LLMs are fundamentally probabilistic systems built on vector spaces and matrix inference, making deterministic arithmetic inherently unreliable. Alvaro Videla's Rune project explores a novel approach: monitoring the internal state of an LLM during inference to detect when arithmetic parameters are identified, then injecting the correct result back into the inference pipeline without relying on external calculator tools. While the approach partially worked, it was ultimately deemed a failure, reinforcing that language models are the wrong tool for replacing even basic calculators.
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