mlsanityData to 14 Oct 2026

Addition in Four Movements: Mapping Layer-wise Information Trajectories in LLMs

arXiv 2506.07824 ↗First posted 9 Jun 2025cs.AIcited by 4

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Abstract (arXiv)

Multi-digit addition is a clear probe of the computational power of large language models. To dissect the internal arithmetic processes in LLaMA-3-8B-Instruct, we combine linear probing with logit-lens inspection. Inspired by the step-by-step manner in which humans perform addition, we propose and analyze a coherent four-stage trajectory in the forward pass:Formula-structure representations become linearly decodable first, while the answer token is still far down the candidate list.Core computational features then emerge prominently.At deeper activation layers, numerical abstractions of the result become clearer, enabling near-perfect detection and decoding of the individual digits in the sum.Near the output, the model organizes and generates the final content, with the correct token reliably occupying the top rank.This trajectory suggests a hierarchical process that favors internal computation over rote memorization. We release our code and data to facilitate reproducibility.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 13 of its 22 references that are in the map. First posted on arXiv 9 Jun 2025.

Builds on

13 of 22 references.

References · 13

  1. 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,090
  2. 2021Probing Classifiers: Promises, Shortcomings, and Advancescited by 876
  3. 2023Progress measures for grokking via mechanistic interpretabilitycited by 839
  4. 2024Arithmetic Without Algorithms: Language Models Solve Math With a Bag of Heuristicscited by 97
  5. 2024AceMath: Advancing Frontier Math Reasoning with Post-Training and Reward Modelingcited by 77
  6. 2025Language Models Use Trigonometry to Do Additioncited by 70
  7. 2023Towards a Mechanistic Interpretation of Multi-Step Reasoning Capabilities of Language Modelscited by 50
  8. 2024Pre-trained Large Language Models Use Fourier Features to Compute Additioncited by 39
  9. 2023Understanding Addition in Transformerscited by 34
  10. 2024Backward Lens: Projecting Language Model Gradients into the Vocabulary Spacecited by 32
  11. 2024Language Models Encode Numbers Using Digit Representations in Base 10cited by 32
  12. 2024Interpreting Arithmetic Mechanism in Large Language Models through Comparative Neuron Analysiscited by 31
1 more
  1. 2024Language Models Encode the Value of Numbers Linearlycited by 20

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Verbalizable Representations Form a Global Workspace in Language Modelscited by 75
  2. 2026Directional Reasoning Trajectory Change (DRTC): Identifying Critical Trace Segments in Reasoning Modelscited by 1
  3. 2026The Diminishing Returns of Early-Exit Decoding in Modern LLMscited by 1
  4. 2026The Shape of Addition: Geometric Structures of Arithmetic in Large Language Modelscited by 0