Geometric Analysis of Nonconvex Optimization Landscapes for Overcomplete Learning
Authors: Qing Qu, Yuexiang Zhai, Xiao Li, Yuqian Zhang, Zhihui Zhu
ICLR 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, our theoretical results are justified by numerical simulations. |
| Researcher Affiliation | Academia | Qing Qu Center for Data Science New York University qq213@nyu.edu Yuexiang Zhai EECS UC Berkeley ysz@berkeley.edu Xiao Li Eletronic Engineering CUHK xli@ee.cuhk.edu.hk Yuqian Zhang Electrical & Computer Engineering Rutgers University yqz.zhang@rutgers.edu Zhihui Zhu Electrical & Computer Engineering University of Denver zhihui.zhu@du.edu |
| Pseudocode | Yes | Algorithm 1 Finding one filter with data-driven initialization |
| Open Source Code | No | The paper provides a link to its arXiv preprint ('https://arxiv.org/abs/1912.02427') which contains the full version of the paper, but there is no explicit statement or link for open-source code for the methodology described. |
| Open Datasets | No | The paper states: 'We generate data Y AX, with dictionary A P Rnˆm being UNTF, and sparse code X P Rmˆp i.i.d. BGpθq.' and 'for CDL, we generate measurement according to Equation (1.2) with K 3, where the filters ta0ku K k 1 are drawn uniformly from the sphere Sn 1, and xik i.i.d. BGpθq.' This indicates generated synthetic data, not a publicly available or open dataset. |
| Dataset Splits | No | The paper generates its own data for simulations and does not describe explicit train/validation/test splits of a dataset. It focuses on parameters used for data generation (e.g., n=3, m=4, p=2*10^4). |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., GPU/CPU models, memory) used for running the numerical simulations. |
| Software Dependencies | No | The paper does not list any specific software dependencies with version numbers (e.g., Python, PyTorch, specific libraries or solvers) used for implementing the methods or running experiments. |
| Experiment Setup | Yes | We generate data Y AX, with dictionary A P Rnˆm being UNTF, and sparse code X P Rmˆp i.i.d. BGpθq. To judge the success recovery of one column of A, let ρe min 1ďiďm p1 |xq , ai{ }ai}y|q . We have ρe 0 when q PSn 1paiq, thus we assume a recovery is successful if ρe ă 5 ˆ 10 2. ... First, we fix θ 0.1, and test the limit of the overcompleteness K m{n we can achieve by plotting the phase transition on pm, nq in log scale. For each pair of pm, nq, we repeat the experiment for 12 times. ... Parameters: n 64, θ 0.1, K 3, p 1 ˆ 104. |