Predicting Cable Dynamics with Physical Attention Bias

Learned simulators for deformable linear objects (DLOs) such as cables must predict the motion of instances absent from the training set and remain stable over long rollouts, and their error concentrates where the cable contacts itself or the floor. Attention over all pairs of cable segments is a natural mechanism here, since it can represent contact between parts of the cable that are far apart along its length, but attention encodes no geometry of its own. A cable admits two pairwise distances that coincide only while it is straight: the arc-length distance along the cable, which governs elastic interactions, and the Euclidean distance in space, which governs contact. We propose a \emph{physical attention bias}, a learned-rate additive term on the attention logits, and examine which of the two distances it should carry, comparing no bias, each distance alone, and both distances assigned to disjoint attention heads, with the rest of the model and the training protocol held fixed. We show that a physical bias improves prediction on unseen cables, and that the improvement is largest when attention is the only mechanism coupling distant segments, where the arc-length bias reduces prediction error by $15\%$ and more than halves the drift in segment length. Neither distance is sufficient on its own, whereas assigning both across heads is best or near-best on every metric reported.