Locally Observable Maze Navigation

• Locally observable maze navigation is the challenge of reaching targets using only local sensory inputs that require integrating successive observations to infer the complete state.
• It encompasses methods from reinforcement learning with transformers, recurrent memory networks, reactive control laws, and explicit world modeling to overcome partial observability.
• The research identifies key issues such as state aliasing, looping failures, and the need for robust localization and memory mechanisms to ensure effective path planning.

Locally observable maze navigation is the problem of reaching a target in a maze or maze-like environment when the agent does not observe the full global state at each step, but instead must act from local sensory input, coordinate feedback, short-range range sensing, textual observations, or a restricted visual field, often while preserving an internal representation over time. Across reinforcement learning, embodied language-model evaluation, computational neuroscience, and robot control, the central difficulty is partial observability: the current observation is not sufficient to determine the true state, so successful navigation depends on temporal integration, belief tracking, localization, map construction, or reactive control laws that remain effective without a global map (Eggen et al., 2024, Einarsson, 27 Jul 2025, Potapov, 1 Jul 2026).

1. Formal characterization and observability assumptions

A standard formalization treats locally observable navigation as a partially observable decision process. In the partially observable Morris Water Maze, the task is modeled as a POMDP

$$(\mathcal{S}, \mathcal{A}, P, R, \Omega, \mathcal{O}),$$

where the observation function $\mathcal{O} : \mathcal{S} \rightarrow \Omega$ returns only partial information $o_t$ from the true state $s_t$ (Eggen et al., 2024). This formulation captures the basic condition shared across otherwise disparate benchmarks: the agent acts from observations that are strictly weaker than the full environment state.

The specific form of local observability varies by domain. In the 2D circular Morris Water Maze, the agent observes only 12 evenly spaced sight lines over a fixed 1-radian field of view aligned with its facing direction; each sight line contains distance to the boundary and the color of the intersected boundary segment, yielding $\boldsymbol{o}_t \in \mathbb{R}^{24}$ (Eggen et al., 2024). In MazeEval, the agent receives its current position as $(x,y)$ coordinates, the goal position coordinates, the number of cells it can move in each cardinal direction before hitting a wall, and the full history of previously visited positions together with the visibility distances observed there; it never sees the maze layout as an image or grid (Einarsson, 27 Jul 2025). In AGI Maze, the maze itself is not shown, and the agent is given the maze size, the starting position, available actions, inventory information, and textual feedback after each move such as “you hit a wall/monolith,” “you moved,” or “you picked up a key” (Potapov, 1 Jul 2026). In pixel-based multi-room MiniGrid environments, the agent observes only a 7×7 top-down window centered on itself and cannot see through walls or closed doors (Tinguy et al., 2023).

These observation models differ in modality, but they share the same structural property: multiple global states can be consistent with the same local observation. In the map-reading setting of DeepMind Lab, the agent is given a global map image but “does not know where on the map it currently is,” and several map positions can correspond well with the current first-person view (Brunner et al., 2017). In robotics settings without SLAM, the robot must infer corridors, rooms, and dead ends from local contact or proximity information and its own motion history rather than from a constructed global map (Butterworth et al., 2019). This suggests that local observability is not defined by the absence of rich sensors alone; it is defined by state aliasing and the need to recover hidden structure from sequential interaction.

2. Environment families and task structure

Locally observable maze navigation has been studied in several benchmark families with distinct task semantics. The Morris Water Maze instantiation is a 2D circular pool with radius 10 units, a hidden platform of radius 0.75 units, a fixed visual landmark covering $1/8$ of the circumference, and episodes ending when the platform is reached or after 500 steps (Eggen et al., 2024). The agent starts randomly on the boundary and faces the center, a setup described as equivalent to keeping the agent fixed and rotating the environment (Eggen et al., 2024). The task inherits its significance from rodent experiments while imposing explicit local visual constraints.

