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..
Legendre Decomposition for Tensors
Authors: Mahito Sugiyama, Hiroyuki Nakahara, Koji Tsuda
NeurIPS 2018 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We empirically show that Legendre decomposition can more accurately reconstruct tensors than other nonnegative tensor decomposition methods. We empirically examine performance of our method in Section 3 |
| Researcher Affiliation | Academia | Mahito Sugiyama National Institute of Informatics JST, PRESTO EMAIL Hiroyuki Nakahara RIKEN Center for Brain Science EMAIL Koji Tsuda The University of Tokyo NIMS; RIKEN AIP EMAIL |
| Pseudocode | Yes | Algorithm 1: Legendre decomposition by gradient descent. Algorithm 2: Legendre decomposition by natural gradient. |
| Open Source Code | Yes | Implementation is available at: https://github.com/mahito-sugiyama/Legendre-decomposition |
| Open Datasets | Yes | We used the MNIST dataset (Le Cun et al., 1998)... URL http://yann.lecun.com/exdb/mnist/. We picked up the first entry from the fourth mode (corresponds to lighting) from the dataset... This dataset is originally distributed at http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html and also available from the R r Tensor package (https://CRAN.R-project.org/package=r Tensor). |
| Dataset Splits | No | The paper mentions using synthetic and real-world datasets (face images, MNIST) and describes how subsets were created (e.g., |
| Hardware Specification | Yes | We used Amazon Linux AMI release 2018.03 and ran all experiments on 2.3 GHz Intel Xeon CPU E5-2686 v4 with 256 GB of memory. |
| Software Dependencies | Yes | The Legendre decomposition was implemented in C++ and compiled with icpc 18.0.0. We used the Tensor Ly implementation (Kossaifiet al., 2016) for the nonnegative Tucker and CP decompositions and the tensor toolbox (Bader et al., 2017; Bader and Kolda, 2007) for CP-APR. |
| Experiment Setup | Yes | We set B = B3(l) and varied the number of parameters |B| with increasing l. In Algorithm 2, we used the outer loop (from line 3 to 8) as one iteration for fair comparison and fixed the learning rate ε = 0.1. |