Embodied World Models Emerge from Navigational Task in Open-Ended Environments (2504.11419v2)

Abstract: Spatial reasoning in partially observable environments has often been approached through passive predictive models, yet theories of embodied cognition suggest that genuinely useful representations arise only when perception is tightly coupled to action. Here we ask whether a recurrent agent, trained solely by sparse rewards to solve procedurally generated planar mazes, can autonomously internalize metric concepts such as direction, distance and obstacle layout. After training, the agent consistently produces near-optimal paths in unseen mazes, behavior that hints at an underlying spatial model. To probe this possibility, we cast the closed agent-environment loop as a hybrid dynamical system, identify stable limit cycles in its state space, and characterize behavior with a Ridge Representation that embeds whole trajectories into a common metric space. Canonical correlation analysis exposes a robust linear alignment between neural and behavioral manifolds, while targeted perturbations of the most informative neural dimensions sharply degrade navigation performance. Taken together, these dynamical, representational, and causal signatures show that sustained sensorimotor interaction is sufficient for the spontaneous emergence of compact, embodied world models, providing a principled path toward interpretable and transferable navigation policies.

• The paper shows that GRU agents using Meta-RL with NES can develop stable internal spatial representations for navigating complex mazes.
• It introduces a novel analysis combining Hybrid Dynamical Systems, Ridge Representations, and Canonical Correlation Analysis to decode agent behavior.
• Intervention experiments confirm the causal role of key neural dimensions, offering practical insights for robot navigation and interpretable AI.

This paper investigates how artificial agents, specifically neural networks, can develop an internal understanding of spatial concepts like direction, distance, and obstacle avoidance through active interaction with their environment, drawing inspiration from embodied cognition theory. The focus is on planar navigation tasks in open-ended, randomly generated maze environments (2504.11419).

Core Problem and Approach

The central question is whether an agent, perceiving only local information and influencing the environment through its actions, can form stable internal representations of spatial properties, going beyond simple stimulus-response learning.

To address this, the authors employ:

1. Agent Architecture: A Gated Recurrent Unit (GRU) network is used. GRUs are suitable for tasks with partial observability as their gating mechanisms allow them to maintain and update internal memory states over time, integrating past observations to inform future actions.
2. Training Framework: Meta-Reinforcement Learning (Meta-RL) combined with Natural Evolution Strategies (NES) is used. NES optimizes the network parameters across a population of agents evaluated on diverse, randomly generated mazes. Meta-RL encourages rapid adaptation within a specific maze instance. A "Goal-Reset" mechanism is used where, upon reaching the goal, the agent's position is reset, but its GRU hidden state persists, allowing it to leverage learned information in subsequent trials within the same maze.
3. Environment: The task involves navigating 10x10 discrete grid mazes with randomly placed obstacles (~30% density). Critically, the agent has only a limited 3x3 local view of its surroundings, forcing reliance on memory and exploration.

Key Methodologies for Analysis

The paper introduces several techniques to analyze the agent's learned internal representations and link them to behavior:

