Llama-3.1-8B uses base-10 addition rather than modular addition to compute cyclic concept sums

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• We hypothesize that Llama-3.1-8B deploys the same base-10 addition circuitry for cyclic reasoning as it uses for general arithmetic, independent of the concept domainhypothesis0.902
  Predictive hypothesis about domain-generality of the identified mechanism
• Llama-3.1-8B implements a two-stage algorithm: (1) compute integer sum via base-10 addition (e.g., six + August = 14), then (2) map sum to cyclic concept space (14 → February)finding0.882
  The complete mechanistic algorithm discovered for cyclic concept reasoning
• Llama-3.1-8B reuses a single generic addition mechanism across all cyclic tasks independently of concept-specific geometryfinding0.858
  Key mechanistic finding showing task-agnostic reuse of arithmetic circuitry
• Llama-3.1-8B uses task-agnostic Fourier features with periods 2, 5, and 10 (base-10) rather than concept-specific periods (e.g., 12 for months)finding0.833
  The specific Fourier feature periods identified confirm base-10 rather than modular computation
• An addition module in layer 18 of Llama-3.1 8B performs arithmetic using circular geometric representations of numbers.quote0.830
  Verbatim summary of the main discovery.
• How does Llama-3.1-8B reason over cyclic concepts?question0.830
  The empirical question the paper addresses through mechanistic investigation
• Base-10 Addition Mechanism in Llamaconcept0.821
• Llama-3.1-8B representations for cyclic concepts are circularly structuredfinding0.808
  The representation geometry finding that motivates the question about whether computation mirrors it