The Emergent Symbolic Structure of Artificial Neural Networks

[Submitted connected 30 Aug 2026]

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Abstract:Modern systems successful artificial intelligence (AI) someway excel successful domains for which they look poorly suited. Intelligence has traditionally been modeled arsenic operating complete system combinations of symbols, specified arsenic logical formulas. However, the strongest modern AI systems are based connected neural networks, which alternatively correspond accusation successful continuous vectors. Vectors look inadequate for capturing the building of language, logic, and different cognitive domains, yet neural networks execute awesome capacity successful these areas. How do they do it? In this work, we propose a imaginable answer: Despite appearances, possibly the soul representations of neural networks implicitly recognize symbolic structure. In support of this hypothesis, we show that the vector representations of a assortment of neural networks tin beryllium intimately approximated pinch symbolic structures: we tin switch the network's full representation-generating process pinch a closed-form equation instantiating a symbolic structure, and the network's behaviour remains mostly unchanged. This uncovering holds for some small-scale neural networks trained to manipulate lists arsenic good arsenic ample connection models (LLMs) operating successful 4 domains that are cardinal successful symbolic traditions: arithmetic, logic, machine code, and language. Further, our symbolic approximation allows america to modify an LLM's behaviour successful targeted ways via precise interventions connected its soul representations, showing that the LLM's behaviour is reliant connected the symbolic structures we person identified. This activity provides a imaginable measurement to reconcile longstanding symbolic conceptions of intelligence pinch the vector-based quality of modern AI.