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..
Understanding Deflation Process in Over-parametrized Tensor Decomposition
Authors: Rong Ge, Yunwei Ren, Xiang Wang, Mo Zhou
NeurIPS 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We prove that for orthogonally decomposable tensor, a slightly modified version of gradient flow would follow a tensor deflation process and recover all the tensor components.Our proof suggests that for orthogonal tensors, gradient flow dynamics works similarly as greedy low-rank learning in the matrix setting, which is a first step towards understanding the implicit regularization effect of over-parametrized models for low-rank tensors. |
| Researcher Affiliation | Academia | Rong Ge Duke University EMAIL Yunwei Ren* Shanghai Jiao Tong University EMAIL Xiang Wang* Duke University EMAIL Mo Zhou* Duke University EMAIL |
| Pseudocode | Yes | Algorithm 1 Tensor Deflation Process |
| Open Source Code | No | The paper does not contain any explicit statements or links indicating that source code for the described methodology is publicly available. |
| Open Datasets | No | The paper constructs a synthetic tensor (T = P i [5] aie 4 i) for illustrative purposes in Figure 1, but does not use or provide access information for any publicly available or open datasets. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments that require specifying training, validation, or test dataset splits. |
| Hardware Specification | No | The paper does not specify any hardware used for experiments, such as specific GPU or CPU models. |
| Software Dependencies | No | The paper does not mention any specific software dependencies with version numbers required to replicate the work. |
| Experiment Setup | Yes | Input: Number of components m, initialization scale δ0, re-initialization threshold δ1, increasing rate of epoch length γ, target accuracy ϵ, regularization coefficient λ" and "Theorem 1. For any ϵ exp( o(d/ log d)), there exists γ = Θ(1), m = poly(d), λ = min{O(log d/d), O(ϵ/d1/2)}), α = min{O(λ/d3/2), O(λ2), O(ϵ2/d4)}, δ1 = O(α3/2/m1/2), δ0 = Θ(δ1α/ log1/2(d)) such that with probability 1 1/poly(d) in the (re)-initializations, Algorithm 2 terminates in O(log(d/ϵ)) epochs and returns a tensor T such that |