Depth-L transformers with W parameters have VC dimension Theta(L W log(T W)), yielding matching O(L W log((T+T')W)) upper and Omega(L W log((T+T')W/L)) lower bounds on sample complexity for chain-of-thought learning.
An analysis of attention via the lens of exchangeability and latent variable models
3 Pith papers cite this work. Polarity classification is still indexing.
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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).
Spectrum-adaptive post-hoc generalization bounds for multi-layer Transformers are derived using layerwise Schatten quantities whose indices are chosen after training based on singular-value profiles.
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Tight Sample Complexity of Transformers
Depth-L transformers with W parameters have VC dimension Theta(L W log(T W)), yielding matching O(L W log((T+T')W)) upper and Omega(L W log((T+T')W/L)) lower bounds on sample complexity for chain-of-thought learning.
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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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Spectrum-Adaptive Generalization Bounds for Trained Deep Transformers
Spectrum-adaptive post-hoc generalization bounds for multi-layer Transformers are derived using layerwise Schatten quantities whose indices are chosen after training based on singular-value profiles.