Noether's Razor: Learning Conserved Quantities
Authors: Tycho van der Ouderaa, Mark van der Wilk, Pim de Haan
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate a proof-ofprinciple on n-harmonic oscillators and n-body systems. We find that our method correctly identifies the correct conserved quantities and U(n) and SE(n) symmetry groups, improving overall performance and predictive accuracy on test data. |
| Researcher Affiliation | Collaboration | Tycho F. A. van der Ouderaa Imperial College London London, UK Mark van der Wilk University of Oxford Oxford, UK Pim de Haan Cusp AI Amsterdam, NL |
| Pseudocode | No | The paper provides mathematical derivations and descriptions of the method, but it does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | The code is available at https://github.com/tychovdo/noethers-razor. |
| Open Datasets | No | The paper describes the process of generating synthetic training data by sampling initial conditions from Gaussian or unit normal distributions for each experiment (Simple Harmonic Oscillator, n Harmonic Oscillators, n-Body System) rather than using a pre-existing publicly available dataset with concrete access information. |
| Dataset Splits | No | The paper discusses train and test data splits, but no explicit validation data split is described for the experiments conducted. The word 'validation' appears only in the context of other research or as something their method 'does not require'. |
| Hardware Specification | Yes | All experiments were run on a single NVIDIA RTX 4090 GPU with 24Gi B of GPU memory. |
| Software Dependencies | No | The paper mentions optimizers like Adam but does not provide specific version numbers for software dependencies such as deep learning frameworks (e.g., PyTorch, TensorFlow), programming languages (e.g., Python), or CUDA versions. |
| Experiment Setup | Yes | We use an MLP with 2 hidden layers, each consisting of 200 hidden neurons and a linear exponential unit activation function with α = 2. For symmetrisation, we use S = 200 samples from a uniform measure for µ(τ). We use 20 Euler steps for time integration. We use fixed output noise and closed-form prior variance (Appendix D). We optimise the ELBO in full batch with Adam [Kingma and Ba, 2014] (β1 = 0.9, β2 = 0.999) trained for 2000 epochs with a learning rate of 0.001, cosine annealed to 0. |