Extending Structural Causal Models for Autonomous Vehicles to Simplify Temporal System Construction & Enable Dynamic Interactions Between Agents

TL;DR

This work extends structural causal models (SCMs) to the autonomous vehicle (AV) domain by introducing modular, time-aware extensions that support dynamic multi-agent interactions while maintaining a fixed, memory-efficient graph structure. Key contributions include monadic handling of side-effects, a global variable context for temporal reasoning, temporal variables (including Previous Time Step, time scaling, time differences, and time-conditioned selectors), buffer and socket constructs for encapsulation and modular composition, and retrospective causal stationarity to accommodate mutable input sets. The authors provide theoretical proofs (PTS Variable Recursion and Mutable Input Set RCS) and demonstrate practical applicability through counterfactual analysis on AV scenarios derived from the highD dataset. Overall, the approach yields transparent, explainable AV reasoning with scalable multi-agent attribution and realistic modeling of dynamic environments, enabling robust post-hoc explanations and accountability in embodied AI systems.

Abstract

In this work we aim to bridge the divide between autonomous vehicles and causal reasoning. Autonomous vehicles have come to increasingly interact with human drivers, and in many cases may pose risks to the physical or mental well-being of those they interact with. Meanwhile causal models, despite their inherent transparency and ability to offer contrastive explanations, have found limited usage within such systems. As such, we first identify the challenges that have limited the integration of structural causal models within autonomous vehicles. We then introduce a number of theoretical extensions to the structural causal model formalism in order to tackle these challenges. This augments these models to possess greater levels of modularisation and encapsulation, as well presenting temporal causal model representation with constant space complexity. We also prove through the extensions we have introduced that dynamically mutable sets (e.g. varying numbers of autonomous vehicles across time) can be used within a structural causal model while maintaining a relaxed form of causal stationarity. Finally we discuss the application of the extensions in the context of the autonomous vehicle and service robotics domain along with potential directions for future work.

Figures (15)

• Figure 1: Illustration of example fault attribution scenario. Subfigures show the initial scene with plan on the left and the final outcome on the right.
• Figure 2: The left side depicts the overall AV SCM-based architecture, including AV agent interactions via links. The right side depicts the components of this architecture and how they interact causally with the collision scenario depicted in Fig. \ref{['fig:scenes']}.
• Figure 3: The SCMs depict the calculation of velocity $v$ from acceleration $a$ by calculating the velocity difference $\Delta v$ and adding it to the velocity from the previous time step. A typical time series SCM would be coupled along with time series data, corresponding with time indexed variables --- indicated via subscripts. In contrast the extended SCM representation uses PTS variables and buffer variables. These allow the SCM a fixed-size graph while still capturing causal links between time steps, in addition to providing data encapsulation.
• Figure 4: Illustration of merging and un-merging SCMs without and without socket variables. Here solid borders denote endogenous variables, dashes borders exogenous variables, and dotted borders socket variables.
• Figure 5: Visualisation of crash scene within SCM architecture. Subfigures show the initial scene with plan on the left and the final outcome on the right.

Theorems & Definitions (5)

• Definition 1: Retrospective Causal Stationarity
• Theorem 2: Mutable Input Set RCS
• Lemma 3: Base Case
• Lemma 4: Introduction Induction Step
• Lemma 5: Status Quo / Removal Induction Step