The part that eludes me is how you get from this to the capability to debug arbitrary coding problems. How does statistical inference become reasoning? For a long time, it seemed the answer was it doesn't. But now, using Claude code daily, it seems it does.
Because it's not statistical inference on words or characters but rather stacked layers of statistical inference on ~arbitrarily complex semantic concepts which is then performed recursively.
If I were to describe this to a nontechnical person, I would say:
LLMs are big stacks of layers of "understanders" that each teach the next guy something.
Imagine you are making a large language model that has 4 layers. Each layer will talk to it's immediate neighbor.
The first layer will get the bare minimum, in the LLM's of today, that's groups of letters that are common to come up together, called "tokens". This layer will try to derive a bit of meaning to tell the next layer, such as grouping of letters into words.
The next layer may be a little bit more semantic, for example interpreting that the word "hot" immediately followed by the word "dog" maps to a phrase "hot dog".
The layer after that, becoming a bit more intelligent given it's predecessors have already had some chances at smaller interpretations may now try to group words into bigger blobs, such as "i want a hot dog" as one combined phrase rather than a set of separated concepts.
The final layer may do something even more intelligent afterward, like realize that this is a quote in a book.
The point is that each layer tries to add a little meaning for the next layer.
I want to stress this: the layers do not actually correspond to specific concepts the way I just expressed, the point is that each layer adds a bit more "semantic meaning" for the next layer.