# A Categorical Analysis of Large Language Models and Why LLMs Circumvent the Symbol Grounding Problem

arXiv: https://arxiv.org/abs/2512.09117 · HTML: https://mlsanity.com/paper/2512.09117/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 64 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Builds on (most cited first, 22 of 22)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [A Survey of Hallucination in Large Foundation Models](https://mlsanity.com/paper/2309.05922/) (2023)
- [Experience Grounds Language](https://mlsanity.com/paper/2004.10151/) (2020)
- [Grounding Large Language Models in Interactive Environments with Online Reinforcement Learning](https://mlsanity.com/paper/2302.02662/) (2023)
- [A Categorical Archive of ChatGPT Failures](https://mlsanity.com/paper/2302.03494/) (2023)
- [Meaning without reference in large language models](https://mlsanity.com/paper/2208.02957/) (2022)
- [The Vector Grounding Problem](https://mlsanity.com/paper/2304.01481/) (2023)
- [Provable Separations between Memorization and Generalization in Diffusion Models](https://mlsanity.com/paper/2511.03202/) (2025)
- [A Survey of Automatic Hallucination Evaluation on Natural Language Generation](https://mlsanity.com/paper/2404.12041/) (2024)
- [Transforming Agency. On the mode of existence of Large Language Models](https://mlsanity.com/paper/2407.10735/) (2024)
- [Categorical Stochastic Processes and Likelihood](https://mlsanity.com/paper/2005.04735/) (2020)
- [The Mechanistic Emergence of Symbol Grounding in Language Models](https://mlsanity.com/paper/2510.13796/) (2025)
- [Knowledge Representation in Bicategories of Relations](https://mlsanity.com/paper/1706.00526/) (2017)
- [Category-Theoretical and Topos-Theoretical Frameworks in Machine Learning: A Survey](https://mlsanity.com/paper/2408.14014/) (2024)
- [OracleAgent: A Multimodal Reasoning Agent for Oracle Bone Script Research](https://mlsanity.com/paper/2510.26114/) (2025)
- [Forget BIT, It is All about TOKEN: Towards Semantic Information Theory for LLMs](https://mlsanity.com/paper/2511.01202/) (2025)
- [Notes on Category Theory with examples from basic mathematics](https://mlsanity.com/paper/1912.10642/) (2019)
- [A Roadmap for Embodied and Social Grounding in LLMs](https://mlsanity.com/paper/2409.16900/) (2024)
- [A Rose by Any Other Name Would Smell as Sweet: Categorical Homotopy Theory for Large Language Models](https://mlsanity.com/paper/2508.10018/) (2025)
- [Higher-Order Regularization Learning on Hypergraphs](https://mlsanity.com/paper/2510.26533/) (2025)

## Built on by (most cited first, 3 of 3)

- [Can We Predict Before Executing Machine Learning Agents?](https://mlsanity.com/paper/2601.05930/) (2026)
- [LLMs Don't Pay for the Jump](https://mlsanity.com/paper/2608.14397/) (2026)
- [The LLM Proposes, the Executive Disposes: A Self-Verifying Agent Instrument that Dissociates Commitment Drift from Binding Drift in Long-Horizon Agents](https://mlsanity.com/paper/2608.04066/) (2026)

## Abstract (arXiv)

This paper presents a formal, categorical framework for analysing how humans and large language models (LLMs) transform content into truth-evaluated propositions about a state space of possible worlds W , in order to argue that LLMs do not solve but circumvent the symbol grounding problem.