Grid-based evaluation frameworks emphasize stripped-down sequential decision-making. MazeEval uses perfect mazes generated by depth-first search, with exactly one solution path from start to end; main evaluation sizes range from $5\times 5$ to $15\times 15$, with additional experimentation up to $30\times 30$ and failure at $\mathcal{O} : \mathcal{S} \rightarrow \Omega$0 for one model (Einarsson, 27 Jul 2025). Termination is determined by reaching the goal, visiting any cell at most 10 times, and remaining within a move budget of $\mathcal{O} : \mathcal{S} \rightarrow \Omega$1 for an $\mathcal{O} : \mathcal{S} \rightarrow \Omega$2 maze (Einarsson, 27 Jul 2025). AGI Maze instead frames the problem as a world-modeling task in a text-based grid maze, typically from about 3×3 to 8×8, with walls, a monolith border, exactly one exit opening, a key, a treasure chest, and sometimes an additional exit key (Potapov, 1 Jul 2026). Transition rules are stateful: stepping into a wall or monolith consumes a step without changing position, the treasure requires the key, exiting requires the treasure, and some mazes also require an exit key (Potapov, 1 Jul 2026).

Additional mechanics can make local observability substantially harder. AGI Maze introduces rivers, where stepping onto a river cell causes forced downstream movement without revealing the flow direction, and pit cycles, where stepping into a pit teleports the agent to the next pit in a cycle (Potapov, 1 Jul 2026). These mechanics create what the paper explicitly describes as “POMDP-like ambiguity” and require explicit hypotheses and localization or mapping under uncertainty (Potapov, 1 Jul 2026). In multi-room MiniGrid environments, aliasing arises because multiple rooms may share the same color or configuration, so local appearance alone does not uniquely identify location (Tinguy et al., 2023).

Robotics-oriented studies use maze-like indoor or obstacle-cluttered continuous spaces rather than discrete mazes. One line studies simulated Foot-Bots in ARGoS navigating procedurally generated indoor environments with rooms and corridors using local sensors and wheel-speed control (Butterworth et al., 2019). Another studies a Dubins-like vehicle in a planar maze-like environment with one obstacle domain, constant forward speed, bounded angular velocity, and access only to local obstacle distance and target bearing (Matveev et al., 2011). A separate hybrid-control framework formulates navigation in $\mathcal{O} : \mathcal{S} \rightarrow \Omega$3-dimensional Euclidean space cluttered with spherical obstacles, using range sensing and switching between motion-to-destination and obstacle-avoidance modes without requiring a global map (Cheniouni et al., 2024). Across these environments, the maze is not merely a spatial layout; it is a source of hidden-state structure whose inference burden depends on sensing, dynamics, and transition ambiguity.

3. Algorithmic approaches

One major family of methods uses learned sequence models to compensate for local observability. In the partially observable Morris Water Maze, the Q-function approximator is a stacked decoder-only transformer, equivalent to a GPT-2-style architecture, used as a deep Q-network (Eggen et al., 2024). The model takes a sequence of $\mathcal{O} : \mathcal{S} \rightarrow \Omega$4 consecutive observations,

$\mathcal{O} : \mathcal{S} \rightarrow \Omega$5

embeds each observation into dimension $\mathcal{O} : \mathcal{S} \rightarrow \Omega$6, augments it with learned positional encoding, and processes it with a 2-layer, 8-head decoder-only transformer with masked self-attention (Eggen et al., 2024). The paper emphasizes that masking preserves the autoregressive property and removes the need for recurrence. Learning follows the standard DQN Bellman objective with a target network and replay buffer, and, following Esslinger et al. (2022), the sequence loss is computed by summing the individual DQN losses over every sequence element (Eggen et al., 2024).

A contrasting approach decomposes navigation into learned perception, learned localization, deterministic planning, and actor-critic control. In the DeepMind Lab map-reading system, the architecture comprises a Visible Local Map Network, a Recurrent Localization Cell, a Map Interpretation Network, and a Reactive Agent trained with A3C-style on-policy learning and off-policy replay losses (Brunner et al., 2017). The localization cell updates egomotion and local-map estimates over time,

$\mathcal{O} : \mathcal{S} \rightarrow \Omega$7

and then correlates the estimated local map against the rasterized global map to produce a discrete location distribution $\mathcal{O} : \mathcal{S} \rightarrow \Omega$8 (Brunner et al., 2017). The planner computes a short-term target direction from a learned reward map, and the reactive agent combines approximate orientation, uncertainty, target-direction information, and estimated distance to act (Brunner et al., 2017).

