Arithmetic Without Numbers: How LLMs Do Math
Original: Arithmetic Without Numbers – How LLMs Do Math
A technical explainer on how LLM activations can expose arithmetic structure without prompt parsing.
The article asks whether LLM arithmetic is memorization, heuristics, real computation, or experimental assistance. It summarizes Rune experiments that decode operations and operands from frozen Llama activations, then route them to Python under a no-parser rule. The strongest supported claim is narrow: activation-derived tool arguments worked in scoped audits, while residual-state JIT replacement, long-number generation, and cross-model transfer remain brittle.
This interactive long-form article discusses a question stricter than "letting an LLM call a calculator": when a model answers gcd, lcm, multiplication, or division-remainder problems, does it internally form an operation and operands that can be read out? Using the Rune project as the main thread, the author distinguishes several easily confused situations: directly parsing the prompt with regex, having the model produce code or a tool call, correcting the answer at the final token, reading tool arguments out of activations, and writing the computed result back into the residual stream so the model naturally continues. The article emphasizes that being able to make the model output the correct number does not mean the model actually performed the calculation; and being able to read a variable out of the residual stream does not mean that location is a safely writable API.
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Summaries are AI-generated; the original article is authoritative.