Matt L. Sampson

Matt L. Sampson, Peter Melchior

Latent ODE models provide flexible descriptions of dynamic systems, but they can struggle with extrapolation and predicting complicated non-linear dynamics. The latent ODE approach implicitly relies on encoders to identify unknown system parameters and initial conditions, whereas the evaluation times are known and directly provided to the ODE solver. This dichotomy can be exploited by encouraging time-independent latent representations. By replacing the common variational penalty in latent space with an $\ell_2$ penalty on the path length of each system, the models learn data representations that can easily be distinguished from those of systems with different configurations. This results in faster training, smaller models, more accurate interpolation and long-time extrapolation compared to the baseline ODE models with GRU, RNN, and LSTM encoder/decoders on tests with damped harmonic oscillator, self-gravitating fluid, and predator-prey systems. We also demonstrate superior results for simulation-based inference of the Lotka-Volterra parameters and initial conditions by using the latents as data summaries for a conditional normalizing flow. Our change to the training loss is agnostic to the specific recognition network used by the decoder and can therefore easily be adopted by other latent ODE models.

Angelina Yan, Matt L. Sampson, Peter Melchior

12-lead ECGs with high sampling frequency are the clinical gold standard for arrhythmia detection, but their short-term, spot-check nature often misses intermittent events. Wearable ECGs enable long-term monitoring but suffer from irregular, lower sampling frequencies due to battery constraints, making morphology analysis challenging. We present an end-to-end classification pipeline to address these issues. We train a latent ODE to model continuous ECG waveforms and create robust feature vectors from high-frequency single-channel signals. We construct three latent vectors per waveform via downsampling the initial 360 Hz ECG to 90 Hz and 45 Hz. We then use a gradient boosted tree to classify these vectors and test robustness across frequencies. Performance shows minimal degradation, with macro-averaged AUC-ROC values of 0.984, 0.978, and 0.976 at 360 Hz, 90 Hz, and 45 Hz, respectively, suggesting a way to sidestep the trade-off between signal fidelity and battery life. This enables smaller wearables, promoting long-term monitoring of cardiac health.

Matt L. Sampson, Peter Melchior

The learning rate schedule is one of the most impactful aspects of neural network optimization, yet most schedules either follow simple parametric functions or react only to short-term training signals. None of them are supported by a comprehensive temporal view of how well neural networks actually train. We present a new learning rate scheduler that models the training performance of neural networks as a dynamical system. It leverages training runs from a hyperparameter search to learn a latent representation of the training process. Given current training metrics, it predicts the future learning rate schedule with the best long-term validation performance. Our scheduler generalizes beyond previously observed training dynamics and creates specialized schedules that deviate noticeably from common parametric functions. It achieves SOTA results for image classification with CNN and ResNet models as well as for next-token prediction with a transformer model. The trained models are located in flatter regions of the loss landscape and thus provide better generalization than those trained with other schedules. Our method is computationally efficient, optimizer-agnostic, and can easily be layered on top of ML experiment-tracking platforms. An implementation of our scheduler will be made available after acceptance.