Comment by wongarsu
24 days ago
Which should be expected, since the same is true for humans. The "adding numbers digit by digit with carry" works well on paper, but it's not an effective method for doing math in your head, and is certainly not how I calculate 14+17. In fact I can't really tell you how I calculate 14+17 since that's not in the "inner monologue" part of my brain, and I have little introspection in any of the other parts
Still, feeding humans their completely made-up self-reflection back can be an effective strategy
The difference is that if you are honest and pragmatic and someone asked you how you added two numbers, you would only say you did long addition if that's what you actually did. If you had no idea what you actually did, you would probably say something like "the answer came to me naturally".
LLMs work differently. Like a human, 14+17=31 may come naturally, but when asked about their though process, LLMs will not self-reflect on their condition, instead they will treat it like "in your training data, when someone is asked how he added number, what follows?", and usually, it is long addition, so that is the answer you will get.
It is the same idea as to why LLMs hallucinate. They will imitate what their dataset has to say, and their dataset doesn't have a lot of "I don't know" answers, and a LLM that learns to answer "I don't know" to every question wouldn't be very useful anyways.
>if you are honest and pragmatic and someone asked you how you added two numbers, you would only say you did long addition if that's what you actually did. If you had no idea what you actually did, you would probably say something like "the answer came to me naturally".
To me that misses the argument of the above comment. The key insight is that neither humans nor LLMs can express what actually happens inside their neural networks, but both have been taught to express e.g. addition using mathematical methods that can easily be verified. But it still doesn't guarantee for either of them not to make any mistakes, it only makes it reasonably possible for others to catch on to those mistakes. Always remember: All (mental) models are wrong. Some models are useful.
Life lesson for you: the internal functions of every individual's mind are unique. Your n=1 perspective is in no way representative of how humans as a category experience the world.
Plenty of humans do use longhand arithmetic methods in their heads. There's an entire universe of mental arithmetic methods. I use a geometric process because my brain likes problems to fit into a spatial graph instead of an imaginary sheet of paper.
Claiming you've not examined your own mental machinery is... concerning. Introspection is an important part of human psychological development. Like any machine, you will learn to use your brain better if you take a peek under the hood.
> Claiming you've not examined your own mental machinery is... concerning
The example was carefully chosen. I can introspect how I calculate 356*532. But I can't introspect how I calculate 14+17 or 1+3. I can deliberate the question 14+17 more carefully, switching from "system 1" to "system 2" thinking (yes, I'm aware that that's a flawed theory), but that's not how I'd normally solve it. Similarly I can describe to you how I can count six eggs in a row, I can't describe to you how I count three eggs in a row. Sure, I know I'm subitizing, but that's just putting a word on "I know how many are there without conscious effort". And without conscious effort I can't introspect it. I can switch to a process I can introspect, but that's not at all the same