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This research establishes a theoretical equivalence between one-layer transformers and multiclass one-nearest-neighbor classifiers, resolving previous limitations regarding standard argmax heads. By utilizing simplex encoding, the study provides rigorous proof that these architectures function identically in high-dimensional spaces without relying on non-standard rounding methods. This finding deepens our understanding of the fundamental representational capacity of shallow transformer models in nearest-neighbor regimes.
One-Layer Transformer Provably Learns Multiclass One-Nearest Neighbor in Context
arXiv:2609.01311v1 Announce Type: new Abstract: We extend recent work establishing an equivalence between one-layer transformers and nearest-neighbor classifiers in the binary setting to the multiclass case. By leveraging the simplex encoding, we show that one-layer transformers with an argmax classification head behave identically to a one-nearest-neighbor classifier in the multiclass setting. This closes a gap left by prior work, whose multiclass result relied on a non-standard rounding-based approach rather than the typical argmax head used in practice.
Abstract:We extend recent work establishing an equivalence between one-layer transformers and nearest-neighbor classifiers in the binary setting to the multiclass case. By leveraging the simplex encoding, we show that one-layer transformers with an argmax classification head behave identically to a one-nearest-neighbor classifier in the multiclass setting. This closes a gap left by prior work, whose multiclass result relied on a non-standard rounding-based approach rather than the typical argmax head used in practice.
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2609.01311 [cs.LG]
(or arXiv:2609.01311v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.01311 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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