REVIEW 5 cited by
Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
The purpose of this article is to review the achievements made in the last few years towards the understanding of the reasons behind the success and subtleties of neural network-based machine learning. In the tradition of good old applied mathematics, we will not only give attention to rigorous mathematical results, but also the insight we have gained from careful numerical experiments as well as the analysis of simplified models. Along the way, we also list the open problems which we believe to be the most important topics for further study. This is not a complete overview over this quickly moving field, but we hope to provide a perspective which may be helpful especially to new researchers in the area.
Forward citations
Cited by 5 Pith papers
-
Implicit Bias of SGD in Multivariate ReLU Networks: Effective Width Collapse
Noisy SGD in the mean-field regime forces wide multivariate ReLU networks to an effective width of at most 2P-1, yielding a continuous piecewise-affine predictor whose hyperplanes are non-redundant with respect to the...
-
Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators
Vector-valued neural networks, DeepONets, and hypernetworks are shown to live in integral vector-valued reproducing kernel Banach spaces with representer theorems that recover the architectures.
-
Mathematical analysis of the gradients in deep learning
For deep feedforward networks with piecewise-smooth activations, the autodiff gradient is shown to be the unique limit of gradients of smoothed activations, a limiting Frechet subgradient, and equal to the true gradie...
-
ResKoopNet: Learning Koopman Representations for Complex Dynamics with Spectral Residuals
ResKoopNet learns Koopman eigenpairs by minimizing the spectral residual over neural-network dictionaries, reporting fuller spectra and better latent-state separation than existing Koopman methods.
-
Layer Separation Deep Learning Model with Auxiliary Variables for Partial Differential Equations
LySep separates the layers and derivatives of a PINN into auxiliary variables, yielding a shallow, easier-to-optimize loss that remains provably consistent with the original PINN loss.
Discussion (0). Continue with ORCID to comment.