Semantic Cognition Over Potential Exploration (SCOPE)

• SCOPE is an embodied AI framework that formalizes exploration by merging geometric occupancy with semantic cognition to build detailed environmental maps.
• It employs a receding-horizon strategy where visual language models score candidate frontiers by assessing semantic richness, explorability, and goal relevance.
• Experimental evaluations show that SCOPE improves mapping accuracy, navigation efficiency, and calibration over traditional geometric-only exploration methods.

Semantic Cognition Over Potential-based Exploration (SCOPE) refers to a family of embodied AI methodologies in which frontier-driven, potential-based exploration is guided and structured by semantic reasoning. SCOPE frameworks formalize and operationalize the use of visual-semantic information to prioritize robot or agent exploration in unknown environments, integrating geometric occupancy, semantic scene understanding, and high-level goal representations through explicit spatial memory and frontier analysis. These approaches have demonstrated significant improvements in both map quality and task performance when compared to purely geometric or unscored exploration, underpinning state-of-the-art results in embodied visual navigation and semantic scene understanding (Simons et al., 4 Apr 2025, Wang et al., 12 Nov 2025).

1. Foundations and Conceptual Frameworks

SCOPE formalizes exploration as a receding-horizon, potential-based decision process in which an agent (e.g., robot, embodied agent in simulation) incrementally builds both geometric and semantic representations of its environment. At each navigation step, SCOPE interleaves:

• Sampling of candidate viewpoints or frontiers based on collision-free regions or boundary clusters;
• Computation of a utility (potential) function that reflects both the expected information gain (e.g., geometric entropy reduction) and semantic acquisition (e.g., semantic-feature convergence or richness);
• Selection of the next pose or frontier to visit via maximizing the utility function;
• Navigation and map update, during which geometric occupancy grids and dense semantic feature maps are incrementally populated with new visual and depth data.

Crucially, SCOPE extends these elements with a computation of explicit semantic cognition, leveraging vision-LLMs (VLMs) as oracles to evaluate the frontier's semantic “richness”, “explorability”, and “goal relevance”. This is complemented by the construction of a spatio-temporal potential graph, which propagates frontier utility across a discretized spatial memory.

2. Mathematical Formulation of Frontier Potential and Utility

At each exploration iteration, SCOPE defines a set of frontier image patches $\mathcal{F}^t = \{\mathcal{F}_i^t\}$ located at the boundary of the explored environment. For each $\mathcal{F}_i^t$, a pretrained VLM (e.g., GPT-4o) is prompted with both the frontier patch and the current goal $q$, outputting a triplet of sub-scores:

• $p_{i,sem}^t$: semantic richness,
• $p_{i,explore}^t$: explorability,
• $p_{i,goal}^t$: goal relevance.

The scalar frontier potential $P_i^t$ for each frontier is computed by aggregation:

$$P_i^t = \omega_{sem}\,p_{i,sem}^t + \omega_{explore}\,p_{i,explore}^t + \omega_{goal}\,p_{i,goal}^t,$$

where aggregation weights are typically uniform (e.g., $[\tfrac{1}{3}, \tfrac{1}{3}, \tfrac{1}{3}]$), but can be tuned or learned.

A 2D grid $\mathcal{G}$ discretizes the explored environment. Each cell $v_{m,n}$ accumulates:

• $P_{m,n}^t$: propagated potential,
• $n_{m,n}^t$: visit-count,
• $$p_{m,n}^{sem,t}, p_{m,n}^{explore,t}, p_{m,n}^{goal,t}$$: aggregated local subscores.

Frontier scores propagate to nearby grid cells within radius $R$ with a linear kernel:

$$\alpha_{m,n}^t = \max\left(0, 1 - \frac{\|\mathbf{p}_{m,n} - \mathbf{p}_{\mathcal{F}_i}\|}{R}\right),$$

and the cell values are updated as

$$P_{m,n}^t = (1-\alpha_{m,n}^t) P_{m,n}^{t-1} + \alpha_{m,n}^t P_i^t.$$

An exploration value for each node is thus evaluated: $$E_{m,n}^t = \left[ \omega_{pot} P_{m,n}^t + \omega_{sem} p_{m,n}^{sem,t} + \omega_{explore} p_{m,n}^{explore,t} + \omega_{goal} p_{m,n}^{goal,t} \right] \times \frac{1}{1 + \gamma n_{m,n}^t},$$ where $\gamma$ penalizes repeated visitation.

In robotic scenarios focused initially on map building, the utility function is:

$U(p) = \alpha I(p) + \beta S(p)$

where $I(p)$ is the summed geometric entropy over visible voxels and $S(p)$ is an average of normalized semantic entropy over non-converged cells.

3. Algorithmic Workflow and Pseudocode

The SCOPE operational loop consists of:

1. Initialization of semantic and occupancy maps.
2. Capture and semantic processing of panoramic RGB–D observations.
3. Detection and clustering of frontiers via occupancy map analysis.
4. Scoring of each frontier by VLM to obtain $P_i^t$.
5. Propagation of scores to potential graph nodes within radius $R$.
6. Computation of node-level exploration values with revisit penalties.
7. Selection of the highest-scoring node or memory recall.
8. Policy decisions via a prompt-based LLM invocation, which may propose either further frontier exploration or retrieval/confirmation of stored memory snapshots.
9. A self-reconsideration module, which issues VLM validation queries to reject overconfident or incorrect memory-based actions and triggers policy re-evaluation if uncertain.

