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Predicting Cable Dynamics with Physical Attention Bias

Avihai Giuili, Rotem Atari, Avishai Sintov, Maya Bechler-Speicher

arXiv:2610.11975v1cs.RO

TL;DR

Learned cable simulators must generalize to unseen cables and remain stable over long rollouts, but global attention lacks geometric information about cable interactions. This paper adds a learned physical bias to attention logits and compares arc-length and Euclidean distances, separately and across disjoint head sets. Physical biases improve prediction, with the arc-length bias reducing error by 15% when attention alone connects distant segments and dual-metric allocation best or near-best across reported metrics.

  • Problem

    Learned DLO simulators must predict unseen cables and remain stable over long rollouts, while attention over all segment pairs has no geometric notion of the cable’s two distinct distances.

    Source: §1 · pp. 1–2

  • Method

    The study adds a learned-rate pairwise distance term to attention logits and compares unbiased, single-distance, and dual-distance head allocations with the rest of the model and protocol fixed.

    Source: §1 · p. 2, §2 · p. 3

  • Results

    With the local stream off, Chain reduces rel ℓ2 by 15% versus unbiased attention, while Euclidean+Chain only is lowest or within one seed standard deviation of lowest across all six Table 1 cells.

    Source: §4 · p. 4

  • Takeaways & Limitations

    The results tentatively favor dual-metric bias, with both distances spread across heads and no head left unbiased.

    Source: §5 · p. 4

    Test cables lie inside the training range, and the local-on ranking lies within the window spread.

    Source: §5 · p. 4

Abstract

from arXiv · show

Learned simulators for deformable linear objects (DLOs) such as cables have to predict the motion of cables they were not trained on and stay stable over long rollouts. Most of their error occurs where the cable touches itself or the floor. Attention over all pairs of cable segments can represent contact between parts of the cable that are far apart along its length, but attention has no notion of geometry. A cable has two pairwise distances, which agree only while it is straight: the arc-length distance along the cable, which governs elastic forces, and the Euclidean distance in space, which governs contact. We add a physical attention bias, an additive term on the attention logits with a learned rate, and ask which distance it should use. We compare no bias, each distance alone, and both distances on disjoint sets of heads, keeping the rest of the model and the training protocol fixed. A physical bias improves prediction on unseen cables. The gain is largest when attention is the only mechanism that connects distant segments: there, the arc-length bias reduces prediction error by 15% and more than halves the drift in segment length. The Euclidean bias alone stays close to unbiased attention, while assigning both distances across heads is best or near-best on every metric we report. Code and per-run records: https://github.com/avihaig/dlogps.

1. Introduction

Learned cable simulators must generalize to unseen cables and remain stable over long rollouts, while errors concentrate around folding and contact. This study asks which of a cable’s two geometric distances should bias global attention, and whether the answer depends on local message passing.

1. Introduction

  • Learned DLO simulators must predict unseen cables and handle hundreds of closed-loop steps, where their own errors become subsequent inputs.Rod mechanics is expensive to solve and requires material parameters that are hard to identify for a new cable.Source: §1 · p. 1
  • A cable’s arc-length distance governs elastic forces, while its Euclidean distance governs self-contact; folding makes the two diverge where rollout errors accumulate.The distances agree while the cable is straight.Source: §1 · p. 2
  • Hybrid graph transformers provide dense attention alongside local message passing, allowing either pairwise distance to enter attention without changing the graph.Prior work leaves open which distance should bias attention during rollouts and whether the answer changes when the local stream is removed.Source: §1 · p. 2
  • The study varies pairwise attention distance while holding the backbone, optimizer, seeds, and evaluation windows fixed, and tests with the local stream on and off.It compares five bias variants, including two that allocate the distances to disjoint head subsets, against chain-only, per-node MLP, and global LSTM baselines.Source: §1 · p. 2

2. Method

The model combines local chain message passing with dense attention and adds a learned, distance-based term to attention logits. Five variants allocate the two cable distances differently across attention heads.

2. Method

  • The cable has 33 vertices, and the network predicts per-node displacement from velocity history, material parameters, and clipped floor distance without absolute coordinates.Training is one-step with random-walk input noise, while evaluation is autoregressive.Source: §2 · p. 2
  • Each layer runs a GatedGCN over chain edges in parallel with dense multi-head attention over all vertices, then applies residual updates and normalization.Turning off either stream yields attention-only or chain-only message passing.Source: §2 · p. 2
  • A learned per-head decay rate scales an additive physical term on attention logits, with variants differing in which distance each head receives.Rates are positive and shared across layers; during rollout, arc-length distance stays fixed while Euclidean distance is recomputed from predicted positions.Source: §2 · pp. 2–3
  • The five bias variants are unbiased, Euclidean, Chain, Mixed, and Euclidean+Chain only, with the two dual-metric variants assigning distances to separate heads.Mixed leaves some heads unbiased, whereas Euclidean+Chain only uses half the heads for each distance and leaves none unbiased.Source: §2 · p. 3

3. Experimental protocol

The experiments use simulated falls of cables drawn from a defined material and length range, with test cables absent from training. Models share a fixed training protocol and are evaluated on identical long-rollout windows.

