Optimal Algorithms for the Inhomogeneous Spiked Wigner Model
Authors: Aleksandr Pak, Justin Ko, Florent Krzakala
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Figure 1: Performance of the inhomogeneous AMP algorithm against the informationtheoretical optimal MMSE. The variance profile is proportional to = 1 3 3 2 with two equally sized blocks with standard Gaussian prior when N =500 at various snr. [...] Even at very moderate sizes, the agreement between theory and simulation is clear. Figure 3: Illustration of the spectrum of Y R2500 2500 evaluated at noise profiles with snr λ( ) = 0.7 (left, before the transition) and on the left and 1.8 on the right (after the transition). There is no outlying eigenvalue in contrast to the transformed matrix: the transition for a naive spectral method is sub-optimal. Figure 4: Illustration of the spectrum of Y R2500 2500 evaluated at noise profiles with snr λ( ) = 0.7 (left, before the transition) and on the left and 1.8 on the right (after the transition), with the outlying eigenvector correlated with the spike arises at eigenvalue one. This is at variance with the results of the naive method in Fig.3 |
| Researcher Affiliation | Academia | Justin Ko ENS de Lyon justin.ko@ens-lyon.fr Florent Krzakala EPFL florent.krzakala@epfl.ch Aleksandr Pak ENS de Lyon, EPFL aleksandr.pak@epfl.ch |
| Pseudocode | No | The paper describes algorithms and recursions mathematically but does not present them in a clearly labeled 'Pseudocode' or 'Algorithm' block format. |
| Open Source Code | No | The paper does not provide any links to open-source code or explicitly state that code for the described methodology is being released. |
| Open Datasets | No | The paper defines a model and runs simulations based on theoretical distributions (e.g., 'standard Gaussian prior') rather than using a publicly available dataset for training in the typical machine learning sense. Therefore, there is no information regarding public dataset availability. |
| Dataset Splits | No | The paper does not describe dataset splits for training, validation, or testing, as it focuses on theoretical models and simulations rather than typical machine learning dataset usage. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., GPU models, CPU types, memory) used to run the simulations or experiments. |
| Software Dependencies | No | The paper does not provide specific version numbers for any software libraries, frameworks, or programming languages used in the research or simulations. |
| Experiment Setup | No | The paper describes the theoretical model and the mathematical derivations but does not specify experimental setup details such as hyperparameters, optimizer settings, or training configurations for any computational experiments beyond the simulation size 'N=500' or 'N=2500'. |