Trajectory Flow Matching with Applications to Clinical Time Series Modeling

Modeling stochastic and irregularly sampled time series is a challenging problem found in a wide range of applications, especially in medicine. Neural stochastic differential equations (Neural SDEs) are an attractive modeling technique for this problem, which parameterize the drift and diffusion terms of an SDE with neural networks. However, current algorithms for training Neural SDEs require backpropagation through the SDE dynamics, greatly limiting their scalability and stability. To address this, we propose Trajectory Flow Matching (TFM), which trains a Neural SDE in a simulation-free manner, bypassing backpropagation through the dynamics. TFM leverages the flow matching technique from generative modeling to model time series. In this work we first establish necessary conditions for TFM to learn time series data. Next, we present a reparameterization trick which improves training stability. Finally, we adapt TFM to the clinical time series setting, demonstrating improved performance on three clinical time series datasets both in terms of absolute performance and uncertainty prediction.

Making Logic Learnable With Neural Networks

While neural networks are good at learning unspecified functions from training samples, they cannot be directly implemented in hardware and are often not interpretable or formally verifiable. On the other hand, logic circuits are implementable, verifiable, and interpretable but are not able to learn from training data in a generalizable way. We propose a novel logic learning pipeline that combines the advantages of neural networks and logic circuits. Our pipeline first trains a neural network on a classification task, and then translates this, first to random forests or look-up tables, and then to AND-Inverter logic. We show that our pipeline maintains greater accuracy than naive translations to logic, and minimizes the logic such that it is more interpretable and has decreased hardware cost. We show the utility of our pipeline on a network that is trained on biomedical data from patients presenting with gastrointestinal bleeding with the prediction task of determining if patients need immediate hospital-based intervention. This approach could be applied to patient care to provide risk stratification and guide clinical decision-making.