Ordinary Least Squares is a Special Case of Transformer
The statistical essence of the Transformer architecture has long remained elusive: Is it a universal approximator, or a neural network version of known computational algorithms? Through rigorous algebraic proof, we show that the latter better describes Transformer's basic nature: Ordinary Least Squares (OLS) is a special case of the single-layer Linear Transformer. Using the spectral decomposition of the empirical covariance matrix, we construct a specific parameter setting where the attention mechanism's forward pass becomes mathematically equivalent to the OLS closed-form projection. This means attention can solve the problem in one forward pass, not by iterating. Building upon this pro...
| Authors | Xiaojun Tan, Yuchen Zhao |
|---|---|
| Primary category | cs.LG |
| Published | 15 April 2026 |
| Last updated at source | 15 April 2026 |
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