Analysis of stochastic Lanczos quadrature for spectrum approximation
Authors: Tyler Chen, Thomas Trogdon, Shashanka Ubaru
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The quality of our bounds is demonstrated using numerical experiments. 5. Numerical verification and discussion |
| Researcher Affiliation | Collaboration | 1Department of Applied Mathematics, University of Washington, Seattle, Washington, USA 2IBM T.J. Watson Research Center, Yorktown Heights, New York, USA. |
| Pseudocode | Yes | Algorithm 1 Stochastic Lanczos Quadrature and Algorithm 2 Lanczos |
| Open Source Code | No | The paper does not contain any explicit statements or links indicating that the source code for the described methodology is publicly available. |
| Open Datasets | Yes | resnet20 is a Hessian for the ResNet20 network (He et al., 2016) trained on the Cifar-10 dataset. The California and Erdos992 examples are graph adjacency matrices from the sparse matrix suite (Davis & Hu, 2011) and the MNIST cov example is the covariance matrix of the MNIST training data |
| Dataset Splits | No | The paper mentions using standard datasets like CIFAR-10 and MNIST but does not provide specific details on how these datasets were split into training, validation, or test sets for reproduction. |
| Hardware Specification | No | The paper does not provide specific hardware details (such as GPU/CPU models, processor types, or memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper mentions using 'Py Hessian (Yao et al., 2020)' but does not provide specific version numbers for this or any other key software dependencies required for replication. |
| Experiment Setup | Yes | In Figure 2 for several test problems. Qualitatively, we observe several types of behavior in both the true Wasserstein distance and the bounds. From left to right, nv = 2, 6, 9, 68, 11 chosen so that nv is roughly of size O(n 1). Legend: d W(Φ[A], [Ψi]gq k ( ), bound Pn j=0 max{[di]j, [di]j+1}([θi]j+1 θi]j) ( ), bound 12I[A](2k 1) 1 ( ), (Φ(d ) Φ(c)) |d c| described in (2) ( ), I[A]n 1 ( ). |