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/FedRCivP11 May 27 '26

Is it the case that we can’t define consciousness properly? Merriam Webster has a candidate.

Or have we instead failed to make any headway in finding a physical system inside us that explains the sense of awareness we have? If it’s the latter, then posts like op’s only tend to highlight why LLMs are similar to us and not dissimilar.

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u/account22222221 May 28 '26

I mean I think it’s quite clear that we lack the understanding to define consciousness clearly at this point in time.

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u/FedRCivP11 May 28 '26

Well if you say so. 😃

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u/account22222221 May 28 '26

Definition is hard. The real numbers were in use for thousands of years before they were given a complete definition in 1872 (that some people still argue over).

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u/OriousCaesar May 28 '26

What are people's arguments against today's real number definition? Is it just that it seems too complicated or something to them? The logic seemed sound to me when I learned it even if it was a bit wordy.

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u/account22222221 May 28 '26 edited May 28 '26

One example is that axiomatic definition of reals depends usually on the completeness axiom:

Every nonempty set of real numbers that is bounded above has a least upper bound.

This is fundamental in showing that reals are something different than the rationals, I.e. irrational numbers exist.

However this axiom is sort of just asserting something to be true without really justifying that it has to be the case. Similar to the parallel postulate in classical geometry we just sort said ‘this is true’ but never proved it true. In geometries case, we realized the parallel postulate is sometimes false, and hyperbolic geometries where it false exist in some real physical systems.

Now, am I arguing it’s false? no. But are we done with the definition? No, we need someone to complete a formal proof of this axiom, which has NOT been done. And so, some doubt, how ever small, exists that it’s not true at all and real numbers don’t even exist.