Latent SDEs on Homogeneous Spaces
Authors: Sebastian Zeng, Florian Graf, Roland Kwitt
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments demonstrate that a latent SDE of the proposed type can be learned efficiently by means of an existing one-step geometric Euler-Maruyama scheme. Despite restricting ourselves to a less rich class of SDEs, we achieve competitive or even state-of-the-art results on various time series interpolation/classification problems. |
| Researcher Affiliation | Academia | University of Salzburg, Austria |
| Pseudocode | Yes | Algorithm 1 Geometric Euler-Maruyama Algorithm (g-EM) [36]. Listing 1 SDE solver in Lie algebra so(n). Listing 2 Generate basis in so(n). Listing 3 Generate SDE solution on Sn 1. Listing 4 Example usage with dummy K, µ, κ. |
| Open Source Code | Yes | Source code is available at https://github.com/plus-rkwitt/Latent SDEon HS. |
| Open Datasets | Yes | Human Activity: https://doi.org/10.24432/C57G8X Physio Net (2012): [51] Rotating MNIST: [9] |
| Dataset Splits | Yes | Human Activity: The dataset is split into 4,194 sequences for training, 1,311 for testing, and 1,049 for validation. Pendulum regression: 2,000 images are used for training, 1,000 images for testing and an additional 1,000 images for validation and hyperparameter selection. Rotating MNIST: 360 images are used for training, 360 for testing, and 36 for validation and hyperparameter selection. |
| Hardware Specification | Yes | All experiments were executed on systems running Ubuntu 22.04.2 LTS (kernel version 5.15.0-71-generic x86_64) with 128 GB of main memory and equipped with either NVIDIA Ge Force RTX 2080 Ti or Ge Force RTX 3090 Ti GPUs. |
| Software Dependencies | Yes | All experiments are implemented in Py Torch (v1.13 and also tested on v2.0). The reference implementation of the power spherical distribution from [8] as well as the einops package are needed. |
| Experiment Setup | Yes | We optimize all model parameters using Adam [28] with a cyclic cosine learning rate schedule [18] (990 epochs with cycle length of 60 epochs and learning rate within [1e-6, 1e-3]). The weighting of the KL divergences in the ELBO is selected on validation splits (if available) or set to 1e-5 without any annealing schedule. We fix the dimensionality of the latent space to n = 16 and use K = 6 polynomials in Eq. (11), unless stated otherwise. |