SCOPE Navigation Loop Pseudocode (abridged):

Initialize grid G; t = 0 while not Done: t += 1 I_t = capturePanorama() F_t = detectFrontiers(I_t) for F_i in F_t: p_i = VLM(F_i, goal_q) # 3-dim scores P_i = Aggregate(p_i) for v_mn within R of F_i: alpha = max(0, 1 - dist(v_mn, pos(F_i)) / R) G.P[mn] = (1-alpha)*G.P[mn] + alpha*P_i # update semantic/explore/goal subscores similarly for v_mn: E[mn] = weighted_sum(G.P, G.p_sem, ...) / (1 + gamma * G.count[mn]) m_star, n_star = argmax E[mn] a0 = policy(goal, G, target=(m_star, n_star)) a = SELF_REFINE(a0, goal, G) execute(a) update G.count for visited cells

The self-reconsideration module ensures reliability by rejecting memory-recall actions that do not pass a VLM confirmation check, thereby improving calibration.

4. Semantic Cognition Representation and Decision Policy

SCOPE maintains a multi-modal, structured memory integrating:

• Visual embeddings of both current frontiers and historical memory snapshots (VLM visual encoder outputs),
• Deep language feature representations from the navigation goal (which may be text, image, category),
• Structured spatial memory in a discretized grid storing potentials, semantic features, and visit-counts.

At each decision point, the LLM policy is invoked with a chain-of-thought prompt incorporating the current goal, all memory snapshots, and all detected frontiers with their associated potentials. The policy returns either a recommended frontier to explore or a memory snapshot to revisit for confirmation. The selection between exploration and memory recall is made via comparison of normalized exploration scores ($E_{m,n}$) and retrieval confidences ($C_i$).

5. Implementation, Complexity, and Sampling Strategies

• Vision-LLM backbone: GPT-4o (API: top_p=0.95, max_tokens=4096).
• Grid specification: Typical cell resolution 0.5 m, for a $40 \times 40$ grid in a $20 \times 20$ m environment.
• Frontier clustering: 10–20 clusters per iteration, with propagation radius $R = 3$ m.
• Computation cost: VLM inference ($\sim$200 ms per call) dominates step latency; per-step end-to-end latency is $0.5$–$1$ s. Update cost is $\mathcal{O}$(#frontiers $\times \pi R^2$) cell updates per step.
• Hardware: 8$\times$ NVIDIA A800 80GB GPUs for local map/policy, VLM inference in the cloud.
• Sampling strategies: Both uniform sampling (random in free space, rejection of obstructed points) and importance sampling (GMM fit to utility-weighted pose distribution) are supported, with trade-offs in coverage and computational effort.

Hyperparameter	Value
Grid cell size	0.5 m
Propagation radius R	3 m
Visit penalty γ	0.1
Aggregation weights	[0.25, 0.25, 0.25, 0.25]
VLM model	gpt-4o-2024-11-20

Uniform sampling provides rapid coverage improvement, while importance sampling sharpens concentration on utility maxima.

6. Experimental Evaluation and Performance

SCOPE has been evaluated on benchmarks including GOAT-Bench (goal-conditioned navigation) and A-EQA (embodied visual question answering). Key performance metrics are:

• Success Rate (SR): Fraction of successful episodes.
• SPL: SR penalized by trajectory efficiency.
• Correctness (Corr.): Final answer accuracy.
• Efficiency (Eff.): Path optimality ratio.
• Expected Calibration Error (ECE): Confidence calibration of the agent.

On GOAT-Bench and A-EQA, SCOPE achieved:

Method	Success Rate (%)	SPL (%)	Correctness (%)	Efficiency (%)
3D-Mem	69.1	48.9	52.6	42.0
SCOPE (Ours)	73.7	53.5	59.1	41.0

In significance testing, SCOPE’s mean SR (70.14% ± 1.88) outperformed 3D-Mem (65.47% ± 4.02, $p=0.046$) and reduced ECE by a substantial margin (from 11.6 to 3.8 on GOAT-Bench). This suggests that explicit frontier-potential estimation and reconsideration mechanisms yield statistically robust performance improvements.

In mobile robot mapping scenarios, SCOPE with uniform sampling achieved up to 0.938 coverage and 0.673 average semantic entropy in simulation, with strong outperformance over frontier-exploration baselines (Simons et al., 4 Apr 2025). Physical trials confirmed these trends.

7. Significance and Research Context

SCOPE, as formalized in (Simons et al., 4 Apr 2025, Wang et al., 12 Nov 2025), advances embodied AI by unifying information-theoretic exploration, semantic reasoning via VLM, and structured spatio-temporal memory. Compared to prior baselines relying solely on geometric or unscored exploration, SCOPE leverages cross-modal semantic cognition to guide exploration towards both maximal information gain and task-oriented objectives. Its propagation-based potential graph and confidence-driven self-reconsideration modules address common issues of overconfidence and inefficient re-exploration.

The use of VLMs as frontier-potential oracles enables robust zero-shot generalization to new tasks and environments, contingent on prompt design and VLM accuracy. A plausible implication is that the integration of frontier semantics, potential spreading, and memory calibration mechanisms constitutes an architectural pattern likely to remain central in future embodied navigation systems. Limitations include reliance on VLM inference speed and inference costs, suggesting continued research into more efficient learned frontier-potential predictors and scalable memory architectures.