The authors investigate learned simulators for deformable linear objects such as cables, focusing on improving generalization to unseen cables and stability over long rollouts. They note that most prediction error arises when the cable contacts itself or the floor, and that standard self‑attention over all segment pairs can capture long‑range interactions but lacks geometric awareness. To inject geometry, they introduce a physical attention bias—an additive term on the attention logits whose magnitude is learned—and test whether this bias should encode the arc‑length distance (which dictates elastic forces) or the Euclidean distance (which dictates contact). Experiments keep the base model and training protocol unchanged while comparing four configurations: no bias, arc‑length bias only, Euclidean bias only, and a split‑head approach that assigns both distances to different attention heads. Results show that adding any physical bias improves prediction on unseen cables, with the greatest benefit when attention is the sole mechanism linking distant segments. In that setting, the arc‑length bias cuts prediction error by 15 % and reduces segment‑length drift by more than half. The Euclidean bias alone yields little improvement over the unbiased baseline, whereas employing both distances across heads attains the best or near‑best performance across all reported metrics.
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