the
list goes on and on. By conflating IS with OUGHT they commit the first and
most egregious transgression against ethics and they even do so in the name
of "ethics". AIs that cannot comprehend the cognitive _structure_ of the
_entire_ corpus on which they are trained, cannot critically examine the
utterances contained therein for self-consistency. That means they are
incapable of _constructing_ truth even as defined _relative_ to the corpus
as the universe of observations being modeled. I one pointed Chomsky to his
colleague, Marvin Minsky's final plea to the field of AI, that they take
seriously Algorithmic Information Theory's power in discerning truth.
Minsky was so forceful in his admonition that he recommended everyone spend
the rest of their lives studying it. Chomsky's response? People should take
Minsky's advice.

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