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 Shift Toward Open and Reproducible AI Research," Under Review, 2026. doi: 10.48550/arXiv.2606.16974..
Eigenvalue Decay Implies Polynomial-Time Learnability for Neural Networks
Authors: Surbhi Goel, Adam Klivans
NeurIPS 2017 | Venue PDF | LLM Run Details | Input Tokens: 16,831 Total number of tokens sent to the LLM as input for this paper's analysis. | Output Tokens: 2,379 Total number of tokens produced by the LLM (including reasoning/thinking tokens) for this paper's analysis.
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work we show that a natural distributional assumption corresponding to eigenvalue decay of the Gram matrix yields polynomial-time algorithms in the non-realizable setting for expressive classes of networks (e.g. feed-forward networks of Re LUs). We make no assumptions on the structure of the network or the labels. Given sufficiently-strong eigenvalue decay, we obtain fully-polynomial time algorithms in all the relevant parameters with respect to square-loss. This is the first purely distributional assumption that leads to polynomial-time algorithms for networks of Re LUs. Further, unlike prior distributional assumptions (e.g., the marginal distribution is Gaussian), eigenvalue decay has been observed in practice on common data sets. |
| Researcher Affiliation | Academia | Surbhi Goel Department of Computer Science University of Texas at Austin EMAIL Adam Klivans Department of Computer Science University of Texas at Austin EMAIL |
| Pseudocode | Yes | Algorithm 1 Compressed Kernel Regression |
| Open Source Code | No | The paper does not provide explicit statements or links for open-source code for the described methodology. |
| Open Datasets | No | The paper is theoretical and does not describe training on a specific, publicly available dataset with access information. It discusses 'common data sets' in a general sense but no details for reproducibility. |
| Dataset Splits | No | The paper is theoretical and does not describe empirical experiments, thus no validation dataset splits are mentioned. |
| Hardware Specification | No | The paper does not mention any specific hardware used for running experiments. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe empirical experiments; therefore, it does not provide details on experimental setup or hyperparameters. |