Regression Accuracy Is Not Enough: Destination-Agnostic Graph Embeddings for Potential-Field Navigation

Potential-field navigation using destination-conditioned Graph Neural Networks(GNNs) requires a new forward pass whenever the target goal changes. To eliminate this per-goal computational bottleneck, we propose a destination-agnostic embedding framework. By executing a single forward pass per map, our model assigns a D-dimensional vector zi to each free cell such that the distance $||z_i-z_{goal}||$ approximates the shortest path to an arbitrary goal, enabling instantaneous inference for any goal without retraining or additional forward passes. We train the network using a combined objective of pairwise distance regression and an order-preserving ranking loss. Model performance is evaluated on both distance-regression accuracy and task-level navigation success rate via greedy descent. Through extensive hyperparameter sweeps over ranking-loss weights (from 1000 down to 1) and anchor/pair sampling densities, we reveal that regression accuracy (Mean Squared Error, MSE) and navigation success are surprisingly decoupled: while MSE improves monotonically toward the smallest weight, completion rate and ranking correctness peak at an intermediate weight. Thus, the configuration that minimizes regression error fails to maximize navigability. We trace this phenomenon to specific map topographies—including cases where completion rate remains unchanged despite substantial MSE improvements—and attribute it to structural limitations of symmetric embeddings in greedy goal-reaching. Our findings demonstrate that regression error alone is an unreliable proxy for downstream planning success, highlighting the need for future evaluation protocols to report task-level navigability alongside embedding accuracy.