Recurrent memory has also been introduced through neuroevolution. In generalized indoor maze navigation, NEAT evolves neural-network topology and weights, while NEAT-GRU extends NEAT by allowing Gated Recurrent Units to be inserted into the evolving network as mutable nodes (Butterworth et al., 2019). The controller maps sensor readings to left and right wheel speeds. The paper’s argument is explicitly comparative: if a hand-designed bug algorithm such as I-Bug must remember values over time, then evolved controllers may also require long-term memory to match or exceed it (Butterworth et al., 2019).

Another line does not learn a policy end-to-end, but instead proves convergence properties for reactive local-navigation laws. For a Dubins-car robot, the biologically inspired control law has two modes: pure pursuit when far from the obstacle and obstacle avoidance when near it, with switching determined by obstacle distance relative to a threshold and by the sign of $\mathcal{O} : \mathcal{S} \rightarrow \Omega$9 (Matveev et al., 2011). In the hybrid feedback controller for cluttered Euclidean spaces, the discrete mode variable $o_t$0 selects motion-to-destination or one of two symmetric obstacle-avoidance modes, and the control law

$o_t$1

blends straight goal-seeking with locally optimal tangent avoidance (Cheniouni et al., 2024). These methods treat local observability as a geometric control problem rather than a latent-state inference problem.

A further family is explicitly model-based. AGI Maze is designed to pressure agents into building persistent representations such as an explicit map, a graph, a set of constraints, or a programmatic simulator (Potapov, 1 Jul 2026). The benchmark’s own baseline planning agent uses prompt history as working memory by first writing notes to itself about exploration status, location, known objects, and future plans, then making the actual tool call (Potapov, 1 Jul 2026). In hierarchical active inference, the agent learns a three-layer hierarchy consisting of a cognitive map, an allocentric world model, and an egocentric world model, coupled through a hierarchical generative model spanning locations, places, poses, and motor actions (Tinguy et al., 2023). In computational neuroscience, flexible maze navigation is modeled through layout-conforming replay: exploration learns inter-place-cell connectivity based on shortest-path distance in the maze, replay in rest learns place-cell-to-striatum value structure, and replay during navigation provides lookahead trajectories for path selection (Gao, 2022).

4. Memory, localization, and world modeling

A recurrent theme across the literature is that local observability makes memory a first-class computational requirement. In the Morris Water Maze, the platform is hidden, so successful navigation requires integrating information over time, and longer observation sequences generally improve performance until gains saturate around sequence length $o_t$2 observations (Eggen et al., 2024). In indoor robot navigation, the harder no-bearing setting provides only distance to the target, so the controller must infer useful behavior by integrating distance changes over time, which is precisely the setting where NEAT-GRU succeeds and plain NEAT fails (Butterworth et al., 2019). In MazeEval, the benchmark is designed to test whether a model can build a mental map from local, coordinate-based observations rather than from visual input (Einarsson, 27 Jul 2025).

Localization is one specific form of memory. In the DeepMind Lab system, the current observation alone does not determine state because multiple positions can look similar locally, so the Recurrent Localization Cell builds an egocentric local map over time and matches it against the global map (Brunner et al., 2017). In the multi-room active-inference model, local observations are aliased because rooms can look similar or identical, and the cognitive map is the only level that can correctly predict trajectories across room boundaries by using connectivity and location memory (Tinguy et al., 2023). In AGI Maze, later mechanics can create ambiguous localization, so the agent may no longer know with certainty where it is after certain transitions (Potapov, 1 Jul 2026).

World modeling is the more general requirement that subsumes localization, hidden-transition inference, and state tracking. AGI Maze explicitly argues that ordinary LLMs are fundamentally static next-token predictors and that the benchmark demands maintenance of beliefs about hidden state, updating those beliefs from interaction, and using memory to plan (Potapov, 1 Jul 2026). The benchmark is designed to encourage explicit, computable representations of the world rather than raw inference from prompt context alone (Potapov, 1 Jul 2026). MazeEval reaches an adjacent conclusion from a different interface: most models can exploit immediate local distance feedback but fail to maintain a durable spatial state and avoid loops over time (Einarsson, 27 Jul 2025).

