I don't doubt that it can perform addition in multiple ways. I would go as far as saying it can probably attempt to perform addition in more ways than the average person as it has probably been trained on a bunch of math. Can it perform it correctly? Sometimes. That's ok, people make mistakes all the time too. I don't take away from LLMs just because they make mistakes. The ability to do math in multiple ways is not evidence of thinking though. That is evidence that it's been trained on at least a fair bit of math. I would say if you train it on a lot of math, it will attempt to do a lot of math. That's not thinking, that's just increasing the weighting on tokens related to math. If you were to train an LLM on nothing but math and texts about math, then asked it an art question, it would respond somewhat nonsensically with math. That's not thinking, that's just choosing the statistically most likely next token.

I had no idea about artificial neurons, TIL. I suppose that makes "neural networks" make more sense. In my readings on ML they always seemed to go straight to the tensor and overlook the neuron. They would go over the functions to help populate the weights but never used that term. Now I know.

I would point out I think you might be overly confident in the manner in which it was trained addition. I'm open to being wrong here, but when you say "It was not trained to do trigonometry to solve addition problem", that suggests to me either you know how it was trained, or are making assumptions about how it was trained. I would suggest unless you work at one of these companies, you probably are not privy to their training data. This is not an accusation, I think that is probably a trade secret at this point. And if the idea that there would be nobody training an LLM to do addition in this manner, I invite you to glance the Wikipedia article on addition. Really glance at literally any math topic on Wikipedia. I didn't notice any trigonometry in this entry but I did find the discussion around finding the limits of logarithmic equations in the "Related Operations" section: https://en.m.wikipedia.org/wiki/Addition. They also cite convolution as another way to add in which they jump straight to calculus: https://en.m.wikipedia.org/wiki/Convolution.

This is all to say, I would suggest that we don't know how they're training LLMs. We don't know what that training data is or how it is being used exactly. What we do know is that LLMs work on tokens and weights. The weights and statistical relevance to each of the other tokens depends on the training data, which we don't have access to.

I know this is not the point, but up until this point I've been fairly pedantic and tried to use the correct terminology, so I would point out that technically LLMs have "tensors" not "neurons". I get that tensors are designed to behave like neurons, and this is just me being pedantic. I know what you mean when you say neurons, just wanted to clarify and be consistent. No shade intended.

I don't think you can disconnect how an LLM was trained from how it operates. If you train an LLM to use trigonometry to solve addition problems, I think you will find the LLM will do trigonometry to solve addition problems. If you train an LLM in only Russian, it will speak Russian. I would suggest that regardless of what you train it on it will choose the statistically most likely next token based on its training data.

I would also suggest we don't know the exact training data being used on most LLMs, so as outsiders we can't say one way or another on how the LLM is being trained to do anything. We can try to extrapolate from posts like the one that you linked to how the LLM was trained though. In general if that is how the LLM is coming to its next token, then the training data must be really heavily weighted in that manner.

My apologies, I was too vague. I'm saying "thinking" by definition is not "statistics". Where Monkeys, birds, and human babies all "think", LLMs use algorithms and "statistics". I also think that "statistics" not meaning the same thing that "thinking" is a valid argument. I would go farther and say it's important that words have meaning. That is what I was attempting to convey. I'm happy to clear up anything I was unclear about.

I think you can make a strong argument that they don't think rooted in words should mean something and that statistics and thinking don't mean the same thing. To me, that feels like a fairly valid argument.

Is the argument that LLMs are thinking because they make guesses when they don't know things combined with no provided quantity or quality to describe thinking?

If so, I would suggest that the word "guessing" is doing a lot of heavy lifting here. The real question would be "is statistics guessing"? I would say guessing and statistics are not the same thing, and Oxford would agree. An LLM just grabs tokens based on training data on what word or token most likely comes next, it will just be using what the statistically most likely next token or word is. I don't think grabbing the highest likely next token counts as guessing. That feels very algorithmic and statistical to me. It is also possible I'm missing the argument still.

If the LLM could reason, shouldn't it be able to say "my token training prevents me from understanding the question as asked. I don't know how many 'r's there are in Strawberry, and I don't have a means of finding that answer"? Or at least something similar right? If I asked you what some word in a language you didn't know, you should be able to say "I don't know that word or language". You may be able to give me all sorts of reasons why you don't know it, and that's all fine. But you would be aware that you don't know and would be able to say "I don't know".

If I understand you correctly, you're saying the LLM gets it wrong because it doesn't know or understand that words are built from letters because all it knows are tokens. I'm saying that's fine, but it should be able to reason that it doesn't know the answer, and say that. I assert that it doesn't know that it doesn't know what letters are, because it is incapable of coming to that judgement about its own knowledge and limitations.

Being able to say what you know and what you don't know are critical to being able to solve logic problems. Knowing which information is missing and can be derived from known things, and which cannot be derived is key to problem solving based on reason. I still assert that LLMs cannot reason.

I don't think the current common implementation of AI systems are "thinking" and I'll base my argument on Oxford's definitions of words. Thinking is defined as "the process of using one's mind to consider or reason about something". I'll ignore the word "mind" and focus on the word "reason". I don't think what AIs are doing counts as reasoning as defined by Oxford. Let's go to that definition: "the power of the mind to think, understand, and form judgments by a process of logic". I take issue with the assertion that they form judgments. For completeness, but I don't think it's definition is particularly relevant here, a judgment is: "the ability to make considered decisions or come to sensible conclusions".

I think when you ask an LLM how many 'r's there are in Strawberry and questions along this line you can see they can't form judgments. These basic but obscure questions are where you see that the ability to form judgements isn't there. I would also add that if you "form judgments" you probably don't need to be reminded you formed a judgment immediately after forming one. Like if I ask an LLM a question, and it provides an answer, I can convince it that it was wrong whether or not I'm making junk up or not. I can tell it it made a mistake and it will blindly change it's answer whether it made a mistake or not. That also doesn't feel like it's able to reason or make judgments.

This is where all the hype falls flat for me. It feels like sometimes it looks like a concrete wall, but occasionally that concrete wall is made of wet paper. You can see how impressive the tool is and how paper thin it is at the same time. It's cool, it's useful, it's fake, and that's ok. Just be aware of what the tool is.

If you think about it, this was perhaps the most humane way to conduct war. No humans were harmed in this attack, and the ability to harm humans was severely degraded. You had drones smash into unmanned airplanes. Nothing but money and hardware was lost. This is the utopian version of war if such a thing could ever exist. One country removes another country's ability to harm humans with nobody getting hurt and everyone gets to go home.