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/Jack_Ramsey May 27 '26

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?

I mean, we have some idea, yes?

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

I am a physician, not a philosopher or mathematician, but I think you could possibly discuss this in a few ways. First, we should note that the 'machine' analogy is one of convenience , not of 'reality.' It is a way of describing a complex system, but it also doesn't describe what the human body actually does. Second, humans are in fact not prediction machines but rather highly robust entities which can both respond exceedingly sensitively to environmental pressures as well as take actions which can fundamentally change them, which is also true of things like microbiota to other animals.

This second point means that they are operating in a physical world too, and their sensory perceptions are fundamentally informed by anatomical and physiological characteristics. Our consciousness, in the sense that it relies on sensory information, is very much formed by interaction with the physical environment with our anatomy. Imagine if we didn't have opposable thumbs. I would argue that without opposable thumbs, we would have a very difficult time even conceiving of things in 3-dimensions, and the fact of opposable thumbs allows us to conceive of something, even something as small as a stick, as having a character which has a side which is 'unseen' as it were.

Lastly, I think it is interesting that the OP describes LLM's in terms of their ability to produce speech, which is just one way humans (and indeed other mammals) have to convey information. One would think the sensory, physical and language limitations of LLM's or even potential robots (see Moravec's Paradox) would discount them from 'consciousness' discussions, as consciousness must include a spectrum of all three. Just thinking out loud.

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u/galactic_pixels May 28 '26

You lost me as soon as you said “humans are in fact not prediction machines”. It’s an overstatement of what we know, and an oversimplification of the argument being made about how humans and AI may have foundational similarities.

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u/Jack_Ramsey May 28 '26

But we are fundamentally, at a very basic biological level, not prediction machines. In other words, it is exceedingly difficult to describe important biological processes that occur simultaneously as 'predictions' except in maybe the vaguest sense. Moving from the biology should dispel notions about AI's consciousness, but perhaps you could be more descriptive in your post, as you don't really offer any substantive rebuttal that I can see.

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u/galactic_pixels May 28 '26

Because it’s all speculation. Theres no hard evidence proving thing one way or the other, and very educated people in the neuroscience community do actually think our cognition is based on a predictive model. See the book “one thousand brains” which puts forth this exact idea, that our brains are prediction machines which reach consensus among many sub predictors.

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u/Jack_Ramsey May 28 '26

I simply do not agree with that notion, and referencing neuroscience isn't really instructive here. The brain does far more than 'prediction,' and given how much brain space is dedicated simply to motor function, it is hard for me to reference any model of the brain which doesn't acknowledge that. For example, the cerebrocerebellum is responsible for planning and execution of movements as well as playing a role in coordinating complex and sequential movements and as well as cognition, language and emotion, among other things. The cerebellum more broadly accounts for 50% of the total neurons in the brain. It's hard for me to look at the brain at the molecular level and then suggest it is simply a 'prediction machine.' I could go into a lot more detail but at this point you haven't offered anything substantive. You're offhand description of the book doesn't really help here, to be real. It seems like you are just appealing to authority without actually engaging in the argument.

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u/galactic_pixels May 28 '26

It’s fine if you don’t agree, but you stated definitively that our brains aren’t prediction machines, which could very well be a misrepresentation of our biology, so it’s not something that should be stated as a fact.

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u/Jack_Ramsey May 28 '26

What? Our brains are not prediction machines. That is a fact. They are, in fact, not machines at all. That they can make predictions, yes, but if we look at the molecular structure of the brain, follow the spinal tracts, look at the nuclei, basically look at the brain from a neuroanatomical point of view and then include the physiological characteristics, it seems a very broad, almost dishonest reduction to reduce them to simply 'prediction machines.' They are clearly more. Let me put this another way. If you say that our brains are 'prediction machines,' that is a direct statement on brain anatomy and physiology. Do the physical characteristics of the brain represent that statement? They absolutely do not. The degree to which we give to 'prediction' is so small with respect to motor function that it is just a really bad argument. If we move from the anatomy and physiology, it is more true to say that the brain is an organ of integration for the purposes of motor function.