Anamnesic Neural Differential Equations with Orthogonal Polynomial Projections
Authors: Edward De Brouwer, Rahul G Krishnan
ICLR 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluate our approach on two objectives : (1) the ability of the learned embedding to encode global information about the time series, through the reverse reconstruction performance (or memorization) and (2) the ability of embedding to provide an informative input for a downstream task. We study our methods on the following datasets: Synthetic Univariate. Chaotic Attractors. MIMIC-IIII dataset. Baselines: We compare our approach against two sets of baselines: Neural ODEs architecture and variants of recurrent neural networks architectures designed for long-term memory. [...] Results for these tasks are presented in Table 1 for Synthetic and Lorenz datasets and in Table 2 for MIMIC. |
| Researcher Affiliation | Academia | Edward De Brouwer ESAT-STADIUS KU Leuven Leuven, Belgium edward.debrouwer@kuleuven.be Rahul G. Krishnan Department of Computer Science University of Toronto Toronto, Canada rahulgk@cs.toronto.edu |
| Pseudocode | Yes | Algorithm 1: Poly ODE Training Data: x, matrices Aµ, Bµ, number of dimensions d, number of observations T, number of polynomial coefficients N Result: Training loss L over a whole sequence x t 0 Initialize hj(0) = cj(0) = 0N, 8j 2 1, ..., d, Loss L = 0 for i 1 to T do Integrate c1,...,d(t) and h0,..,d(t) from t = t until t = ti ˆxi h0(t ) Update c1,...,d(ti) and h0,...,d(ti) with xi, mi. L = L + k(ˆxi xi) mik2 |
| Open Source Code | Yes | Our code is available at https://github.com/edebrouwer/polyode. |
| Open Datasets | Yes | MIMIC-IIII dataset. We use a pre-processed version of the MIMIC-III dataset (Johnson et al., 2016; Wang et al., 2020). |
| Dataset Splits | No | The paper mentions training and testing on datasets, but does not explicitly provide details about validation dataset splits (e.g., percentages or sample counts for training, validation, and test sets). |
| Hardware Specification | No | The paper does not provide specific hardware details such as GPU or CPU models, memory amounts, or detailed computer specifications used for running the experiments. |
| Software Dependencies | No | The paper mentions using differentiable numerical solvers and implicit solvers (e.g., Backward Euler or Adams-Moulton) but does not provide specific software names with version numbers for replication, such as specific deep learning frameworks or libraries. |
| Experiment Setup | No | The paper mentions some training details like the loss function and initializations, and states 'Implementation details are available in Appendix H', but it does not provide specific hyperparameter values (e.g., learning rate, batch size, optimizer) or comprehensive system-level training settings within the main text. |