> strong evidence that LLMs has very limited capability to learn logical structures that can't be represented as grammar.
To add multi-digit numbers requires short term memory (are we on the units, or tens? was there a carry?), which LLMs don't have, so that's really the issue.
The normal workaround for lack of memory in LLMs is "think step-by-step" to use it's own output (which gets fed back in as an input) as memory, and I'd assume that with appropriate training data and prompting an LLM could learn to do it in this fashion - not just giving the answer, but by giving all the steps.
I suppose in theory LLMs could do limited precision math even without memory, if they did it in a single pass through their stack of transformer layers (96 for GPT-3) - use first few layers to add units and generate carry, next few layers to add tens, etc. I'm not sure how, or even if, one could train them to do it this way though - perhaps via a curriculum training agenda of first adding single digit numbers, then two-digit ones, etc ?
To add multi-digit numbers requires short term memory (are we on the units, or tens? was there a carry?), which LLMs don't have, so that's really the issue.
The normal workaround for lack of memory in LLMs is "think step-by-step" to use it's own output (which gets fed back in as an input) as memory, and I'd assume that with appropriate training data and prompting an LLM could learn to do it in this fashion - not just giving the answer, but by giving all the steps.
I suppose in theory LLMs could do limited precision math even without memory, if they did it in a single pass through their stack of transformer layers (96 for GPT-3) - use first few layers to add units and generate carry, next few layers to add tens, etc. I'm not sure how, or even if, one could train them to do it this way though - perhaps via a curriculum training agenda of first adding single digit numbers, then two-digit ones, etc ?