| Shallow representation and approximation upper bounds, nonquantitative | statement | theorem 6 | arxiv |
| Global Sobolev-to-Barron embedding for $\operatorname{ReLU}^s$ | statement | lemma 20 | arxiv |
| Reverse OU energies for Gaussians | statement | lemma 7 | arxiv |
| 32RNSNYCG0 | statement | lemma 2 | arxiv |
| Shallow approximation width lower bound | statement | corollary 3 | arxiv |
| 5RK2HM885W | statement | proposition 6 | arxiv |
| Wasserstein and KL lower bounds | statement | proposition 2 | arxiv |
| Perturbative feature learning, single-index ReLU pushforward | example | example 2 | arxiv |
| Hermite decay for ReLU difference and tanh | statement | lemma 31 | arxiv |
| Hermite tail shallow approximation lower bound | statement | proposition 9 | arxiv |
| Stein distance between Gaussians | statement | lemma 5 | arxiv |
| 96WYPKQ15Q | statement | proposition 5 | arxiv |
| Perturbative feature learning, autonomous single-index flows | example | example 3 | arxiv |
| Shallow representation and approximation lower bounds, quantitative | statement | theorem 5 | arxiv |
| Shallow approximation lower bound, ResNet pushforward | statement | theorem 4 | arxiv |
| Rotation-equivariant $D_{\h_k}$ bounds for single-index Gaussian flows | statement | lemma 10 | arxiv |
| Shallow approximation upper bound, nonquantitative | statement | proposition 10 | arxiv |
| Rotation-equivariant $D_{\h_k}$ perturbative lower bound | statement | lemma 9 | arxiv |
| CMR89C1F44 | statement | lemma 17 | arxiv |
| Feature learning comparison, informal | statement | theorem 2 | arxiv |
| First-order $D_{\h_k}$ lower bound | statement | lemma 8 | arxiv |
| Rotation-equivariant kernel | definition | definition 1 | arxiv |
| Integrated shallow approximation lower bound | statement | corollary 1 | arxiv |
| DHWAB1VWJ3 | statement | lemma 23 | arxiv |
| Reverse OU, perturbative single-index flows and tilts | example | example 1 | arxiv |
| Shallow representation lower bound | statement | lemma 28 | arxiv |
| F1T54FHTP6 | statement | lemma 12 | arxiv |
| F95TFDFK4H | example | example 5 | arxiv |
| Triangular structure | statement | lemma 27 | arxiv |
| Shallow representation lower bound | statement | corollary 2 | arxiv |
| FPKEYMG98C | statement | proposition 1 | arxiv |
| Efficient generative modeling of multi-index pushforwards | problem | problem 3 | arxiv |
| GMKKGEKCM6 | statement | proposition 3 | arxiv |
| Shallow function class | definition | definition 7 | arxiv |
| Nonperturbative feature learning, autonomous single-index flows | example | example 4 | arxiv |
| $D_\b$ metric | definition | definition 5 | arxiv |
| Hermite branching lemma | statement | lemma 30 | arxiv |
| JWWQRBWABT | statement | lemma 13 | arxiv |
| Condition for reverse OU (sub)optimality | statement | lemma 1 | arxiv |
| Barron distance between Gaussians | statement | lemma 6 | arxiv |
| Shallow representation upper bound | statement | lemma 29 | arxiv |
| First-order $D_{\b_\phi}$ lower bound | statement | lemma 11 | arxiv |
| Truncated Gaussian averaging operator | definition | definition 9 | arxiv |
| Shallow representation lower bound, ResNet pushforward | statement | theorem 3 | arxiv |
| Early-stopping lower bound | statement | lemma 32 | arxiv |
| Barron space, homogeneous | definition | definition 4 | arxiv |
| Allocation of depth/layerwise supervision | problem | problem 4 | arxiv |
| Wasserstein and KL control | statement | lemma 3 | arxiv |
| Shallow representation bounds for $\operatorname{ReLU}^3$ | statement | proposition 11 | arxiv |
| Efficient generative modeling of ResNet pushforwards | problem | problem 2 | arxiv |
| Denoising suboptimality, informal | statement | theorem 1 | arxiv |
| Cylindrical Schwartz functions are Barron w.r.t. $\operatorname{ReLU}^s$ | statement | lemma 19 | arxiv |
| Hermite width envelope | definition | definition 8 | arxiv |
| SXX0Z938AB | statement | proposition 8 | arxiv |
| T46WY1NAGB | definition | definition 2 | arxiv |
| Triangular ResNet | definition | definition 10 | arxiv |
| Shallow representation upper bound, nonquantitative | statement | lemma 21 | arxiv |
| Early-stopping error, ${\operatorname{KL}}$ | statement | lemma 26 | arxiv |
| Early-stopping error, $\operatorname{TV}$ and $W_1$ | statement | lemma 25 | arxiv |
| Barron space, bounded | definition | definition 3 | arxiv |
| Single-index flows | statement | lemma 14 | arxiv |
| Nonperturbative shortcuts in rotation-equivariant RKHS | statement | proposition 7 | arxiv |
| Shallow approximation lower bound in $L^2(\gamma_n)$ via Hermite tail | statement | lemma 22 | arxiv |
| Third derivative representation lower bound | statement | lemma 18 | arxiv |
| XY43W17K2X | problem | problem 1 | arxiv |
| Y7VW7W8VN9 | statement | lemma 24 | arxiv |
| Single-index tilts | statement | lemma 16 | arxiv |
| Reverse OU, Gaussian-to-Gaussian | statement | proposition 4 | arxiv |
| YXNVWKKPWY | statement | lemma 15 | arxiv |
| Triangular shear measure | definition | definition 6 | arxiv |
| ZKK6Y5KCPZ | statement | lemma 4 | arxiv |
