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/learning-long-term-irregular-ts.

We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent dynamical systems with varying (i.e., \emph{liquid}) time-constants coupled to their hidden state, with outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics, and compute their expressive power by the \emph{trajectory length} measure in a latent trajectory space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to modern RNNs. Code and data are available at https://github.com/raminmh/liquid_time_constant_networks

In this paper, we introduce the notion of liquid time-constant (LTC) recurrent neural networks (RNN)s, a subclass of continuous-time RNNs, with varying neuronal time-constant realized by their nonlinear synaptic transmission model. This feature is inspired by the communication principles in the nervous system of small species. It enables the model to approximate continuous mapping with a small number of computational units. We show that any finite trajectory of an $n$-dimensional continuous dynamical system can be approximated by the internal state of the hidden units and $n$ output units of an LTC network. Here, we also theoretically find bounds on their neuronal states and varying time-constant.

We propose an effective method for creating interpretable control agents, by \textit{re-purposing} the function of a biological neural circuit model, to govern simulated and real world reinforcement learning (RL) test-beds. Inspired by the structure of the nervous system of the soil-worm, \emph{C. elegans}, we introduce \emph{Neuronal Circuit Policies} (NCPs) as a novel recurrent neural network instance with liquid time-constants, universal approximation capabilities and interpretable dynamics. We theoretically show that they can approximate any finite simulation time of a given continuous n-dimensional dynamical system, with $n$ output units and some hidden units. We model instances of the policies and learn their synaptic and neuronal parameters to control standard RL tasks and demonstrate its application for autonomous parking of a real rover robot on a pre-defined trajectory. For reconfiguration of the \emph{purpose} of the neural circuit, we adopt a search-based RL algorithm. We show that our neuronal circuit policies perform as good as deep neural network policies with the advantage of realizing interpretable dynamics at the cell-level. We theoretically find bounds for the time-varying dynamics of the circuits, and introduce a novel way to reason about networks' dynamics.

In this paper, we introduce a novel method to interpret recurrent neural networks (RNNs), particularly long short-term memory networks (LSTMs) at the cellular level. We propose a systematic pipeline for interpreting individual hidden state dynamics within the network using response characterization methods. The ranked contribution of individual cells to the network's output is computed by analyzing a set of interpretable metrics of their decoupled step and sinusoidal responses. As a result, our method is able to uniquely identify neurons with insightful dynamics, quantify relationships between dynamical properties and test accuracy through ablation analysis, and interpret the impact of network capacity on a network's dynamical distribution. Finally, we demonstrate generalizability and scalability of our method by evaluating a series of different benchmark sequential datasets.