Differentiable Euler Characteristic Transforms for Shape Classification
Authors: Ernst Röell, Bastian Rieck
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We conduct a comprehensive suite of experiments to explore and assess its properties. First and foremost, building on the intuition of the ECT being a universal shape descriptor, we are interested in understanding how well ECT-based models perform across different types of data, such as point clouds, graphs, and meshes. Moreover, while recent work has proven theoretical bounds on the number of directions required to unique classify a shape (i.e. the number of directions required to guarantee injectivity) via the ECT (Curry et al., 2022), we strive to provide practical insights into how well classification accuracy depends on the number of directions used to calculate the ECT. Finally, we also show how to use the ECT to transform point clouds, taking on the role of additional optimisation objectives that permit us to adjust point clouds based on a target ECT. |
| Researcher Affiliation | Academia | Ernst Röell1,2, Bastian Rieck1,2 1AIDOS Lab, Institute of AI for Health, Helmholtz Munich 2Technical University of Munich (TUM) |
| Pseudocode | No | The paper describes the computational steps in a numbered list within the 'Computational efficiency and implementation' section, but it is not presented as formal pseudocode or a clearly labeled algorithm block. |
| Open Source Code | Yes | Our code is publicly available under https://github.com/aidos-lab/DECT. |
| Open Datasets | Yes | We use the MNIST dataset with each non-zero pixel viewed as a point in a point cloud. For the synthetic data sets, we add DECT as the first layer of an MLP with 3 hidden layers. For graph classification tasks, we also use DECT as the first layer, followed by two convolutional layers, and an MLP with 3 hidden layers for classification. Moving from point clouds to graphs, we first study the performance of our method on the MNIST-Superpixel data set (Dwivedi et al., 2023). Finally, we show the performance of our DECT when it comes to analysing graphs that contain node coordinates. We use several graph benchmark data sets (Morris et al., 2020). |
| Dataset Splits | Yes | We split data sets following an 80%/20% train/test split, reserving another 20% of the training data for validation. |
| Hardware Specification | Yes | The reported runtime is the in fact slowest of all our experiments, with most other data sets only taking about a minute for a full 100 epochs. We report the values from Dwivedi et al. (2023), noting that the survey uses a single Nvidia 1080Ti (11GB) GPU was used on a cluster, whereas our model was trained on a Nvidia Ge Force RTX 3070 Ti (8GB) GPU on a commodity laptop. |
| Software Dependencies | No | The paper mentions using the 'ADAM optimiser' and refers to 'MLP' and 'CNN' architectures, but does not specify version numbers for any software libraries or dependencies (e.g., PyTorch, TensorFlow, scikit-learn, etc.). |
| Experiment Setup | Yes | For the graph classification, we set the maximum number of epochs to 100. We use the ADAM optimiser with a starting learning rate of 0.001. As a loss term, we either use categorical cross entropy for classification or the mean squared error (MSE) for optimising point clouds and directions. By default, we use 16 different directions for the calculation of the ECT and discretise each curve into 16 steps. This results in a 16 16 image for each input data set. When using convolutional layers, our first convolutional layer has 8 channels, followed by a layer with 16 channels, which is subsequently followed by a pooling layer. Our classification network is an MLP with 25 hidden units per layer and 3 layers in total. |