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)

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• Llama-3.1-8B uses base-10 addition rather than modular addition to compute cyclic concept sumsfinding0.882
  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 domainhypothesis0.841
  Predictive hypothesis about domain-generality of the identified mechanism
• Does Llama compute modular addition or base-10 addition for cyclic tasks?question0.836
  The specific computational question the paper resolves empirically
• Llama-3.1-8B reuses a single generic addition mechanism across all cyclic tasks independently of concept-specific geometryfinding0.827
  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)finding0.825
  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.quote0.822
  Verbatim summary of the main discovery.
• Llama-3.1 8B internal representations for the seven days of the week form seven clusters in a circle in activation space.finding0.804
  Empirical observation establishing that Llama's internal representations for days-of-week have circular geometric structure.
• 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.finding0.799
  Core empirical result demonstrating that manifold steering produces on-target, behavior-aligned outputs.