← 研踪 PaperTrailarXiv:2611.00951 · v2
Why Koopman Structure Does Not Help Differentiable World Models for Humanoid Whole-Body Tracking
首次提交 2026-10-31 21:53
版本更新 2026-11-05 15:49
雷达观测 2026-11-06 12:09
摘要
We test whether Koopman structure helps a differentiable world model used to train a simulated Unitree G1 whole-body tracking policy by backpropagation through imagined rollouts, replacing the MLP world model of an otherwise unchanged pipeline. It does not: return is at best equal (0.823 versus 0.830), one-step error on identical data is 1.3 to 1.6 times the MLP's, and training is about 15% slower. Lifted rollouts diverge or fail to train policies; 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 accuracy cost belongs to this class. At a fixed state, the dynamics' curvature 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 the action. Supplying the policy's action removes most of the remaining gap on G1, Ant and Humanoid. The only tested online repair approaching the MLP feeds the action into the nonlinear lift, abandoning the structure. For this use, the MLP world model remains the better choice.
作者备注：8 pages, 3 figures, 2 tables. Preprint
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v2 · 2026-11-05 15:49 · 最新观测版本
Why Koopman Structure Does Not Help Differentiable World Models for Humanoid Whole-Body Tracking
We test whether Koopman structure helps a differentiable world model used to train a simulated Unitree G1 whole-body tracking policy by backpropagation through imagined rollouts, replacing the MLP world model of an otherwise unchanged pipeline. It does not: return is at best equal (0.823 versus 0.830), one-step error on identical data is 1.3 to 1.6 times the MLP's, and training is about 15% slower. Lifted rollouts diverge or fail to train policies; 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 accuracy cost belongs to this class. At a fixed state, the dynamics' curvature 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 the action. Supplying the policy's action removes most of the remaining gap on G1, Ant and Humanoid. The only tested online repair approaching the MLP feeds the action into the nonlinear lift, abandoning the structure. For this use, the MLP world model remains the better choice.
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