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..
Near Optimal Reconstruction of Spherical Harmonic Expansions
Authors: Amir Zandieh, Insu Han, Haim Avron
NeurIPS 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5 Numerical Evaluation: Noise-free Setting. For a fixed q, we generate a random function f(σ) = Pq ℓ=0 cℓP ℓ d( σ, v ) where v U(Sd 1) and cℓ s are i.i.d. samples from N(0, 1). Then, f is recovered by running Algorithm 1 with s random evaluations of f on Sd 1. We count the number of failures among 100 independent random trials with different choices of d {3, 4}, q {5, . . . , 22}, and s {40, . . . , 2400}. The empirical success probabilities for d = 3 and 4 are reported in Fig. 1(a) and Fig. 1(b), respectively. |
| Researcher Affiliation | Academia | Amir Zandieh Independent Researcher EMAIL Insu Han Yale University EMAIL Haim Avron Tel Aviv University EMAIL |
| Pseudocode | Yes | Algorithm 1 Efficient Spherical Harmonic Expansion 1: Input: accuracy parameter ε > 0, integer q 0 2: Set s = c (βq,d log βq,d + βq,d/ε) for sufficiently large fixed constant c 3: Sample i.i.d. random points w1, w2, . . . , ws from U(Sd 1) 4: Compute K Rs s with Ki,j = Pq ℓ=0 αℓ,d s |Sd 1| P ℓ d ( wi, wj ) for i, j [s] 5: Compute f Rs with fj = 1 s f(wj) for j [s] 6: Solve the regression by computing z = K f 7: Return: y H(q)(Sd 1) with y(σ) := Pq ℓ=0 αℓ,d s |Sd 1| Ps j=1 zj P ℓ d ( wj, σ ) for σ Sd 1 |
| Open Source Code | No | The paper does not provide any explicit statements about open-source code availability or links to code repositories. |
| Open Datasets | No | The paper describes generating random functions and sampling points from them for experiments, rather than using a publicly available or open dataset with concrete access information: "For a fixed q, we generate a random function f(σ) = Pq ℓ=0 cℓP ℓ d( σ, v ) where v U(Sd 1) and cℓ s are i.i.d. samples from N(0, 1)." |
| Dataset Splits | No | The paper does not explicitly provide details about training, validation, or test dataset splits (e.g., percentages, sample counts, or references to standard splits). It describes generating sampled points for evaluation. |
| Hardware Specification | No | The paper does not specify any particular hardware used for its experiments (e.g., specific GPU/CPU models or cloud instances). It only mentions runtime complexity in terms of 'ω < 2.3727 is the exponent of the fast matrix multiplication algorithm'. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers. |
| Experiment Setup | Yes | We count the number of failures among 100 independent random trials with different choices of d {3, 4}, q {5, . . . , 22}, and s {40, . . . , 2400}. The empirical success probabilities for d = 3 and 4 are reported in Fig. 1(a) and Fig. 1(b), respectively. |