# List Counting Failures Are Not One Phenomenon

arXiv: https://arxiv.org/abs/2609.22230 · HTML: https://mlsanity.com/paper/2609.22230/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Builds on (most cited first, 21 of 21)

- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Theoretical Limitations of Self-Attention in Neural Sequence Models](https://mlsanity.com/paper/1906.06755/) (2019)
- [LLMs Know More Than They Show: On the Intrinsic Representation of LLM Hallucinations](https://mlsanity.com/paper/2410.02707/) (2024)
- [Do NLP Models Know Numbers? Probing Numeracy in Embeddings](https://mlsanity.com/paper/1909.07940/) (2019)
- [Investigating the Limitations of Transformers with Simple Arithmetic Tasks](https://mlsanity.com/paper/2102.13019/) (2021)
- [Tokenization counts: the impact of tokenization on arithmetic in frontier LLMs](https://mlsanity.com/paper/2402.14903/) (2024)
- [Under the Hood: Using Diagnostic Classifiers to Investigate and Improve how Language Models Track Agreement Information](https://mlsanity.com/paper/1808.08079/) (2018)
- [Softmax is not Enough (for Sharp Size Generalisation)](https://mlsanity.com/paper/2410.01104/) (2024)
- [Scalable-Softmax Is Superior for Attention](https://mlsanity.com/paper/2501.19399/) (2025)
- [Why Do Large Language Models (LLMs) Struggle to Count Letters?](https://mlsanity.com/paper/2412.18626/) (2024)
- [Language Models Need Inductive Biases to Count Inductively](https://mlsanity.com/paper/2405.20131/) (2024)
- [When Can Transformers Count to n?](https://mlsanity.com/paper/2407.15160/) (2024)
- [Counting in Small Transformers: The Delicate Interplay between Attention and Feed-Forward Layers](https://mlsanity.com/paper/2407.11542/) (2024)
- [From Early Encoding to Late Suppression: Interpreting LLMs on Character Counting Tasks](https://mlsanity.com/paper/2604.00778/) (2026)
- [Repeated-Token Counting Reveals a Dissociation Between Representations and Outputs](https://mlsanity.com/paper/2605.09239/) (2026)

## Abstract (arXiv)

Counting the items in a bracketed list looks trivial, yet open-weight chat models often get it wrong. Prior work usually blames input bottlenecks such as subword fragmentation or attention dilution, which predict that different models should fail in roughly the same way. Across seven instruct models on identical prompts, however, wrong answers form distinct modes: Qwen and Gemma 27B often flip odd lengths to a nearby even integer, OLMo concentrates errors on a few mid-sized integers, and Llama tends to under-count. These modes are useful labels rather than a stable family law (Gemma 9B does not reproduce Gemma 27B's odd-to-even drop), and heavier subword fragmentation does not make counting harder on our benchmark. When the model answers incorrectly, a linear probe can usually still recover the true count from the residual stream. Matching the same odd-to-even error also does not imply the same late-MLP magnitude fix: scaling a late MLP output helps Qwen modestly but is near null on Gemma 27B under the same protocol, while residual steering can move both only by trading odd gains for even losses. These results caution against transferring that magnitude fix across models without a transfer check.