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The Emergent Symbolic Structure of Artificial Neural Networks

arXiv:2608.29530CLAI30 aug 20261 min readHN ×3PDF

Inside neural networks, vectors secretly behave like structured symbols: roles bound to fillers.

0.903

accuracy

Average causal-intervention accuracy, GPT-OSS

Editing symbolic parts of representations changes the LLM's answers as predicted

How it works

  1. Vectors versus symbols

    Language, math and code need structure, such as who did what to whom. Neural networks only store lists of numbers.

  2. Fit a symbolic formula

    DISCOVER replaces a network's internal vectors with a closed-form Tensor Product Representation built from roles and fillers.

  3. Behavior barely changes

    Networks run on the formula's vectors still answer correctly. Editing one role or filler shifts outputs as predicted.

match vectorsTPR vectorsInputsequenceTarget networkencodingsFit TPRequationSwap intonetworkCheck output,intervenematch vectorsTPR vectorsInputsequenceTarget networkencodingsFit TPRequationSwap intonetworkCheck output,intervene
From the paper