An addition module in layer 18 of Llama-3.1 8B performs arithmetic using circular geometric representations of numbers.

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• Llama-3.1-8B uses base-10 addition rather than modular addition to compute cyclic concept sumsfinding0.830
  The central empirical finding that computation does not mirror the circular representational structure
• 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 domainhypothesis0.828
  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)finding0.822
  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 geometryfinding0.818
  Key mechanistic finding showing task-agnostic reuse of arithmetic circuitry
• Does Llama compute modular addition or base-10 addition for cyclic tasks?question0.810
  The specific computational question the paper resolves empirically
• Llama-3.1-8B representations for cyclic concepts are circularly structuredfinding0.785
  The representation geometry finding that motivates the question about whether computation mirrors it
• Steering Llama-3.1 8B along the circular representation manifold produces outputs that follow the natural circle of the behavior manifold, cleanly shifting probability mass from Monday through successive days.finding0.785
  Core empirical result demonstrating that manifold steering produces on-target, behavior-aligned outputs.
• Base-10 Addition Mechanism in Llamaconcept0.780