Equivariant Neural Tangent Kernels
Authors: Philipp Misof, Pan Kessel, Jan E Gerken
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate in numerical experiments that this still holds approximately for finite-width ensembles. By implementing equivariant NTKs for roto-translations in the plane (G = Cn R2) and 3d rotations (G = SO(3)), we show that equivariant NTKs outperform their non-equivariant counterparts as kernel predictors for histological image classification and quantum mechanical property prediction. |
| Researcher Affiliation | Collaboration | 1Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96 Gothenburg, Sweden 2Prescient Design, Genentech Roche, Basel, Switzerland. Correspondence to: Jan Gerken <EMAIL>. |
| Pseudocode | No | The paper describes mathematical derivations and definitions of layers and their recursions, such as in Theorem 4.1 (Kernel recursions for group convolutional layers) and subsequent sections, but does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | The code is provided publicly at https://github.com/Philipp Mi sof CH/equivariant-ntk. |
| Open Datasets | Yes | In the following, we validate the theoretical results of the preceding sections experimentally for various datasets (Cifar10, QM9, MNIST, and histological data), tasks (regression and classification), and groups (SO(3) and C4 R2). We benchmark the NTK-predictor resulting from an SO(3)-invariant network on the QM9 dataset (Ramakrishnan et al., 2014) Medical Image Classification with C4 R2. ... dataset of histological images (Kather et al., 2018) |
| Dataset Splits | No | The same training and test data was used for both models with a test data size of 1000 images. Both architectures have been implemented in the neural-tangents package (Novak et al., 2020). The MAE loss was evaluated on a test set of 100 molecules. While test set sizes are mentioned, comprehensive split information (like training/validation sizes/percentages, or references to standard splits for CIFAR10/MNIST) is not provided in the main text or appendices. |
| Hardware Specification | No | The computations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) and the Swedish National Infrastructure for Computing (SNIC) at C3SE partially funded by the Swedish Research Council through grant agreements 2022-06725 and 2018-05973. This mentions supercomputing infrastructure but does not provide specific hardware details like GPU/CPU models or memory. |
| Software Dependencies | No | An efficient implementation for many layers is available in the Jax-based Python package neural-tangents (Novak et al., 2020). Again, these layers are implemented in the neural-tangents package and the necessary generalized FFTs are provided by the JAX-based package s2fft (Price & Mc Ewen, 2024). For implementing the GCNNs, we used the escnn-package (Weiler & Cesa, 2019). The paper lists specific software packages used for implementation but does not provide their version numbers. |
| Experiment Setup | Yes | The task consists of classifying histological images (Kather et al., 2018) containing nine classes of tissues, two of which are cancerous. The original images have a resolution of 224 224 pixels each and have been down-scaled to a resolution of 32 32 pixels... we constructed target vectors Y = {y0, . . . , y N} from classes c according to ec 1 91... The hyperparameter β in (42) was chosen as described in (Esteves et al., 2023)... The input signals are constructed at a resolution of 12 11 on the sphere, corresponding to a bandlimit of L = 6, which are then downsampled to a bandlimit L = 3 for the group layer. The precise architectures of the MLP based network and the SO(3)-invariant network are listed in Table 2. |