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; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1]
The Ramanujan Library - Automated Discovery on the Hypergraph of Integer Relations
Authors: Itay Beit Halachmi, Ido Kaminer
ICLR 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | During its development and testing, our strategy led to the discovery of 75 previously unknown connections between constants, including a new formula for the first continued fraction constant C1, novel formulas for natural logarithms, and new formulas connecting π and e. [...] Experimenting with the PSLQ algorithm to determine an empirical lower bound for Ro I, beyond which integer relations can be considered significant, shows that an Ro I of 2 seems to comfortably separate random results from false positives, with a generous margin of error (see figure 3). |
| Researcher Affiliation | Academia | Itay Beit-Halachmi and Ido Kaminer The Ramanujan Machine Team, Faculty of Electrical and Computer Engineering Technion Israel Institute of Technology Haifa 3200003, Israel EMAIL, EMAIL |
| Pseudocode | No | The paper describes algorithms (e.g., PSLQ, identify) and a process flow (Figure 2), but it does not present any of these in a structured pseudocode or algorithm block format. |
| Open Source Code | Yes | The code supporting this library is a public, open-source API that can serve researchers in experimental mathematics and other fields of science. [...] The code we have written and the library we have curated are open-source and publicly-accessible, 1 including the novel database of mathematical constants and the hypergraph of integer relations. 1https://github.com/Ramanujan Machine/LIRe C |
| Open Datasets | Yes | In this paper, we present the first library dedicated to mathematical constants and their interrelations. This library can serve as a central repository of knowledge for scientists from different areas, and as a collaborative platform for development of new algorithms. [...] The code we have written and the library we have curated are open-source and publicly-accessible, 1 including the novel database of mathematical constants and the hypergraph of integer relations. |
| Dataset Splits | No | The paper focuses on automated discovery of mathematical relations and building a library of constants, rather than training a model on a dataset with explicit training/test/validation splits. |
| Hardware Specification | Yes | These results were found after running the algorithm on a smaller scale (an 8-core AWS machine) for several months. |
| Software Dependencies | Yes | Access to the database from our code is established using psycopg2 and sqlalchemy (Bayer, 2012). Our code contains for example the automated search algorithm described in section 2.1, along with additional utilities like the C-transform calculator and the numerical identification suite we call identify, which are described in this section. [...] The calculator utilizes three libraries for its computation: sympy (Meurer et al., 2017), gmpy2, and mpmath (mpmath development team, 2023). |
| Experiment Setup | Yes | Experimenting with the PSLQ algorithm to determine an empirical lower bound for Ro I, beyond which integer relations can be considered significant, shows that an Ro I of 2 seems to comfortably separate random results from false positives, with a generous margin of error (see figure 3). As such, this has been decided as the lower cutoff for integer relations generated by PSLQ to be considered significant as part of the algorithm in section 2.1. [...] For each n, we ran PSLQ 100 times with a pre-selected binary precision of 50 + 5n. [...] For each d, n, we ran PSLQ 100 times until tolerance (equal to 65% of the working precision, see appendix B for more details), each with n numbers between 0 and 1, each with d uniformly random binary digits. |