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..
Neural signature kernels as infinite-width-depth-limits of controlled ResNets
Authors: Nicola Muca Cirone, Maud Lemercier, Cristopher Salvi
ICML 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we first illustrate theoretical results established in Section 4 and then outline numerical considerations to scale the computation of signature kernels. To this aim, we consider a homogeneous Res Net ΦM,N φ with activation function φ = Re LU, and (σa, σA, σb) = (0.5, 1., 1.2). For R = 250 realizations of the weights and biases, we run the model on a 2-dimensional path x : t 7 (sin(15t), cos(30t) + 3et) observed at 100 regularly spaced time points in [0, 1]. We then verify that, as N increases, ΦM,N φ (x) converges to a Gaussian random variable with mean zero and variance Kφ(x, x). |
| Researcher Affiliation | Academia | 1Department of Mathematics, Imperial College London, London, United Kingdom 2Department of Mathematics, University of Oxford, Oxford, United Kingdom. |
| Pseudocode | Yes | Algorithm 1 SM,N 1 as Nestor program (in Appendix B.1.1) and Algorithm 2 SM,N 1 as Nestor program (in Appendix C.1.1). |
| Open Source Code | Yes | All the experiments presented in this paper are reproducible following the code at https://github.com/ Muca Cirone/Neural Signature Kernels |
| Open Datasets | No | The paper generates its own data for numerical validation, such as 'a 2-dimensional path x : t 7 (sin(15t), cos(30t) + 3et)' and 'two sample paths from a zero-mean GP with RBF kernel', without providing a specific link, DOI, or formal citation to a pre-existing public dataset. |
| Dataset Splits | No | The paper describes how it runs models on generated paths and estimates errors, but it does not specify any dataset splits like 'training', 'validation', or 'test' percentages or counts. |
| Hardware Specification | No | The paper mentions 'GPU computations' and 'maximum number of threads in a GPU block' but does not specify any exact GPU models (e.g., NVIDIA A100, RTX 2080 Ti), CPU models, or detailed cloud/cluster resource specifications. |
| Software Dependencies | No | The paper mentions 'dedicated python packages such as torchcde' but does not provide specific version numbers for these software components or any other libraries used for replication. |
| Experiment Setup | Yes | To this aim, we consider a homogeneous Res Net ΦM,N φ with activation function φ = Re LU, and (σa, σA, σb) = (0.5, 1., 1.2). |