arXiv Machine Learning
Sharp Approximation Rates for Neural Networks with Affine Latent Parameterizations
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arXiv Machine Learning
1d ago
A Closed-Form Formula for Consistent Lipschitz Regression on Metric Spaces with Sparse Neural Network Realizations
arXiv:2609. 03129v1 Announce Type: cross Abstract: Several classical machine-learning methods, such as KRRs and SVRs, are both computationally and analytically tractable since their estimators either admit closed-form expressions or are obtained by minimizing convex training objectives; neither feature is generally available for deep neural networks.
arXiv Machine Learning
Jul 14
Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width
arXiv:2607. 10589v1 Announce Type: cross Abstract: In contrast to most studies on neural network approximation theory that characterize results through a single parameter, such as the total number of network parameters, \cite{shen2020deep} pioneered the characterization of approximation rates as a joint function of the width parameter $N$ and the depth parameter $L$, thereby granting greater architectural flexibility.
arXiv Machine Learning
Jul 9
On Explicit Super-Expressive Approximation for Neural Networks
arXiv:2607. 06781v1 Announce Type: new Abstract: In this work, we investigate the fixed-architecture neural network approximation with explicit parameter bounds and elementary activations.
arXiv Machine Learning
1d ago
Parameterized Hardness of Zonotope Containment and Neural Network Verification
The paper proves that several decision and approximation problems for ReLU neural networks are computationally hard. For any number of layers λ≥2, deciding whether a network’s output is positive (and thus whether it is surjective) is W[ℓ−1]-hard when parameterized by the input dimension d. In particular, for two-layer networks, the related geometric problem of zonotope non‑containment is W[1]-hard in the ambient dimension, and computing or approximating the Lp‑Lipschitz constant is NP‑hard and W[ℓ−1]-hard with respect to d. The results also show that these problems remain hard when parameterized by the number of layers for constant d, implying that naive enumeration algorithms running in n^{(ℓ−1)d}·poly(N) time are essentially optimal under the Exponential Time Hypothesis.
arXiv Machine Learning
Jul 27
Approximation and learning of anisotropic and mixed smooth functions by deep ReLU neural networks
arXiv:2605. 31152v2 Announce Type: replace-cross Abstract: This paper studies how efficiently deep ReLU neural networks can approximate and learn smooth functions.
arXiv Machine Learning
Jun 2
Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise
arXiv:2605. 18528v2 Announce Type: replace-cross Abstract: A growing lesson from neural network optimization is that optimizer design should respect how the model is parametrized.