[Paper Review] Causal Navigation by Continuous-time Neural Networks

Charles Vorbach, Ramin Hasani+3 more|arXiv (Cornell University)|Jun 15, 2021

Domain Adaptation and Few-Shot Learning85 references25 citations

TL;DR

The paper introduces continuous-time neural networks with causal structure (liquid time-constant networks) to learn causal representations from visual input for drone navigation, showing superior robustness in closed-loop tasks compared to traditional RNNs.

ABSTRACT

Imitation learning enables high-fidelity, vision-based learning of policies within rich, photorealistic environments. However, such techniques often rely on traditional discrete-time neural models and face difficulties in generalizing to domain shifts by failing to account for the causal relationships between the agent and the environment. In this paper, we propose a theoretical and experimental framework for learning causal representations using continuous-time neural networks, specifically over their discrete-time counterparts. We evaluate our method in the context of visual-control learning of drones over a series of complex tasks, ranging from short- and long-term navigation, to chasing static and dynamic objects through photorealistic environments. Our results demonstrate that causal continuous-time deep models can perform robust navigation tasks, where advanced recurrent models fail. These models learn complex causal control representations directly from raw visual inputs and scale to solve a variety of tasks using imitation learning.

Motivation & Objective

• Motivate learning causal representations that generalize under domain shifts in vision-based control.
• Propose continuous-time neural networks with causal structure (LTCs) as a framework to model interventions.
• Demonstrate through high-dimensional visual drone navigation tasks that LTC-based models capture causal dependencies.
• Compare LTC-based models with traditional discrete-time and continuous-time baselines in passive and active (closed-loop) settings.

Proposed method

• Formulate causal structures within continuous-time neural networks by relating LTC dynamics to dynamic causal models (DCMs).
• Use bilinear (DCM-inspired) approximations of Neural ODEs to construct liquid time-constant networks (LTCs) with interpretable interventions.
• Argue that standard Neural ODEs are not causal, while LTCs enable internal and external interventions via learned parameters.
• Train LTCs via gradient-based methods (adjoint or BPTT) leveraging the uniqueness of LTC solutions to obtain causal mappings.
• Evaluate learned LTC-based policies in end-to-end imitation learning on photorealistic drone navigation tasks.

Experimental results

Research questions

• RQ1 Can continuous-time neural networks with causal structure (LTCs) learn interventions and causal mappings from high-dimensional visual input?
• RQ2 Do LTC-based models provide robust, interpretable closed-loop navigation in photorealistic environments where traditional models fail?
• RQ3 How do LTCs compare to ODE-RNNs, LSTMs, and CT-GRUs in static and dynamic target pursuit under occlusions and environmental perturbations.

Key findings

• LTC-based models (Neural Circuit Policies) can learn causal attention to targets directly from raw vision and maintain it over time, unlike other models.
• In closed-loop tests, LTC-based models achieve higher success rates across static target, moving target chase, and marker-based hiking tasks than LSTM, ODE-RNN, and CT-GRU baselines.
• NCPs demonstrate greater robustness to environmental perturbations such as rain and fog than non-causal models.
• Discretized CNNs fail to leverage temporal dependencies under occlusion, while LTC-based models sustain performance in challenging visual scenes.
• Theoretical results show LTCs provide unique solutions and explicit intervention coefficients, enabling dynamical causal modeling in forward and backward passes.