1. Hybrid Dynamical Systems (HDS): Instead of analyzing the agent and environment separately, HDS models their interaction as a single, closed-loop dynamical system. The state is represented as a pair (Q, X), where Q is the discrete environmental state (agent's position) and X is the continuous neural state (GRU hidden state vector).
   • Implementation: This involves simulating the agent-environment loop and recording the sequence of (Q, X) states.
   • Goal: To identify stable patterns, particularly limit cycles, in this joint space. A limit cycle indicates that the agent has settled into a repeatable, robust strategy involving synchronized environmental and neural dynamics. Lyapunov exponents are used to assess the stability of these cycles against perturbations.
   • Cyclic Stimulation: To confirm that observed cycles are internal attractors and not just artifacts of environmental feedback, a fixed sequence of representative observations (recorded from successful paths) is repeatedly fed to the agent, bypassing real-time environmental input. If the agent's state converges to the same cycle under various initial conditions, it confirms the strategy is robustly internalized.
2. Ridge Representation: This technique converts variable-length 2D navigation paths into fixed-size grayscale images, creating a standardized "behavioral metric space."
   • Implementation: For each point on a trajectory, a linearly decaying "radiation field" is generated on a fixed grid (e.g., 21x21). The intensities from all points are combined using a maximum value rule, forming a "ridge" image that encodes the path's geometry (shape, direction, turns). Euclidean distance (L2 norm) between these images provides a metric for behavioral similarity.
   • Goal: To provide a quantitative, fixed-dimensional representation of behavior suitable for comparison with neural states and for techniques like PCA or CCA. PCA applied to Ridge images often reveals ring-like structures corresponding to path direction and length, similar to patterns observed in neural state PCA.
3. Canonical Correlation Analysis (CCA): CCA is used to quantify the linear relationship between the high-dimensional neural state space (e.g., 128-dim GRU states) and the high-dimensional behavioral space (e.g., 441-dim flattened Ridge images).
   • Implementation: Takes the time-aligned neural states and corresponding Ridge images as input. It finds pairs of projection vectors (canonical modes) for each space such that the correlation between the projected data is maximized.
   • Goal: To assess the strength and dimensionality of the alignment between internal representations and external behavior. High correlations across multiple canonical modes (e.g., $\rho > 0.8$ for the top 5-10 modes) suggest a deep, multi-faceted encoding of behavioral features in the neural activity.
4. Intervention Experiments: These experiments test the causal role of the neural dimensions identified as important by CCA.
   • Implementation: Select the neural dimensions most strongly correlated with behavior via CCA. During navigation, intervene by:
     • Zeroing out these dimensions.
     • Randomizing their values.
     • Injecting pre-recorded "optimal" neural state components corresponding to successful trajectories into these dimensions.
   • Goal: To determine if these neural dimensions actively drive navigation decisions. If perturbing them significantly degrades performance (longer paths, lower success rates, slower convergence) compared to baseline or control interventions (e.g., perturbing low-correlation dimensions), it confirms their causal importance.

Key Findings

• Agents trained with GRU+Meta-RL successfully learn efficient navigation strategies in diverse random mazes.
• HDS analysis reveals stable limit cycles in the joint agent-environment state space, representing internalized optimal strategies confirmed via cyclic stimulation and Lyapunov stability analysis.
• PCA visualizations show analogous ring-like structures in both neural state projections and Ridge representation projections, hinting at shared geometric encoding of direction and distance.
• CCA demonstrates strong, statistically significant correlations (often $\rho > 0.8$) across multiple dimensions between the GRU hidden states and the Ridge representations of the navigation paths, far exceeding random baselines.
• Intervention experiments confirm a causal link: disrupting the high-correlation neural dimensions identified by CCA significantly impairs navigation performance, while injecting optimal states improves it.

Practical Implications and Applications

• Building More Interpretable Agents: The HDS, Ridge Representation, CCA, and intervention framework provides a methodology for analyzing the internal workings of embodied agents, particularly those relying on recurrent networks in tasks with complex state spaces and partial observability. It helps move beyond black-box performance metrics to understand how agents represent and use spatial information.
• Robot Navigation: The principles and analysis techniques could be applied to understand and debug navigation policies learned by real-world robots, especially in complex or unknown environments where internal world models are crucial.
• Validating Learned Representations: This work shows how to verify if an agent has learned generalizable spatial concepts (direction, distance, relative positioning) rather than just memorizing specific sequences or stimulus-response mappings.
• Improving Training: Understanding which neural components are critical for performance could potentially inform more targeted training methods or network architectures. The Goal-Reset mechanism is a practical trick to accelerate learning in episodic tasks within a single environment instance.
• Bridging Theory and Practice: The paper provides concrete evidence supporting the embodied cognition hypothesis—that interaction is key to developing meaningful internal representations—and offers practical tools (HDS, Ridge Rep, CCA, Interventions) to paper this phenomenon in AI systems.

Limitations

• The paper uses a simplified 2D discrete grid world. Applying these methods to continuous state/action spaces, 3D environments, or real-world robotic platforms presents further challenges.
• The analysis focuses on GRUs. How other architectures (LSTMs, Transformers) encode spatial information in similar tasks remains an open question.
• The scale of experiments, while involving thousands of trials, could be expanded to more complex and dynamic scenarios (e.g., moving obstacles).