Semantic Content Determines Algorithmic Performance

2026-01-29

AI Summary

This work investigates the susceptibility of large language models (LLMs) to input semantics when performing algorithmic tasks that should be semantically agnostic, such as counting. Challenging the fundamental principle that algorithmic behavior ought to be independent of semantic content, the study introduces WhatCounts—an atomic counting benchmark designed to isolate semantic effects. Through controlled ablation studies and comparisons across semantic categories, while eliminating confounding factors like reasoning complexity and prompt interference, the authors systematically demonstrate for the first time that mainstream LLMs exhibit substantial implicit dependence on input semantics. Experimental results reveal counting accuracy disparities exceeding 40% between semantic classes (e.g., cities vs. chemicals), and show that fine-tuning can unpredictably alter this dependency. These findings indicate that current models merely approximate, rather than genuinely possess, general-purpose algorithmic capabilities.

Technology Category

• Natural Language Processing: (Large) Language Models
• Machine Learning: Large Multimodal Models (LMMs)
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

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.

Problem

• semantic content
• algorithmic invariance
• large language models
• counting task
• input dependency

Innovation

• semantic sensitivity
• algorithmic invariance
• large language models
• WhatCounts benchmark
• input-dependent approximation