claim

active

claim:circular-representational-structure-does-not-imply-that-the-model-computes-using-the-corresponding-modular-arithmetic

Circular representational structure does not imply that the model computes using the corresponding modular arithmetic

The paper's primary interpretive claim, directly answering the central question

Source paper

extracted_from

Arithmetic in the Wild: Llama uses Base-10 Addition to Reason About Cyclic Concepts

(2026) · Sheridan Feucht · Tal Haklay · Usha Bhalla · Daniel Wurgaft +8

Neighborhood — ranked by edge-count

Findings (4)

finding

Llama-3.1-8B uses base-10 addition rather than modular addition to compute cyclic concept sums
associated_withsupports
The central empirical finding that computation does not mirror the circular representational structure
Llama-3.1-8B reuses a single generic addition mechanism across all cyclic tasks independently of concept-specific geometry
supports
Key mechanistic finding showing task-agnostic reuse of arithmetic circuitry
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)
supports
The complete mechanistic algorithm discovered for cyclic concept reasoning
Llama-3.1-8B representations for cyclic concepts are circularly structured
supports
The representation geometry finding that motivates the question about whether computation mirrors it

Questions (1)

question

Does structure in representations imply structure in computation?
gates
The central research question motivating the paper

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Representation-computation mismatch (Feucht: cyclic concepts computed in base-10, not circular geometry) will force About Blank to decouple 'representational geometry' from 'operational structure' in prediction0.778
The analogous circular structure between representation manifold and behavior manifold is downstream of training data and its implicit cyclic conceptual structure.claim0.768
The paper's causal explanation for why representation and behavior geometry both appear circular for days of the week.
We hypothesize that representation geometry drives model behavior — the geometric structure of internal representations causally shapes what models do externally.hypothesis0.761
The causal hypothesis motivating the use of causality (intervention) as the lens connecting representation and behavior geometry.
Representation and computation can diverge; cyclic geometry is representational invariant while operations use generic substrate.claim0.761
How do representations differ or converge between architectures, tasks, and modalities?question0.749
Broader research question MAS is positioned to address, citing multiple recent works.
geometric structure in neural network representations drives model behaviorclaim0.748
Interpretive assertion that representation geometry is not epiphenomenal but causally shapes what models do externally.
An addition module in layer 18 of Llama-3.1 8B performs arithmetic using circular geometric representations of numbers.quote0.748
Verbatim summary of the main discovery.
How does representation geometry causally drive model behavior?question0.748
The central scientific question the paper addresses through the lens of interventional causality.