Notice: This website is continuously updated as new conference proceedings and journal volumes are published. Consequently, the figures presented here may differ from those reported in our publications.
A brief overview of our methodology is provided on the Methods page, along with references to publications documenting our approach and links to the code and data used in each study.
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.
The Separation Capacity of Random Neural Networks
Authors: Sjoerd Dirksen, Martin Genzel, Laurent Jacques, Alexander Stollenwerk
JMLR 2022 | Venue PDF | LLM Run Details | Input Tokens: 37,718 Total number of tokens sent to the LLM as input for this paper's analysis. | Output Tokens: 3,265 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 the present article, we enhance the theoretical understanding of random neural networks by addressing the following data separation problem: under what conditions can a random neural network make two classes X , X + Rd (with positive distance) linearly separable? We show that a su๏ฌciently large two-layer Re LU-network with standard Gaussian weights and uniformly distributed biases can solve this problem with high probability. Crucially, the number of required neurons is explicitly linked to geometric properties of the underlying sets X , X + and their mutual arrangement. |
| Researcher Affiliation | Academia | Sjoerd Dirksen EMAIL Mathematical Institute Utrecht University 3584 CD Utrecht, Netherlands; Martin Genzel EMAIL Mathematical Institute Utrecht University 3584 CD Utrecht, Netherlands; Laurent Jacques EMAIL ISPGroup, INMA, ICTEAM Institute Universit e Catholique de Louvain 1348 Louvain-la-Neuve, Belgium; Alexander Stollenwerk EMAIL ISPGroup, INMA, ICTEAM Institute Universit e Catholique de Louvain 1348 Louvain-la-Neuve, Belgium |
| Pseudocode | No | The paper contains definitions, theorems, lemmas, and detailed mathematical proofs, but no structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any statements about releasing source code, nor does it provide links to any code repositories. The work is theoretical in nature, focusing on mathematical proofs and analysis. |
| Open Datasets | No | The paper focuses on theoretical analysis of random neural networks and does not conduct experiments using specific datasets. The sets X and X+ are abstract, defined as 'X , X + Rd'. |
| Dataset Splits | No | The paper does not involve empirical experiments with datasets, thus no information on dataset splits is provided. |
| Hardware Specification | No | The paper is theoretical and does not describe any experimental setup or hardware used for computation. |
| Software Dependencies | No | The paper is theoretical and does not mention any specific software or library versions used for implementation or experiments. |
| Experiment Setup | No | As a theoretical paper, no experimental setup details such as hyperparameters or training configurations are discussed. |