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..
Learning Orthogonal Multi-Index Models: A Fine-Grained Information Exponent Analysis
Authors: Yunwei Ren, Jason D. Lee
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We include simulation results for Stage 1 in this section. The goal here is to provide empirical evidence that (i) if we have both the secondand L-th order terms, then the sample complexity of online SGD scales linearly with d and (ii) without the higher-order terms, online SGD cannot recovery the exact directions. All experiments are performed on the authors laptop without using GPUs, and it takes less than one day to complete the experiments. |
| Researcher Affiliation | Academia | Yunwei Ren Princeton University EMAIL Jason D. Lee Princeton University EMAIL |
| Pseudocode | Yes | Initialization: a0,i = 1, v0,i i.i.d. Unif(Sd 1), v0,m/2+i = v0,i i [m/2]; Stage 1: ˆvt+1,i = vt,i + ηf (xt) viϕ(vi x), vt+1,i = ˆvt+1,i/ ˆvt+1,i , i [m], t [T]; Stage 2: a = argmin a 1 2N n=1 l(x T +n; a , VT ) + λ a 2 . |
| Open Source Code | Yes | Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [Yes] Justification: See the supplementary material. |
| Open Datasets | No | Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected? Answer: [NA] Justification: The simulations use synthetic data. |
| Dataset Splits | No | We assume the input x follows the standard Gaussian distribution N (0, Id) and the target function has form f (x) = PP k=1 ϕ(v k x)... Let {(xt, f (xt))}t N be our samples where {xt} are i.i.d. standard Gaussian vectors... The paper describes the synthetic data generation process but does not specify how these samples are split into training, validation, or test sets. |
| Hardware Specification | Yes | All experiments are performed on the authors laptop without using GPUs, and it takes less than one day to complete the experiments. |
| Software Dependencies | No | The paper does not explicitly mention specific software dependencies or library versions used for the experiments. |
| Experiment Setup | Yes | The setting is the same as the one we have described in Section 2. We choose the hyperparameters roughly according to Theorem 2.1. To reduce the demand of computational resources, we choose m = Θ(P 2) instead of Ω(P 8). Note that by the Coupon Collector problem, we need m = Ω(P log P) to ensure that for each p [P], there exists at least one neuron v with v2 p maxq P v2 q. Since we are mostly interested in the dependence on d, for the learning rate, we choose η = c/d, where c is a tunable constant that is independent of d but can depend on everything else. T is chosen according to Theorem 2.1 and we early-stop the training when for all p [P], there exists a neuron with v2 p 0.95 (in the moving average sense). |