Grounding Continuous Representations in Geometry: Equivariant Neural Fields

Authors: David Wessels, David Knigge, Riccardo Valperga, Samuele Papa, Sharvaree Vadgama, Efstratios Gavves, Erik Bekkers

ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental First, we show the ability of Equivariant Neural Fields (ENFs) to reconstruct datasets of input fields f i.e. to associate a latent point cloud zfj to a given dataset of samples fj D that accurately reconstructs them. Then, we validate ENFs as an improved Ne F-based downstream representation for various tasks requiring geometric reasoning; classification, segmentation and forecasting. To show the flexibility of Ne F-based representations, we perform these tasks on a range of modalities. Each downstream experiment consists of two stages: (1) fitting a ENF backbone fθ for reconstruction of the input fields fj D to obtain latents pointclouds zfj, and (2) training a downstream model that takes zfj as input for each specific task.
Researcher Affiliation Academia 1AMLab, 2VISLab, University of Amsterdam, 3Archimedes/Athena RC EMAIL, EMAIL
Pseudocode Yes Algorithm 1 Meta-learning ENF ... Algorithm 2 Autodecoding ENF
Open Source Code Yes Code attached to submission here. Code for a clean and minimal repo here. ... As supplementary material we added a codebase containing code to reproduce results for the CIFAR10 and OMBRIA experiments. Code for all other experiments will be released during the rebuttal phase of the review process, containing all settings to reproduce the experiments in config files.
Open Datasets Yes Image data We show results for reconstruction trained with Meta-Learning on CIFAR10 Krizhevsky et al. (2009), Celeb A64 64 (Liu et al., 2015) and Image Net1K (Deng et al., 2009)... For voxel data we take train and test splits from the 16-class Shape Net-Part segmentation dataset (Yi et al., 2016)... To create the signed distance functions from Shape Net Core V2 Chang et al. (2015) objects... Flood Map Segmentation For a more challenging segmentation task we apply ENFs on multi-modal flood mapping dataset (Drakonakis et al., 2022). ... ERA5 Climate forecasting Following (Yin et al., 2022; Knigge et al., 2024) we evaluate our Ne F-based representation on dynamics forecasting. ERA5 (Hersbach et al., 2019) is a dataset of hourly global temperature observations.
Dataset Splits Yes For voxel data we take train and test splits from the 16-class Shape Net-Part segmentation dataset... This small dataset (759/85 train/test split) provides dual-modal temporal data... From the training and test sets, we extract 5693 and 443 pairs of subsequent observations Tt, Tt+1 for train and test sets respectively.
Hardware Specification Yes We run all experiments on a single H100.
Software Dependencies No No specific software versions for libraries like PyTorch, TensorFlow, or Python are mentioned. The paper mentions 'Adam (Kingma & Ba, 2014)' as an optimizer and 'Point Cloud Utils (Williams, 2022)' as a tool, but no version numbers for general software dependencies used for implementation.
Experiment Setup Yes We provide hyperparameters per experiment. We optimize the weights of the neural field fθ in all experiments with Adam (Kingma & Ba, 2014) with a learning rate of 1e-4, and an inner step size of 30.0 for ci and 1.0 for pi... For CIFAR10 (Krizhevsky et al., 2009) reconstruction and classification we use a hidden dim of 128 with 3 heads, 25 latents of size 64, a batch size of 32 and restrict the cross-attention operator to k=4 nearest latents for each input coordinate x. For σq, σv we choose 1.0 and 3.0 respectively. We train the ENF model and the classifier for 100 epochs.