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--> Computer Science > Computation and Language arXiv:2608.29530 (cs) [Submitted on 30 Aug 2026] Title: The Emergent Symbolic Structure of Artificial Neural Networks Authors: R. Thomas McCoy , Paul Soulos , Tal Linzen , Paul Smolensky View a PDF of the paper titled The Emergent Symbolic Structure of Artificial Neural Networks, by R. Thomas McCoy and Paul Soulos and Tal Linzen and Paul Smolensky View PDF HTML (experimental) Abstract: Modern systems in artificial intelligence (AI) somehow excel in domains for which they seem poorly suited. Intelligence has traditionally been modeled as operating over structured combinations of symbols, such as logical formulas. However, the strongest modern AI systems are based on neural networks, which instead represent information in continuous vectors. Vectors seem inadequate for capturing the structure of language, logic, and other cognitive domains, yet neural networks achieve impressive performance in these areas. How do they do it? In this work, we propose a potential answer: Despite appearances, perhaps the internal representations of neural networks implicitly realize symbolic structure. In support of this hypothesis, we show that the vector representations of a variety of neural networks can be closely approximated with symbolic structures: we can replace the network's entire representation-generating process with a closed-form equation instantiating a symbolic structure, and the network's behavior remains largely unchanged. This finding holds for both small-scale neural networks trained to manipulate lists as well as large language models (LLMs) operating in four domains that are central in symbolic traditions: arithmetic, logic, computer code, and language. Further, our symbolic approximation allows us to modify an LLM's behavior in targeted ways via precise interventions on its internal representations, showing that the LLM's behavior is reliant on the symbolic structures we have identified. This work provides a potential way to reconcile longstanding symbolic conceptions of intelligence with the vector-based nature of modern AI. Comments: 30 pages, plus 29 pages of references and appendices Subjects: Computation and Language (cs.CL) ; Artificial Intelligence (cs.AI) Cite as: arXiv:2608.29530 [cs.CL] (or arXiv:2608.29530v1 [cs.CL] for this version) https://doi.org/10.48550/arXiv.2608.29530 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tom McCoy [ view email ] [v1] Sun, 30 Aug 2026 03:32:13 UTC (1,107 KB) Full-text links: Access Paper: View a PDF of the paper titled The Emergent Symbolic Structure of Artificial Neural Networks, by R. Thomas McCoy and Paul Soulos and Tal Linzen and Paul Smolensky View PDF HTML (experimental) TeX Source view license Current browse context: cs.CL < prev | next > new | recent | 2026-08 Change to browse by: cs cs.AI References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation &times; loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? )