Llama-3.1-8B representations for cyclic concepts are circularly structured

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• How does Llama-3.1-8B reason over cyclic concepts?question0.828
  The empirical question the paper addresses through mechanistic investigation
• Linear structure in LLaMA-2-13B representations emerges rapidly in early-middle layers, later for conjunctive statementsfinding0.814
  Layer-wise PCA analysis shows hierarchical development of truth representations across forward pass
• Llama-3.1-8B reuses a single generic addition mechanism across all cyclic tasks independently of concept-specific geometryfinding0.811
  Key mechanistic finding showing task-agnostic reuse of arithmetic circuitry
• Llama-3.1-8B uses base-10 addition rather than modular addition to compute cyclic concept sumsfinding0.808
  The central empirical finding that computation does not mirror the circular representational structure
• Llama-3.1 8B internal representations for the seven days of the week form seven clusters in a circle in activation space.finding0.801
  Empirical observation establishing that Llama's internal representations for days-of-week have circular geometric 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 domainhypothesis0.794
  Predictive hypothesis about domain-generality of the identified mechanism
• 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.finding0.788
  Core empirical result demonstrating that manifold steering produces on-target, behavior-aligned outputs.
• 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)finding0.787
  The complete mechanistic algorithm discovered for cyclic concept reasoning