A standard Transformer with O(ε^{-d0/α}) blocks can approximate any bounded d0-dimensional Hölder function of smoothness α to accuracy ε, but at least Ω(ε^{-d0/(4α)}) blocks are required.
Nonparametric regression using deep neural networks with ReLU activation function , volume=
7 Pith papers cite this work, alongside 203 external citations. Polarity classification is still indexing.
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A per-layer risk estimator for hybrid deep networks shows that replacing learned layers with known operators shrinks the bound and scales sample needs with the number of replaced parameters, validated on CT reconstruction.
Finite-sample risk bounds for DQN with ReLU networks are extended to τ-mixing data, showing an extra dimensionality penalty in the convergence rate due to dependence.
A recipe translates ReLU approximations to softmax attention with target-specific economic bounds for multiplication, reciprocal computation, and min/max primitives.
A semi-supervised kernel two-sample test integrates unlabeled covariate data to achieve asymptotic normality under the null, higher power than standard kernel tests, and consistency against fixed and local alternatives.
Neural feature maps create expressive kernels that enable fast, scalable, and consistent exact Gaussian process inference for regression and classification.
The deep SPAR model shows concurrent floods and droughts becoming more likely in the Upper Danube by 2100 under high emissions, with changes in the dependence between catchments contributing substantially to the increase.
citing papers explorer
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Approximation Error Upper and Lower Bounds for H\"{o}lder Class with Transformers
A standard Transformer with O(ε^{-d0/α}) blocks can approximate any bounded d0-dimensional Hölder function of smoothness α to accuracy ε, but at least Ω(ε^{-d0/(4α)}) blocks are required.
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A Deep Risk Estimator for Known Operator Learning
A per-layer risk estimator for hybrid deep networks shows that replacing learned layers with known operators shrinks the bound and scales sample needs with the number of replaced parameters, validated on CT reconstruction.
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Beyond the Independence Assumption: Finite-Sample Guarantees for Deep Q-Learning under $\tau$-Mixing
Finite-sample risk bounds for DQN with ReLU networks are extended to τ-mixing data, showing an extra dimensionality penalty in the convergence rate due to dependence.
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Transformer Approximations from ReLUs
A recipe translates ReLU approximations to softmax attention with target-specific economic bounds for multiplication, reciprocal computation, and min/max primitives.
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A Semi-Supervised Kernel Two-Sample Test
A semi-supervised kernel two-sample test integrates unlabeled covariate data to achieve asymptotic normality under the null, higher power than standard kernel tests, and consistency against fixed and local alternatives.
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Scalable Gaussian process inference via neural feature maps
Neural feature maps create expressive kernels that enable fast, scalable, and consistent exact Gaussian process inference for regression and classification.
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Exploring climate change effects on concurrent floods and concurrent droughts via statistical deep learning
The deep SPAR model shows concurrent floods and droughts becoming more likely in the Upper Danube by 2100 under high emissions, with changes in the dependence between catchments contributing substantially to the increase.