The Neural Covariance SDE: Shaped Infinite Depth-and-Width Networks at Initialization

Authors: Mufan Li, Mihai Nica, Dan Roy

NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Using simulations, we show that the SDE closely matches the distribution of the random covariance matrix of finite networks. Additionally, we recover an if-and-only-if condition for exploding and vanishing norms of large shaped networks based on the activation function. We provide simulations to verify theoretical predictions and help interpret properties of real DNNs. See Figures 1 and 2 and supplemental simulations in Appendix F.
Researcher Affiliation Academia Mufan (Bill) Li University of Toronto, Vector Institute Mihai Nica University of Guelph, Vector Institute Daniel M. Roy University of Toronto, Vector Institute
Pseudocode No No pseudocode or algorithm blocks found.
Open Source Code Yes All of our simulations (at initialization only) are contained the file Correlation.ipynb.
Open Datasets No The paper describes simulations, not experiments on a publicly available dataset. No concrete access information for a dataset used for training or evaluation is provided.
Dataset Splits No No specific dataset splits (training, validation, test) are mentioned, as the paper focuses on simulations rather than using a standard dataset.
Hardware Specification No Our simulations were small enough that it did not require GPUs. No specific hardware details (e.g., CPU model, memory) are provided.
Software Dependencies No No specific software dependencies with version numbers are mentioned.
Experiment Setup Yes Simulation details: n = d = 150, ρ0 = 0.3, 213 samples for each. In right column: c+ = 0, c = 1, DE step size 1e 2.