Ordinal Neural Collapse as a Representation Prior for Visual Navigation

In end-to-end imitation learning for robot navigation, the vision encoder is often trained using only an indirect action loss. This frequently leads to ambiguous, action-agnostic representations that fail in complex environments. The authors investigate whether explicitly structuring the encoder's latent space to reflect the natural ordinal relationship of navigation actions—where neighboring directions are visually similar and opposing directions are distinct—can improve navigation robustness and consistency.

To address this, the authors propose ORION (Ordinal Neural Collapse for Visual Navigation). Unlike standard neural collapse, which assumes all classes are equally distant, ORION leverages the fact that navigation actions (e.g., Far Left to Far Right) have an inherent ordinal structure. The method operates in two stages:

1. Pretraining: The vision encoder is trained using three specific objectives: class separability (minimizing intra-class variance), supervised ordinal projection (aligning class means along a 1D axis), and orthogonal compactness (suppressing variance perpendicular to that axis).
2. Fine-tuning: The pretrained encoder is integrated into a diffusion-based navigation framework (NoMaD) and fine-tuned end-to-end on the full navigation task.

ORION consistently outperforms standard end-to-end baselines and traditional neural collapse methods across both simulated and real-world environments. In complex, multi-intersection scenarios, ORION demonstrated significant improvements in navigation success rates and reduced heading jerk—a metric of directional stability. The results suggest that by forcing the encoder to learn a representation space that respects the ordinal nature of steering commands, the model becomes more robust to visual distractors and ambiguous decision points.