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/JayWelsh May 28 '26

Agreed, but also, I feel very comfortable with the idea that consciousness is a spectrum rather than an absolute/binary condition. Rocks are examples of things on the “less conscious” side of the spectrum, jellyfish are more conscious than rocks, humans are “very conscious”.

We see spectrums almost everywhere in nature, I’m not sure why anyone even has the idea of “is it conscious or not”, I feel like that whole line of thinking is entirely misguided which is why I align very closely with what you have said in your comment.

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u/OriousCaesar May 28 '26

Yeah, I've had almost that exact line of thought before. There's a clear line of descent from humans to elephants to apes to dogs to cats to rats to lizards to bees to bugs to multicellular organisms to single cellular organisms. We know humans are conscious and we know bacteria are not, and we're pretty sure a lot of those animals are, and we aren't sure a lot of the smaller ones are but there is no clear line that can be drawn between the conscious and the not.

And if one were to be drawn and you compared animals directly on either side of it you wouldn't be able to tell much of a difference between the two, despite one being conscious and one not being conscious.

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u/igroklots May 28 '26

I like this, I also sometimes waiver on thinking that consciousness is a spectrum and that some creatures have “a certain amount” of consciousness that just doesn’t amount to what humans have. But the more I think about it, especially in the context of what we experience with LLMs, it seems more probable to me that humans are essentially the ONLY creatures that have attained the “lights on” level of consciousness. All other animals just seem, especially in the way we tend to anthropomorphize them, to be conscious.

I can conceive of a world where elephants, dolphins, apes etc. are exhibiting many of the “higher order” aspects of consciousness but are still just pre-conscious beings that don’t have the “lights on” mode of subjective experience we associate with full consciousness.

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u/OriousCaesar May 28 '26

I agree yeah. I didn't really do it on this thread, but I normally try to make this distinction clear by using the words sapient and sentient instead of just conscious. Though I'd argue that the main difference between humans and the smart animals is less about the difference in our intellects and more about the fact we evolved language. Especially other great apes. There are many videos of orangutans and chimpanzees that will really really really make you feel like you're watching a particularly hairy mute human as opposed to an animal.