One Trajectory, Two Requirements: Accuracy and Local Stability in Euler Sampling for Flow Matching Policies
Overview
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.
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Event evidence and corrections
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Reported quantity · Euler steps: 4 other · Basis not reported · Differing source assertions
“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”
Exact source · revision 1Source owner not reported
Reported quantity · Euler steps: 9 other · Basis not reported · Differing source assertions
“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”
Exact source · revision 1Source owner not reported
Reported quantity · Euler steps: 87 other · Basis not reported · Differing source assertions
“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”
Exact source · revision 1Source owner not reported
Reported quantity · Euler steps: 112 other · Basis not reported · Differing source assertions
“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”
Exact source · revision 1Source owner not reported
Reported quantity · Reported accuracy: 5 percent · Basis not reported · Differing source assertions
“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”
Exact source · revision 1Source owner not reported
Reported quantity · Reported accuracy: 1 percent · Basis not reported · Differing source assertions
“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”
Exact source · revision 1Source owner not reported
Reported quantity · policy inputs: 30 other · Basis not reported
“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”
Exact source · revision 1Source owner not reported
Reported quantity · LIBERO-10 tasks: 10 other · Basis not reported
“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”
Exact source · revision 1Source owner not reported
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- arXiv Robotics — research abstractsSignalOne 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.
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