# Deep Learning Calabi-Yau four folds with hybrid and recurrent neural network architectures

arXiv: https://arxiv.org/abs/2405.17406 · HTML: https://mlsanity.com/paper/2405.17406/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 57 references that are in the map.
- First posted on arXiv 27 May 2024.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [ReZero is All You Need: Fast Convergence at Large Depth](https://mlsanity.com/paper/2003.04887/) (2020)
- [Gated Feedback Recurrent Neural Networks](https://mlsanity.com/paper/1502.02367/) (2015)
- [Sequencer: Deep LSTM for Image Classification](https://mlsanity.com/paper/2205.01972/) (2022)
- [Machine Learning CICY Threefolds](https://mlsanity.com/paper/1806.03121/) (2018)
- [The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning](https://mlsanity.com/paper/1812.02893/) (2018)
- [Machine learning for complete intersection Calabi-Yau manifolds: a methodological study](https://mlsanity.com/paper/2007.15706/) (2020)
- [Machine Learning Calabi-Yau Four-folds](https://mlsanity.com/paper/2009.02544/) (2020)
- [Machine Learning Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2112.06350/) (2021)
- [Inception Neural Network for Complete Intersection Calabi-Yau 3-folds](https://mlsanity.com/paper/2007.13379/) (2020)
- [Explore and Exploit with Heterotic Line Bundle Models](https://mlsanity.com/paper/2003.04817/) (2020)
- [Deep multi-task mining Calabi-Yau four-folds](https://mlsanity.com/paper/2108.02221/) (2021)
- [Deep learning complete intersection Calabi-Yau manifolds](https://mlsanity.com/paper/2311.11847/) (2023)

## Built on by (most cited first, 2 of 2)

- [New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures](https://mlsanity.com/paper/2604.24337/) (2026)
- [Two-dimensional Hyperbolic RNN Neural Quantum State](https://mlsanity.com/paper/2606.25600/) (2026)

## Abstract (arXiv)

In this work, we report the results of applying deep learning based on hybrid convolutional-recurrent and purely recurrent neural network architectures to the dataset of almost one million complete intersection Calabi-Yau four-folds (CICY4) to machine-learn their four Hodge numbers h1,1, h2,1, h3,1, h2,2. In particular, we explored and experimented with twelve different neural network models, nine of which are convolutional-recurrent (CNN-RNN) hybrids with the RNN unit being either GRU (Gated Recurrent Unit) or Long Short Term Memory (LSTM). The remaining four models are purely recurrent neural networks based on LSTM. In terms of the h1,1, h2,1, h3,1, h2,2 prediction accuracies, at 72% training ratio, our best performing individual model is CNN-LSTM-400, a hybrid CNN-LSTM with the LSTM hidden size of 400, which obtained 99.74%, 98.07%, 95.19%, 81.01%, our second best performing individual model is LSTM-448, an LSTM-based model with the hidden size of 448, which obtained 99.74%, 97.51%, 94.24%, and 78.63%. These results were improved by forming ensembles of the top two, three or even four models. Our best ensemble, consisting of the top four models, achieved the accuracies of 99.84%, 98.71%, 96.26%, 85.03%. At 80% training ratio, the top two performing models LSTM-448 and LSTM-424 are both LSTM-based with the hidden sizes of 448 and 424. Compared with the 72% training ratio, there is a significant improvement of accuracies, which reached 99.85%, 98.66%, 96.26%, 84.77% for the best individual model and 99.90%, 99.03%, 97.97%, 87.34% for the best ensemble. By nature a proof of concept, the results of this work conclusively established the utility of RNN-based architectures and demonstrated their effective performances compared to the well-explored purely CNN-based architectures in the problem of deep learning Calabi Yau manifolds.