3. Experimental protocol

  • Training uses 46 simulated cables and testing uses 40 distinct cables interpolated within the training parameter hull.Training cables span rest lengths of 0.80–1.60 m, diameters of 1.5–10 mm, and five Young’s moduli from 10^6 to 10^9 Pa.Source: §3 · p. 3
  • Each model trains for 100k steps and is evaluated on 400 test windows, each rolled out for 400 predicted frames.Models use Adam, batch 512, width 128, eight heads, four layers, and 891k parameters; the last checkpoint is reported.Source: §3 · p. 3
  • Evaluation tracks relative position error, link-length drift from rest length, and self-intersection rate across predicted frames.A self-intersection is counted when non-adjacent segments pass closer than the cable diameter.Source: §3 · p. 3
  • The comparison includes five bias variants with the local stream on and off, plus chain-only, per-node MLP, and global LSTM baselines, for 39 runs.There are three seeds per configuration, and no significance tests are run.Source: §3 · p. 3

4. Results

Physical attention biases improve relative position error over unbiased attention, especially when attention alone connects distant segments; the arc-length bias has the largest reported effect in that setting. Across reported metrics, assigning both distances to separate heads is best or near-best, while floor contact is a particularly difficult phase.

4. Results

  • Every GPS row lowers mean rel ℓ2 versus chain-only message passing by 65–68% with the local stream on and 57–63% with it off.Removing the local stream raises rel ℓ2 by 7–23% but multiplies drift by up to 5.6×.Source: §4 · pp. 3–4
  • With the local stream off, Chain reduces rel ℓ2 from 0.0399 ± 0.0002 to 0.0339 ± 0.0008, a 15% reduction, and more than halves drift.The seed means do not overlap; with the local stream on, the largest gap is 9% and lies inside the window spread.Source: §4 · p. 4
  • Every physical bias beats unbiased attention on rel ℓ2 in both blocks, with larger gains when attention alone connects distant segments.The Euclidean bias alone lowers rel ℓ2 by 4% with the local stream off, compared with 15% for the intrinsic bias.Source: §4 · p. 4
  • The Euclidean+Chain-only bias is lowest or within one seed standard deviation of the lowest in all six Table 1 cells, with Mixed close behind.The authors tentatively favor dual-metric bias with no head left unbiased.Source: §4 · p. 4, Table 1 · p. 4
  • During local-on rollouts, rel ℓ2 during floor contact is about eight times the free-flight error.Chain ranks third on local-on rel ℓ2 and worst in both phase columns, while Euclidean stays close to unbiased when the local stream is off.Source: §4 · p. 4

5. Conclusion

The physical attention bias adds at most H learned scalars and recovers part of the local stream’s drift benefit. The effect exceeds seed noise clearly only when attention is the sole path between distant segments; the authors tentatively favor a dual-metric bias.

  • A physical attention bias costs at most H learned scalars and closes part of the gap between the two streams.Source: §5 · p. 4
  • The intrinsic distance alone recovers about two thirds of the drift benefit of the whole local stream.Source: §5 · p. 4
  • The effect clearly exceeds seed noise only when attention is the sole path between distant segments; the local-on ranking lies inside the window spread.Source: §5 · p. 4
  • The authors tentatively favor dual-metric bias, while noting that a lowest mean does not establish head specialization and test cables lie within the training range.Source: §5 · p. 4

Appendix A. Data generation

The appendix describes randomized cable-drop episodes in MuJoCo and train/test populations spanning cable properties, with test cables interpolated within the training range.

  • Episodes settle the cable, move grippers quasistatically to randomized poses, release both ends, and record until the speed threshold is met or 5 seconds pass.Source: Appendix A · p. 6
  • The 46-cable training set spans five material classes, four rest lengths, and diameters from 1.5 to 10 mm; test cables are interpolated within that range.Source: Appendix A · p. 6
  • Each test cable contributes 30 episodes, and 400 test windows are capped round-robin across cables so all models use the same windows.Source: Appendix A · p. 6

Appendix B. Architecture and training

The appendix specifies node features, preprocessing, and shared training choices for the models and baselines.

  • At C=70, node features are 215-wide and combine newest-first velocity history, four material parameters, and clipped floor distance; positions are not scaled.Source: Appendix B · p. 6
  • Training-split statistics standardize velocity history, floor distance, edge features, and displacement targets before noise is added, then remain frozen.Source: Appendix B · p. 6
  • Models train for 100k Adam steps at batch 512 with learning-rate decay and gradient clipping; the last checkpoint is reported, and one run takes under an hour on a consumer GPU.Source: Appendix B · p. 7
  • The per-node MLP baseline has three layers of width 2048, while the global LSTM has three layers of width 256 and receives centroid-relative positions.Source: Appendix B · p. 7

Appendix C. Metric definitions and the phase split

The appendix defines rollout error and physical-violation metrics, then splits local-on errors by recorded floor-contact and free-flight phases.

  • Table 2 splits local-on results by recorded-trajectory phase, and every column ordering lies within the seed spread.Source: Table 2 · p. 7
  • Relative ℓ2 is the rollout mean positional error normalized by rest length, scored over predicted frames 1–400 rather than the observed input frame.Source: Appendix C · p. 7
  • Link-length drift measures predicted segment lengths against rest length, while self-intersection uses prediction geometry and non-adjacent segments closer than the cable diameter.Source: Appendix C · p. 7
  • Floor-contact frames are identified from the recorded trajectory using vertex height at or below cable diameter; remaining frames are free flight, with 400 and 345 eligible windows, respectively.Source: Appendix C · p. 7
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