# Can A Neural Network Hear the Shape of A Drum?

arXiv: https://arxiv.org/abs/2203.08073 · HTML: https://mlsanity.com/paper/2203.08073/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 14 Mar 2022.

## Builds on (most cited first, 15 of 15)

- [Expressive Body Capture: 3D Hands, Face, and Body from a Single Image](https://mlsanity.com/paper/1904.05866/) (2019)
- [Generative Adversarial Text to Image Synthesis](https://mlsanity.com/paper/1605.05396/) (2016)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [StackGAN++: Realistic Image Synthesis with Stacked Generative Adversarial Networks](https://mlsanity.com/paper/1710.10916/) (2017)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Tell, Draw, and Repeat: Generating and Modifying Images Based on Continual Linguistic Instruction](https://mlsanity.com/paper/1811.09845/) (2018)
- [SurfNet: Generating 3D shape surfaces using deep residual networks](https://mlsanity.com/paper/1703.04079/) (2017)
- [Geometric Disentanglement for Generative Latent Shape Models](https://mlsanity.com/paper/1908.06386/) (2019)
- [Isospectralization, or how to hear shape, style, and correspondence](https://mlsanity.com/paper/1811.11465/) (2018)
- [Learning hard quantum distributions with variational autoencoders](https://mlsanity.com/paper/1710.00725/) (2017)
- [Unsupervised Learning of Latent Physical Properties Using Perception-Prediction Networks](https://mlsanity.com/paper/1807.09244/) (2018)
- [Enhanced Higgs to τ^+τ^- Searches with Deep Learning](https://mlsanity.com/paper/1410.3469/) (2014)

## Abstract (arXiv)

We have developed a deep neural network that reconstructs the shape of a polygonal domain given the first hundred of its Laplacian eigenvalues. Having an encoder-decoder structure, the network maps input spectra to a latent space and then predicts the discretized image of the domain on a square grid. We tested this network on randomly generated pentagons. The prediction accuracy is high and the predictions obey the Laplacian scaling rule. The network recovers the continuous rotational degree of freedom beyond the symmetry of the grid. The variation of the latent variables under the scaling transformation shows they are strongly correlated with Weyl' s parameters (area, perimeter, and a certain function of the angles) of the test polygons.