Why Koopman Structure Does Not Help Differentiable World Models for Humanoid Whole-Body Tracking
Why Koopman Structure Does Not Help Differentiable World Models for Humanoid Whole-Body Tracking
This research paper investigates whether utilizing Koopman operator theory to linearize dynamics in a lifted state space improves differentiable world models for humanoid whole-body tracking.
The study concludes that incorporating Koopman linear dynamics into a differentiable world model for humanoid whole-body tracking offers no performance benefit over standard MLPs and introduces training inefficiencies, suggesting the MLP remains the superior architectural choice for this specific task.
Source: arXiv Robotics — research abstracts · Read original article ↗
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What the source reports
Publisher-reported claims, with original evidence. These results have not been independently verified by RoboSignal.
- Environment
- SimulationOpen source S2
Reported numbers
return
0.823
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arXiv:2611.00951v1 Announce Type: new Abstract: We test whether Koopman structure, linear dynamics in a lifted state space, helps when a humanoid whole-body tracking policy is trained by backpropagating through a differentiable world model, replacing the MLP world model of an otherwise unchanged pipeline for simulated Unitree G1 tracking. It does not: return is at best equal (0.823 versus 0.830), one-step error on id
Open source S2return
0.83
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arXiv:2611.00951v1 Announce Type: new Abstract: We test whether Koopman structure, linear dynamics in a lifted state space, helps when a humanoid whole-body tracking policy is trained by backpropagating through a differentiable world model, replacing the MLP world model of an otherwise unchanged pipeline for simulated Unitree G1 tracking. It does not: return is at best equal (0.823 versus 0.830), one-step error on id
Open source S2action-affine MLP error ratio
31
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e, the curvature of the true dynamics in the action explains only part of it. Across states, the policy's actions span a curved region, so an affine model fits policy data only as the tangent at the policy's action, the operating point: on G1, the MLP's tangent there is as accurate as the MLP; at the mean action, 31 times worse. The offset must encode, from the state alone, where the policy acts, whereas an MLP reads
Open source S4
- paper: not_reported
Source excerpts and review record
Automatically extracted; no manual editorial approval recorded.
arXiv:2611.00951v1 Announce Type: new Abstract: We test whether Koopman structure, linear dynamics in a lifted state space, helps when a humanoid whole-body tracking policy is trained by backpropagating through a differentiable world model, replacing the MLP world model of an otherwise unchanged pipeline for simulated Unitree G1 tracking. It does not: return is at best equal (0.823 versus 0.830), one-step error on id
Open source S2
entical data is 1.3 to 1.6 times the MLP's, and training is about 15% slower. Lifted rollouts diverge or fail to train a policy; of the schemes tested, re-lifting at every imagined step trains best. Re-lifting never uses the lifted linear dynamics and leaves a model affine in the action, with state-dependent offset and slope; an action-affine MLP also predicts worse, so the cost belongs to this class. At a fixed stat
Open source S3
e, the curvature of the true dynamics in the action explains only part of it. Across states, the policy's actions span a curved region, so an affine model fits policy data only as the tangent at the policy's action, the operating point: on G1, the MLP's tangent there is as accurate as the MLP; at the mean action, 31 times worse. The offset must encode, from the state alone, where the policy acts, whereas an MLP reads
Open source S4
Source：arXiv Robotics — research abstracts · arxiv.org