Learning Long-Term Dependencies in Irregularly-Sampled Time Series

TL;DR

This paper introduces ODE-LSTMs, a novel RNN architecture that effectively models long-term dependencies in irregularly-sampled time series by separating memory from continuous-time states, overcoming gradient issues.

Contribution

The paper proposes ODE-LSTMs, a new RNN model that encodes continuous-time dynamics and maintains stable long-term memory, improving performance on irregular time series data.

Findings

ODE-LSTMs outperform existing RNNs on irregular data

The model effectively captures long-term dependencies

Gradient issues are mitigated by separating memory from state

Abstract

Recurrent neural networks (RNNs) with continuous-time hidden states are a natural fit for modeling irregularly-sampled time series. These models, however, face difficulties when the input data possess long-term dependencies. We prove that similar to standard RNNs, the underlying reason for this issue is the vanishing or exploding of the gradient during training. This phenomenon is expressed by the ordinary differential equation (ODE) representation of the hidden state, regardless of the ODE solver's choice. We provide a solution by designing a new algorithm based on the long short-term memory (LSTM) that separates its memory from its time-continuous state. This way, we encode a continuous-time dynamical flow within the RNN, allowing it to respond to inputs arriving at arbitrary time-lags while ensuring a constant error propagation through the memory path. We call these RNN models ODE-LSTMs. We experimentally show that ODE-LSTMs outperform advanced RNN-based counterparts on non-uniformly sampled data with long-term dependencies. All code and data is available at https://github.com/mlech26l/ode-lstms.