A shallow dense Transformer achieves uniform epsilon-approximation of alpha-Holder functions with O(epsilon^{-d/alpha}) parameters and near-minimax generalization error O(n^{-2alpha/(2alpha+d)} log n).
Finding the homology of submanifolds with high confidence from random samples.Discrete & Computational Geometry, 39(1):419– 441
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Authors introduce the Pursuit of Subspaces (PoS) hypothesis, an axiomatic geometric framework that unifies explanations for representation, computation, and generalization in shallow and deep neural networks.
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Learning Theory of Transformers: Local-to-Global Approximation via Softmax Partition of Unity
A shallow dense Transformer achieves uniform epsilon-approximation of alpha-Holder functions with O(epsilon^{-d/alpha}) parameters and near-minimax generalization error O(n^{-2alpha/(2alpha+d)} log n).
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Axiomatizing Neural Networks via Pursuit of Subspaces
Authors introduce the Pursuit of Subspaces (PoS) hypothesis, an axiomatic geometric framework that unifies explanations for representation, computation, and generalization in shallow and deep neural networks.