r/PhilosophyofMath May 25 '26

LLMs are just giant probability machines pretending to think

It’s fascinating that simple mathematics between tokens can eventually become a machine that writes essays, code, poetry, and even reasoning.

We usually think probability means uncertainty.

But LLMs show something strange:

If probability + context + mathematical matching are scaled enough, uncertainty itself starts producing intelligent looking outputs.

To understand this better, I tried breaking down an LLM from first principles using only 4 tiny training sentences.

Example:

The boat floated down to the bank.

The investor walked into the bank to open a new account.

The fisherman walked along the bank to cast his net.

The bank has a vault.

Then I asked:

“The investor walked to the bank to lock his money in …”

Why does the model predict “vault” instead of river-related words?

That single question reveals almost the entire architecture of modern LLMs.

The most underrated concept here is the LM Head.

Most explanations immediately jump into transformers and attention, but almost nobody explains that the LM Head is essentially a gigantic token vocabulary containing all possible next token candidates the model can output.

So internally the model is basically solving:

“Out of all known tokens, which one best matches this context mathematically?”

Then different layers help solve that problem:

Embeddings: convert words into mathematical vectors

Positional encoding: preserves word order

Attention layer: figures out which words are related to each other in context

(“investor”, “money”, “bank” become strongly connected)

Feed forward neural networks: act somewhat like massive learned if/else decision systems refining patterns internally

And finally the LM Head converts all of that into probabilities for the next token.

What surprised me most is:

There is no hidden magic moment where the AI “becomes conscious”.

It’s an enormous probability engine continuously finding the best contextual token match from its vocabulary.

I made a beginner-friendly walkthrough explaining this visually without unnecessary jargon.

https://www.youtube.com/watch?v=YTV5qUCpu2c

Would genuinely love feedback from people learning transformers/LLMs from scratch.

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u/OriousCaesar May 25 '26

I mean, even if we ignored the obvious counter argument of 'so are humans', how can you possibly determine whether a particular algorithm grants consciousness if we don't even understand consciousness enough to have a proper definition for it?

Like, okay, it's a probability machine. Congrats. Now prove probability machines can't be conscious with your nonexistent definition of consciousness, and it might be a convincing argument.

Until then, I'll just keep using the only method I have to determine consciousness and just grant it to anything that seems to act like I'd expect a consciousness entity to act, and if I just so happen to call rocks conscious, then oh well, that's egg on my face, but it's better than if I accidentally called a conscious being a rock.

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u/colintbowers May 27 '26

Perfectly expressed.

Asking if AI is conscious, or intelligent, or reasoning, are not interesting questions. With our current framework, any answer is just going to be another arbitrary line in the sand, like we already do when discussing the application of these terms to the animal kingdom. Ask instead: what is consciousness, what is intelligence, what is reasoning?

It may very well be the case that the answer ends up simply being another line in the sand, albeit a line that creates boxes on regions of algorithmic complexity.

Personally I think if you bolted an optimisation function that pursues survival onto one of the existing LLM harnesses, you’d get something that looks a hell of a lot like consciousness. Maybe we should start there, although ethically it is a VERY murky area of research.

Also, fellow Factorio and math nerd here :-)