Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
Attention is a smoothed cubic spline
4 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 4representative citing papers
Transformers achieve approximation and generalization error bounds for noisy manifold regression that scale with the intrinsic dimension of the task-level manifold.
Lightning self-attention coefficients are coordinates on an algebraic variety obeying Chow-type, low-rank, Veronese-type, and Sylvester-resultant invariants.
The Transformer is interpreted as discretization of a structured integro-differential equation in continuous domains for tokens and features, unifying attention, feedforward, and normalization via operator and variational views.
citing papers explorer
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Transformers for Learning on Noisy and Task-Level Manifolds: Approximation and Generalization Insights
Transformers achieve approximation and generalization error bounds for noisy manifold regression that scale with the intrinsic dimension of the task-level manifold.
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A Mathematical Explanation of Transformers
The Transformer is interpreted as discretization of a structured integro-differential equation in continuous domains for tokens and features, unifying attention, feedforward, and normalization via operator and variational views.