Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
E(n)-equivariant Graph Neural Cellular Automata
Authors: Gennaro Gala, Daniele Grattarola, Erik Quaeghebeur
TMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We showcase the broad and successful applicability of E(n)GNCAs on three different tasks: (i) isotropic pattern formation, (ii) graph auto-encoding, and (iii) simulation of E(n)-equivariant dynamical systems. ... Figure 2: E(n)-GNCA convergence to a 2D grid (top), a 3D torus (middle) and the Stanford geometric bunny (bottom). The first 4 columns show E(n)-GNCA states at different time steps. We report LINV (cf. Equation 13) for the state in each figure. ... Table 1: Autoencoding results. F1 scores (the higher the better) averaged over 10 different runs. |
| Researcher Affiliation | Collaboration | Gennaro Gala EMAIL Department of Mathematics and Computer Science Eindhoven University of Technology, The Netherlands Daniele Grattarola EMAIL Independent researcher Erik Quaeghebeur EMAIL Department of Mathematics and Computer Science Eindhoven University of Technology, The Netherlands |
| Pseudocode | No | The paper describes the model architecture and training procedures using mathematical equations and descriptive text, but it does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | Our code is available at github.com/gengala/egnca. |
| Open Datasets | Yes | We consider five datasets of featureless graphs of varying size, connectivity and properties: comms (100 graphs, 2 communities, 12 20 nodes) (Liu et al., 2019), planar-s (200 planar graphs, 12 20 nodes), planar-l (200 planar graphs, 32 64 nodes), sbm (200 stochastic block model graphs, 2 5 communities, 44 187 nodes) (Martinkus et al., 2022) and proteins (918 graphs, 100 500 nodes) (Dobson & Doig, 2003). |
| Dataset Splits | Yes | We split all datasets into training (80%), validation (10%) and test (10%) sets. |
| Hardware Specification | Yes | All experiments are run on an NVIDIA Quadro P1000 16GB, and each run does not take more than 2.5 hours to complete. |
| Software Dependencies | No | We are grateful to the developers of the main software packages used for this work: Pytorch (Paszke et al., 2019), Py Torch Geometric (Fey & Lenssen, 2019) and Lightning (Falcon & The Py Torch Lightning team, 2019). The paper lists software packages but does not provide specific version numbers for them. |
| Experiment Setup | Yes | We set h = 16 (hidden dimension) and m = 32 (message dimension) throughout all experiments... We train the model by minimising Equation 13, using Adam (Kingma & Ba, 2015) with initial learning rate of 0.0005. The learning rate is then decreased during training using a reduce-on-plateau schedule. We use gradient clipping and weight decay as regularisation techniques. We increase the batch size during training (from a minimum of 4 to 32)... For each training graph Gn we create a small pool of K states {[X(n,k), H(n,k)]}K k=1. Every H(n,k) is again initialised as 1 whereas input node coordinates X(n,k) now follow an isotropic Gaussian N(0, σ1).6... Every mini-batch state S(n,k) is then run by τθ for t [t1, t2] random time steps... We randomly sample t in [15, 25] at each optimisation step. |