Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Error Bounds for Learning with Vector-Valued Random Features
Authors: Samuel Lanthaler, Nicholas H. Nelsen
NeurIPS 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To study how our theory holds up in practice, we numerically implement the vector-valued RF-RR algorithm on a benchmark operator learning dataset. Figure 2a shows the decay of the relative squared test error as M increases (with λ 1/M) for fixed N. |
| Researcher Affiliation | Academia | Samuel Lanthaler California Institute of Technology EMAIL Nicholas H. Nelsen California Institute of Technology EMAIL |
| Pseudocode | No | The paper contains mathematical proofs and derivations, but no pseudocode or algorithm blocks are provided. |
| Open Source Code | Yes | All code used to produce the numerical results and figures in this paper are available at https://github.com/nickhnelsen/error-bounds-for-vv RF. |
| Open Datasets | Yes | The data {(un, G(un))}N n=1 is noise-free, the {un} are iid Gaussian random fields, and G : L2(T; R) L2(T; R) is a nonlinear operator defined as the time one flow map of the viscous Burgers equation on the torus T. The initial conditions un ν are sampled iid from a centered Matérn-like Gaussian process according to [23, Sect. 6.3, p. 32]. |
| Dataset Splits | No | The paper mentions a test set of size N=500 and a training input set, but does not specify the size of the training set or the splitting methodology for the training/validation/test sets, nor does it mention a validation set. |
| Hardware Specification | No | No specific hardware details (e.g., GPU/CPU models, memory) used for running experiments are provided. |
| Software Dependencies | No | The paper mentions the use of ELU, but does not specify any software names with version numbers for libraries, frameworks, or programming languages used in the experiments. |
| Experiment Setup | Yes | The random features are defined in a similar way to the Fourier Space RFs in [32, Sect. 3.1, p. 15]: φ(u(0); θ) = 2.6 ELU F 1{1(|k| kmax)χk (Fu(0))k (Fθ)k}k Z and θ µ , where µ is also a centered Matérn Gaussian measure with covariance operator 1.82( d2 dx2 +152 Id) 3. In the above display, F maps a function to its Fourier series coefficients, and F 1 expresses a Fourier coefficient sequence as a function expanded in the Fourier basis. The filter χ is given by [32, Eqn. 3.6, p. 15] with δ = 0.32 and β = 0.1. We take kmax = 64. In Figures 2a and 3a, the regularization factor is chosen as λ = 7 10 4/M and as λ = 3 10 6/ N in Figures 2b and 3b. |