# Semantic Content Determines Algorithmic Performance

arXiv: https://arxiv.org/abs/2601.21618 · HTML: https://mlsanity.com/paper/2601.21618/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 42 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 30 of 30)

- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Quantifying Language Models' Sensitivity to Spurious Features in Prompt Design or: How I learned to start worrying about prompt formatting](https://mlsanity.com/paper/2310.11324/) (2023)
- [Prompt Programming for Large Language Models: Beyond the Few-Shot Paradigm](https://mlsanity.com/paper/2102.07350/) (2021)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Large Language Models Fail on Trivial Alterations to Theory-of-Mind Tasks](https://mlsanity.com/paper/2302.08399/) (2023)
- [What Algorithms can Transformers Learn? A Study in Length Generalization](https://mlsanity.com/paper/2310.16028/) (2023)
- [Thinking Like Transformers](https://mlsanity.com/paper/2106.06981/) (2021)
- [Unpacking DPO and PPO: Disentangling Best Practices for Learning from Preference Feedback](https://mlsanity.com/paper/2406.09279/) (2024)
- [What Did I Do Wrong? Quantifying LLMs' Sensitivity and Consistency to Prompt Engineering](https://mlsanity.com/paper/2406.12334/) (2024)
- [Alice in Wonderland: Simple Tasks Showing Complete Reasoning Breakdown in State-Of-the-Art Large Language Models](https://mlsanity.com/paper/2406.02061/) (2024)
- [Tighter Bounds on the Expressivity of Transformer Encoders](https://mlsanity.com/paper/2301.10743/) (2023)
- [The No Free Lunch Theorem, Kolmogorov Complexity, and the Role of Inductive Biases in Machine Learning](https://mlsanity.com/paper/2304.05366/) (2023)
- [Why Do Large Language Models (LLMs) Struggle to Count Letters?](https://mlsanity.com/paper/2412.18626/) (2024)
- [Counting Ability of Large Language Models and Impact of Tokenization](https://mlsanity.com/paper/2410.19730/) (2024)
- [Language Models Need Inductive Biases to Count Inductively](https://mlsanity.com/paper/2405.20131/) (2024)
- [Transformers in Uniform TC0](https://mlsanity.com/paper/2409.13629/) (2024)
- [When Can Transformers Count to n?](https://mlsanity.com/paper/2407.15160/) (2024)
- [Prompts Are Programs Too! Understanding How Developers Build Software Containing Prompts](https://mlsanity.com/paper/2409.12447/) (2024)
- [LLM Whisperer: An Inconspicuous Attack to Bias LLM Responses](https://mlsanity.com/paper/2406.04755/) (2024)
- [Can We Count on LLMs? The Fixed-Effect Fallacy and Claims of GPT-4 Capabilities](https://mlsanity.com/paper/2409.07638/) (2024)
- [Counting and Algorithmic Generalization with Transformers](https://mlsanity.com/paper/2310.08661/) (2023)
- [Robustness in Large Language Models: A Survey of Mitigation Strategies and Evaluation Metrics](https://mlsanity.com/paper/2505.18658/) (2025)
- [The Strawberry Problem: Emergence of Character-level Understanding in Tokenized Language Models](https://mlsanity.com/paper/2505.14172/) (2025)
- [Prompt Stability Matters: Evaluating and Optimizing Auto-Generated Prompt in General-Purpose Systems](https://mlsanity.com/paper/2505.13546/) (2025)
- [ChemPile: A 250GB Diverse and Curated Dataset for Chemical Foundation Models](https://mlsanity.com/paper/2505.12534/) (2025)
- [Evaluating Robustness of Large Language Models Against Multilingual Typographical Errors](https://mlsanity.com/paper/2510.09536/) (2025)
- [LLM Knowledge is Brittle: Truthfulness Representations Rely on Superficial Resemblance](https://mlsanity.com/paper/2510.11905/) (2025)
- [SortBench: Benchmarking LLMs based on their ability to sort lists](https://mlsanity.com/paper/2504.08312/) (2025)

## Abstract (arXiv)

Counting should not depend on what is being counted; more generally, any algorithm's behavior should be invariant to the semantic content of its arguments. We introduce WhatCounts to test this property in isolation. Unlike prior work that conflates semantic sensitivity with reasoning complexity or prompt variation, WhatCounts is atomic: count items in an unambiguous, delimited list with no duplicates, distractors, or reasoning steps for different semantic types. Frontier LLMs show over 40% accuracy variation depending solely on what is being counted - cities versus chemicals, names versus symbols. Controlled ablations rule out confounds. The gap is semantic, and it shifts unpredictably with small amounts of unrelated fine-tuning. LLMs do not implement algorithms; they approximate them, and the approximation is argument-dependent. As we show with an agentic example, this has implications beyond counting: any LLM function may carry hidden dependencies on the meaning of its inputs.