Neural signature kernels as infinite-width-depth-limits of controlled ResNets
Authors: Nicola Muca Cirone, Maud Lemercier, Cristopher Salvi
ICML 2023 | Conference PDF | Archive PDF | Plain Text | 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). |