Let's do the time-warp-attend: Learning topological invariants of dynamical systems
Authors: Noa Moriel, Matt Ricci, Mor Nitzan
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluate our model and its baseline competitors on a diverse, synthetic dataset of noisy (zeromean gaussian), real-world systems drawn from across the sciences. Test datasets include the simple harmonic oscillator ( SO ), its warped variant ( Augmented SO ), a system undergoing a supercritical Hopf bifurcation as described in (Strogatz, 1994)( Supercritical Hopf ), examples based on Li enard equations ( Li enard Polynomial and Li enard Sigmoid ), and systems used to model oscillatory phenomena in nature and engineering applications, namely the van der Pol system, used for modeling electrical circuits in early radios ( Van der Pol ), the Belousov-Zhabotinsky model, a model of chemical oscillations ( BZ reaction ), and the Sel kov oscillator, used in modeling glycolitic cycles ( Sel kov ), see Appendix 7.3 and Strogatz (1994). ... We find that our framework generalizes across a wide range of dynamical systems and classifies distinct dynamical regimes in noisy (zero-mean gaussian) conditions better on average than baseline methods (see Table 1, Table A4, and examples in Fig. A8). |
| Researcher Affiliation | Academia | Noa Moriel The Hebrew University noa.moriel@mail.huji.ac.il Matthew Ricci The Hebrew University matthew.ricci@mail.huji.ac.il Mor Nitzan The Hebrew University mor.nitzan@mail.huji.ac.il |
| Pseudocode | No | The paper describes the methodology and architecture in text and diagrams, but does not include pseudocode or algorithm blocks. |
| Open Source Code | Yes | 1Code available at: https://github.com/nitzanlab/time-warp-attend |
| Open Datasets | Yes | We train on synthetic, augmented data generated from a simple oscillator prototype. ... We obtain the data, compute high-dimensional gene expression velocities per cell and their projection into UMAP space, and each cell s cell-cycle score as described in sc Velo (Bergen et al., 2020), RNA velocity basics tutorial. ... In that study, a single-cell RNA-sequencing dataset was collected where the expression of over 2,000 genes are measured per cell, for a total of 3,600 cells (Bastidas-Ponce et al., 2019); |
| Dataset Splits | No | For training and evaluation, we prepared a dataset comprising 10,000 samples for training and 1,000 samples for testing. |
| Hardware Specification | Yes | All experiments were carried out using pytorch v.1.12 using an NVIDIA RTX 2080 GPU, taking 40 seconds per training experiment. |
| Software Dependencies | Yes | All experiments were carried out using pytorch v.1.12 using an NVIDIA RTX 2080 GPU... We integrate each system from a random point at an interval of 0.1 up to time T = 100 based on the vector field and compute the maximal Lyapunov exponent, λ1, of the trajectory using the python library https://pypi.org/project/nolds. |
| Experiment Setup | Yes | For training and evaluation, we prepared a dataset comprising 10,000 samples for training and 1,000 samples for testing. We employed the ADAM optimizer with a learning rate of 1 10 4 and trained the model for 20 epochs, which we confirmed was enough time to fit the training data. For inference, we still perform dropout and average the output of 10 evaluations for each sample. ... The MLP consists of a hidden layer with 64 dimensions, Re LU activation, and a dropout rate of 0.9. |