# The Validation Gap: A Mechanistic Analysis of How Language Models Compute Arithmetic but Fail to Validate It

arXiv: https://arxiv.org/abs/2502.11771 · HTML: https://mlsanity.com/paper/2502.11771/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 17 Feb 2025.

## Builds on (most cited first, 23 of 23)

- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Generating Sequences by Learning to Self-Correct](https://mlsanity.com/paper/2211.00053/) (2022)
- [FacTool: Factuality Detection in Generative AI -- A Tool Augmented Framework for Multi-Task and Multi-Domain Scenarios](https://mlsanity.com/paper/2307.13528/) (2023)
- [When Can LLMs Actually Correct Their Own Mistakes? A Critical Survey of Self-Correction of LLMs](https://mlsanity.com/paper/2406.01297/) (2024)
- [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (2023)
- [Have Faith in Faithfulness: Going Beyond Circuit Overlap When Finding Model Mechanisms](https://mlsanity.com/paper/2403.17806/) (2024)
- [Verify-and-Edit: A Knowledge-Enhanced Chain-of-Thought Framework](https://mlsanity.com/paper/2305.03268/) (2023)
- [Arithmetic Without Algorithms: Language Models Solve Math With a Bag of Heuristics](https://mlsanity.com/paper/2410.21272/) (2024)
- [Finding Transformer Circuits with Edge Pruning](https://mlsanity.com/paper/2406.16778/) (2024)
- [Evaluating LLMs at Detecting Errors in LLM Responses](https://mlsanity.com/paper/2404.03602/) (2024)
- [Interpreting and Improving Large Language Models in Arithmetic Calculation](https://mlsanity.com/paper/2409.01659/) (2024)
- [A Closer Look at the Self-Verification Abilities of Large Language Models in Logical Reasoning](https://mlsanity.com/paper/2311.07954/) (2023)
- [Intrinsic Self-correction for Enhanced Morality: An Analysis of Internal Mechanisms and the Superficial Hypothesis](https://mlsanity.com/paper/2407.15286/) (2024)

## Built on by (most cited first, 10 of 10)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Attention Illuminates LLM Reasoning: The Preplan-and-Anchor Rhythm Enables Fine-Grained Policy Optimization](https://mlsanity.com/paper/2510.13554/) (2025)
- [Mixture-of-Minds: Multi-Agent Reinforcement Learning for Table Understanding](https://mlsanity.com/paper/2510.20176/) (2025)
- [Reason to Rote: Rethinking Memorization in Reasoning](https://mlsanity.com/paper/2507.04782/) (2025)
- [How LLMs Detect and Correct Their Own Errors: The Role of Internal Confidence Signals](https://mlsanity.com/paper/2604.22271/) (2026)
- [How Does Reasoning Flow? Tracing Attention-Induced Information Flow for Targeted RL in LLMs](https://mlsanity.com/paper/2606.10646/) (2026)
- [A model of errors in transformers](https://mlsanity.com/paper/2601.14175/) (2026)
- [When Tokenization is Secretly Output Supervision](https://mlsanity.com/paper/2609.01386/) (2026)
- [Shared circuits predict whether LLMs generalize across formats in arithmetic reasoning](https://mlsanity.com/paper/2609.04463/) (2026)
- [Rethinking Circuit Evaluation: Do Circuits Explain Model Errors?](https://mlsanity.com/paper/2609.35686/) (2026)

## Abstract (arXiv)

The ability of large language models (LLMs) to validate their output and identify potential errors is crucial for ensuring robustness and reliability. However, current research indicates that LLMs struggle with self-correction, encountering significant challenges in detecting errors. While studies have explored methods to enhance self-correction in LLMs, relatively little attention has been given to understanding the models' internal mechanisms underlying error detection. In this paper, we present a mechanistic analysis of error detection in LLMs, focusing on simple arithmetic problems. Through circuit analysis, we identify the computational subgraphs responsible for detecting arithmetic errors across four smaller-sized LLMs. Our findings reveal that all models heavily rely on textitconsistency heads--attention heads that assess surface-level alignment of numerical values in arithmetic solutions. Moreover, we observe that the models' internal arithmetic computation primarily occurs in higher layers, whereas validation takes place in middle layers, before the final arithmetic results are fully encoded. This structural dissociation between arithmetic computation and validation seems to explain why smaller-sized LLMs struggle to detect even simple arithmetic errors.