One Trajectory, Two Requirements: Accuracy and Local Stability in Euler Sampling for Flow Matching Policies
One Trajectory, Two Requirements: Accuracy and Local Stability in Euler Sampling for Flow Matching Policies
This research paper investigates the trade-off between trajectory accuracy and local stability in Euler sampling for flow matching robot policies. The authors demonstrate that a step count sufficient for nominal noise-to-action trajectory accuracy may be too coarse for strongly contracting directions. Using an exact two-coordinate system and controlled augmentation of six trained flow models, they show that these requirements can differ even when the original learned transport is unchanged. Experiments on a frozen LIBERO checkpoint across 30 policy inputs reveal that while no sampled mode violates the Euler non-expansion condition, accuracy sweeps require varying numbers of steps (4--9 at 5% error, 87--112 at 1%) depending on the input. The study concludes that endpoint accuracy alone cannot rule out a separate stability requirement.
The paper presents a theoretical analysis and controlled experiments on flow matching robot policies, demonstrating that trajectory accuracy and local Euler stability can impose different step requirements at inference time.
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.
Reported numbers
Euler steps
4
View original evidence
eights or action dynamics. Across 30 policy inputs from 10 LIBERO-10 tasks, the Jacobian exhibits strong contracting directions near the action endpoint, yet no sampled mode violates the Euler non-expansion condition. On five of those inputs, accuracy sweeps require 4--9 Euler steps at 5% terminal error and 87--112 at 1%. These five paired cases are therefore consistent with accuracy-limited rather than stability-lim
Open source S4Euler steps
9
View original evidence
eights or action dynamics. Across 30 policy inputs from 10 LIBERO-10 tasks, the Jacobian exhibits strong contracting directions near the action endpoint, yet no sampled mode violates the Euler non-expansion condition. On five of those inputs, accuracy sweeps require 4--9 Euler steps at 5% terminal error and 87--112 at 1%. These five paired cases are therefore consistent with accuracy-limited rather than stability-lim
Open source S4Euler steps
87
View original evidence
eights or action dynamics. Across 30 policy inputs from 10 LIBERO-10 tasks, the Jacobian exhibits strong contracting directions near the action endpoint, yet no sampled mode violates the Euler non-expansion condition. On five of those inputs, accuracy sweeps require 4--9 Euler steps at 5% terminal error and 87--112 at 1%. These five paired cases are therefore consistent with accuracy-limited rather than stability-lim
Open source S4Euler steps
112
View original evidence
eights or action dynamics. Across 30 policy inputs from 10 LIBERO-10 tasks, the Jacobian exhibits strong contracting directions near the action endpoint, yet no sampled mode violates the Euler non-expansion condition. On five of those inputs, accuracy sweeps require 4--9 Euler steps at 5% terminal error and 87--112 at 1%. These five paired cases are therefore consistent with accuracy-limited rather than stability-lim
Open source S4Reported accuracy
5%
View original evidence
eights or action dynamics. Across 30 policy inputs from 10 LIBERO-10 tasks, the Jacobian exhibits strong contracting directions near the action endpoint, yet no sampled mode violates the Euler non-expansion condition. On five of those inputs, accuracy sweeps require 4--9 Euler steps at 5% terminal error and 87--112 at 1%. These five paired cases are therefore consistent with accuracy-limited rather than stability-lim
Open source S4Reported accuracy
1%
View original evidence
eights or action dynamics. Across 30 policy inputs from 10 LIBERO-10 tasks, the Jacobian exhibits strong contracting directions near the action endpoint, yet no sampled mode violates the Euler non-expansion condition. On five of those inputs, accuracy sweeps require 4--9 Euler steps at 5% terminal error and 87--112 at 1%. These five paired cases are therefore consistent with accuracy-limited rather than stability-lim
Open source S4policy inputs
30
View original evidence
eights or action dynamics. Across 30 policy inputs from 10 LIBERO-10 tasks, the Jacobian exhibits strong contracting directions near the action endpoint, yet no sampled mode violates the Euler non-expansion condition. On five of those inputs, accuracy sweeps require 4--9 Euler steps at 5% terminal error and 87--112 at 1%. These five paired cases are therefore consistent with accuracy-limited rather than stability-lim
Open source S4LIBERO-10 tasks
10
View original evidence
eights or action dynamics. Across 30 policy inputs from 10 LIBERO-10 tasks, the Jacobian exhibits strong contracting directions near the action endpoint, yet no sampled mode violates the Euler non-expansion condition. On five of those inputs, accuracy sweeps require 4--9 Euler steps at 5% terminal error and 87--112 at 1%. These five paired cases are therefore consistent with accuracy-limited rather than stability-lim
Open source S4
- paper: not_reported
What remains unknown
Not established in the collected evidence: Environment, Control, Data origin.
Reported performance applies to the described task. It does not establish general autonomy or deployment readiness.
Source excerpts and review record
Automatically extracted; no manual editorial approval recorded.
eights or action dynamics. Across 30 policy inputs from 10 LIBERO-10 tasks, the Jacobian exhibits strong contracting directions near the action endpoint, yet no sampled mode violates the Euler non-expansion condition. On five of those inputs, accuracy sweeps require 4--9 Euler steps at 5% terminal error and 87--112 at 1%. These five paired cases are therefore consistent with accuracy-limited rather than stability-lim
Open source S4
Source：arXiv Robotics — research abstracts · arxiv.org