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 ( ).