A simplified one-layer transformer provably learns parities first with explicit CoT supervision then internalizes to direct computation as CoT tokens are removed.
Hardness of learning fixed parities with neural networks
2 Pith papers cite this work. Polarity classification is still indexing.
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Deep sequence models develop geometric memory in embeddings that encodes novel global relationships, transforming l-fold composition tasks into 1-step navigation via a natural spectral bias connected to Node2Vec.
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Learning through Internalization
A simplified one-layer transformer provably learns parities first with explicit CoT supervision then internalizes to direct computation as CoT tokens are removed.