Machine learning detects terminal singularities
Authors: Tom Coates, Alexander Kasprzyk, Sara Veneziale
NeurIPS 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this paper we demonstrate that machine learning can be used to understand this classification. We focus on eight-dimensional positively-curved algebraic varieties that have toric symmetry and Picard rank two, and develop a neural network classifier that predicts with 95% accuracy whether or not such an algebraic variety is Q-Fano. We trained a feed-forward neural network classifier on a balanced dataset of 5 million examples; these are eight-dimensional Q-factorial Fano toric varieties of Picard rank two, of which 2.5 million are terminal and 2.5 million non-terminal. Testing on a further balanced dataset of 5 million examples showed that the neural network classifies such toric varieties as terminal or non-terminal with an accuracy of 95%. |
| Researcher Affiliation | Academia | Tom Coates Department of Mathematics Imperial College London 180 Queen s Gate London, SW7 2AZ UK EMAIL Alexander M. Kasprzyk School of Mathematical Sciences University of Nottingham Nottingham, NG7 2RD UK EMAIL Sara Veneziale Department of Mathematics Imperial College London 180 Queen s Gate London, SW7 2AZ UK EMAIL |
| Pseudocode | Yes | Algorithm 1 Test terminality for weight matrix W = [[a1, . . . , a N], [b1, . . . , b N]]. |
| Open Source Code | Yes | All code used and trained models are available from Bit Bucket under an MIT licence [12]. Supporting code. https://bitbucket.org/ fanosearch/ml_terminality, 2023. |
| Open Datasets | Yes | The datasets underlying this work and the code used to generate them are available from Zenodo under a CC0 license [11]. A dataset of 8-dimensional Q-factorial Fano toric varieties of Picard rank 2. Zenodo, 2023. doi:10.5281/zenodo.10046893. |
| Dataset Splits | Yes | We tested the model on a balanced subset of 50% of the data (5M); the remainder was used for training (40%; 4M balanced) and validation (10%; 1M). |
| Hardware Specification | No | The paper mentions "30 CPU years" for data generation and "120 CPU hours" for ML-assisted generation, but it does not provide specific hardware details such as CPU models, GPU models, or memory specifications. |
| Software Dependencies | Yes | Data generation and post-processing was carried out using the computational algebra system Magma V2.27-3 [5]. The machine learning model was built using Py Torch v1.13.1 [36] and scikit-learn v1.1.3 [37]. Hyperparameter tuning was partly carried out using Ray Tune [31]. |
| Experiment Setup | Yes | The final best network configuration is summarised in Table 1. Table 1: Final network architecture and configuration. Hyperparameter Value Hyperparameter Value Layers (512, 768, 512) Momentum 0.99 Batch size 128 Leaky Relu slope 0.01 Initial learning rate 0.01 |