One of the most hilarious things you can do with an LLM-based chatbot is to ask it to do calculations. If it’s a well-written chatbot frontend, it can detect requests for arithmetic – like summing 1 and 1 – and pass it on to a dedicated calculator application, even if still cannot correctly count the ‘r’s in ‘strawberry’. This is where [Alvaro Videla] asks the question whether it is at all possible to perform arithmetic with a language model.

Since an LLM at its core is nothing but a vector space of probabilities that a matrix-based inference process uses to create a probabilistic output of tokens you’d not expect a lot of deterministic behavior. How can you do arithmetic without grounding it in some kind of deterministic process?

This is where [Alvaro]’s Rune project comes into play, which is ‘a mechanism-aware JIT compilation project for language-model arithmetic’. Although it is statistically impossible for an LLM to ever correctly perform any random series of arithmetic calculations, you can monitor the internal state of the model and interfere once the parameters of an arithmetic calculation have been identified. By putting the correct result back into the inference process and letting it continue you did not need to rely on external tools.

Ultimately this attempt sort-of worked, but was deemed a failure. It would seem that a language model is the wrong tool after all for replacing the humble calculator.