The neuroscience model provides a biologically grounded version of the same principle. It replaces Euclidean-distance place-cell coupling with geodesic place fields,

$o_t$3

so that replay dynamics conform to maze topology rather than passing unrealistically through walls (Gao, 2022). During goal-directed navigation, replay trajectories are evaluated by the maximal medium spiny neuron activity along each lookahead path, and the rat follows the trajectory with the strongest reward signal (Gao, 2022). This suggests a strong conceptual continuity between learned internal maps in AI systems and topology-sensitive internal dynamics in biologically inspired models: in both cases, local observations are insufficient unless they are integrated into a structured latent representation.

5. Empirical findings, scaling behavior, and failure modes

Empirical studies converge on two robust findings: local geometry is often easier than long-horizon state maintenance, and failure commonly manifests as looping rather than immediate perceptual error. MazeEval makes this distinction explicit. Most failures are not due to exhausting the $o_t$4 move budget; 100% of failures are caused by excessive revisiting of the same cell 10 or more times (Einarsson, 27 Jul 2025). Wall hits remain relatively low even in failed runs, indicating that models usually understand immediate wall constraints, but cannot sustain coherent exploration policies as maze size grows (Einarsson, 27 Jul 2025). The paper interprets the collapse beyond about $o_t$5 to $o_t$6 for many models as a threshold where maze complexity overwhelms spatial working memory (Einarsson, 27 Jul 2025).

A similar phenomenon appears in the transformer-based Morris Water Maze agent. The learned policy often moves toward the center, rotates until the landmark comes into view, and then adjusts its path toward the hidden platform, a strategy described as biologically plausible (Eggen et al., 2024). Yet in about 10% of cases, the agent gets stuck in a repetitive oscillation, rotating back and forth without forming a useful movement plan from past observations (Eggen et al., 2024). The paper takes this as evidence that the transformer captures temporal context well but does not always fully exploit longer histories (Eggen et al., 2024).

Results in AGI Maze sharpen the distinction between plain inference-time memory and explicit externalized working memory. Massive testing of lightweight LLMs showed that none of them solved even simple training mazes reliably, and for 5×4 and larger mazes the tested LLMs do not outperform the random-walk baseline (Potapov, 1 Jul 2026). On the more difficult S3-03 maze with pits and rivers, stronger-model spot checks reached about 30% success for GPT-5.5 and about 40% for Gemini 3.5 Flash with doubled step budget, while the planning agent that writes notes to itself improved those figures to 60% and 70%, respectively (Potapov, 1 Jul 2026). The improvement is real but is described as brittle and inefficient (Potapov, 1 Jul 2026). A common misconception is that if a model can reason about the current local move, then it can navigate the maze; the reported results instead indicate that preserving a stable navigation state over time is the dominant bottleneck.

Not all results are failure-dominated. In the DeepMind Lab map-reading task, the full agent trained only up to 13×13 mazes achieved target-finding success rates of 98% on 15×15, 93% on 17×17 and 19×19, and 91% on 21×21 test mazes (Brunner et al., 2017). In indoor robot navigation, I-Bug achieved 195/209 successes with 93.3% success rate, while some NEAT-GRU controllers exceeded it on success and path-efficiency metrics, including one controller with 196/209 successes and mean normalized length 1.9024, and another with 203/209 successes and mean normalized length 2.3499 (Butterworth et al., 2019). In the biologically grounded replay model, the virtual rat achieved a 100% success rate in the reported goal-fixed, goal-changing, detour, and shortcut tests (Gao, 2022). These results do not erase the broader difficulty of local observability, but they show that strong performance is achievable when the architecture or controller has an adequate mechanism for localization, memory, or topology-sensitive planning.

6. Biological, linguistic, and control-theoretic perspectives

The topic has unusually strong cross-disciplinary continuity. The partially observable Morris Water Maze is explicitly motivated by rodent experiments and is positioned as relevant both to biological navigation and to artificial navigation because it mimics rodent visual constraints while using a transformer as the decision-maker (Eggen et al., 2024). The replay-based model is more directly neurobiological, with place cells, hippocampal interneurons, and striatal medium spiny neurons forming a mechanism in which replay both encodes maze topology and supports lookahead planning (Gao, 2022). In both cases, memory is not treated as an optional add-on but as a constituent part of spatial behavior.

