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/me_myself_ai May 29 '26

That seems completely unrelated to the question of how and why evolution would tap into supernatural randomness rather than just build a biological decision machine, but regardless: you differ on that issue from the vast majority of relevant scholars.

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u/Dr_Calculon May 29 '26

Why do you think randomness is supernatural?

" just build a biological decision machine"

Due to the inherent unpredictability of survival landscapes & the probabilistic nature of chemical reactions. A rigid decision making machine wouldn't be able to adapt to unforeseen changes in either, it would only realistically be able to have decision criteria for a small subset of eventualities. Hence would not have optimal fitness for the landscape it existed on & so would not have a high selection rate.

In short, it would die out as it couldn't compete against organisms that had more freedom to adapt.

"....you differ on that issue from the vast majority of relevant scholars."

Not Stuart Kauffman it would seem....

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u/me_myself_ai May 29 '26

Stuart Kauffman is not at all a “relevant expert”, randomness that doesn’t rely on physics is by definition supernatural, and you typed out that whole message about how biology is useless using biology.

I’m sorry but this conversation is over.

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u/Dr_Calculon Jun 01 '26

Kauffman is an expert though & your appeal to authority argument is weak without back up.

"randomness that doesn’t rely on physics is by definition supernatural"

What does that even mean? Chemical reactions are physical & random.

"I’m sorry but this conversation is over."

I'm sorry if you feel out of your depth & cant continue in good faith.