When Straightening Fails: Diagnosing and Mitigating Pathological Cases in Temporal Straightening for Planning

TL;DR: What if straightening doesn’t always help? Let’s systematically find and analyze cases where temporal straightening hurts planning, then design adaptive methods that can switch strategies.

Research Question: In what types of environments or tasks does temporal straightening degrade planning performance, and how can we detect or mitigate these adverse effects in practice?

Hypothesis: Temporal straightening may harm planning in scenarios with highly curved latent manifolds, discontinuities, or when the geodesic path is inherently non-straight. Adaptive regularization based on trajectory curvature statistics or task cues will outperform static straightening.

Experiment Plan: - Curate or generate tasks with varying latent manifold geometries (e.g., sharp obstacles, topological holes).

• Train planners with and without temporal straightening; evaluate path optimality, success rate, and planning time.
• Analyze latent trajectories for curvature, discontinuities, or mismatch between Euclidean and geodesic distances.
• Design a “curvature monitor” or meta-controller that modulates regularization strength on-the-fly or disables it when harmful.
• Compare the adaptive approach to static baselines.

References:

• Wang, Y., Bounou, O., Zhou, G., Balestriero, R., Rudner, T. G. J., LeCun, Y., & Ren, M. (2026). Temporal Straightening for Latent Planning.
• Nolan, C., & Cuffe, P. (2025). Shortest Path Planning for Fleets of Delivery Drones: Evaluating the Benefit of Including a Temporal Dimension in the Routing Network. Irish Signals and Systems Conference.
• Lai, Z., Lu, H., Li, H., Li, J., & Jensen, C. S. (2025). MovSemCL: Movement-Semantics Contrastive Learning for Trajectory Similarity (Extension). arXiv.org.