Language-model benchmarks introduce a distinct perspective: local observability can be imposed even without vision. MazeEval deliberately eliminates visual reasoning entirely by providing only coordinates, directional distances, and history, and then evaluates both English and Icelandic prompts on identical maze structures (Einarsson, 27 Jul 2025). English significantly outperforms Icelandic for most models, with aggregated Wilcoxon signed-rank statistics $o_t$7, $o_t$8, and Cohen’s $o_t$9, while only one model is language-stable (Einarsson, 27 Jul 2025). The benchmark interprets this as evidence that spatial reasoning in current LLMs is not reliably language-agnostic. This suggests that locally observable maze navigation can also serve as a probe of representation format: the same latent task may become easier or harder depending on how state is serialized into language.

Control-theoretic work emphasizes guarantees unavailable in most learned systems. For the Dubins-car reactive controller, the paper proves finite-time arrival with safety margin under geometric assumptions and, in locked cases, probability-1 success for a randomized turn-direction variant (Matveev et al., 2011). For the hybrid feedback controller in cluttered Euclidean spaces, the main theorem establishes forward invariance of the safe set and global asymptotic stability of the target, while preserving continuous control inputs and collision-free motion (Cheniouni et al., 2024). These results are not based on latent-world inference, but on geometric switching logic and local range sensing. A plausible implication is that locally observable maze navigation comprises at least two partially overlapping research agendas: one seeks latent-state representations that recover hidden structure, while the other seeks reactive or hybrid laws whose geometry makes full reconstruction unnecessary.

7. Limitations, misconceptions, and open directions

Several limitations recur across the literature. One is over-reliance on implicit memory. The Morris Water Maze transformer sometimes exhibits oscillatory stuck behavior and relies mostly on visual inspection rather than formal interpretability analysis (Eggen et al., 2024). AGI Maze reports that vanilla LLMs do not reliably build a persistent latent model of the environment, and that message-history memory helps only modestly and inconsistently (Potapov, 1 Jul 2026). The hierarchical active-inference model is described as best suited to familiar environments learned during training and may have difficulty detecting environmental changes such as altered tile colors (Tinguy et al., 2023). These are not identical weaknesses, but they point to a shared open problem: the stability and generalization of internal spatial representations under partial observability.

Another misconception is that partial observability is mainly a perception problem. MazeEval shows that models often understand immediate local wall constraints yet still fail through looping (Einarsson, 27 Jul 2025). AGI Maze further shows that even when observations are textual and low-dimensional rather than pixel-based, hidden transitions such as rivers and pit cycles can overwhelm agents that do not maintain explicit hypotheses about state (Potapov, 1 Jul 2026). The limiting factor is therefore often not detecting local affordances, but preserving a coherent world model, belief state, or visited-state structure over many steps.

Interpretability remains an important unresolved issue. The transformer-based Morris Water Maze study explicitly proposes explainable AI techniques to study how the agent encodes the landmark, how it internalizes the environment, why oscillatory failure modes occur, and how sequence length affects decision-making (Eggen et al., 2024). AGI Maze similarly frames the benchmark as a test of whether world state is represented persistently and manipulably rather than merely inferred transiently from static context (Potapov, 1 Jul 2026). In the neuroscience model, flexibility arises from continuous re-learning of inter-place-cell and place-cell-to-striatum synaptic strengths so that both topology and reward associations remain aligned with the current maze (Gao, 2022). This suggests a research direction in which representation diagnostics, external memory structures, and adaptive topology learning are studied together rather than as separate problems.

Taken together, the literature defines locally observable maze navigation as a canonical test of sequential spatial competence under hidden state. The agent may see sight lines, coordinates, local pixel windows, wall distances, range scans, or textual feedback, but never the full maze at once. Success depends on what is maintained across time: a history-conditioned policy, a recurrent state, an egocentric-to-allocentric localization mechanism, a topological cognitive map, an explicit external world model, or a reactive control law whose geometry compensates for missing global knowledge. The field’s current results show both strong progress and clear limits: local observations can be sufficient, but only when they are coupled to a mechanism that preserves and updates state over time (Eggen et al., 2024, Einarsson, 27 Jul 2025, Potapov, 1 Jul 2026).