High-precision robot learning depends on expensive task-specific demonstrations, while abundant imperfect data is usually discarded. ε4P upcycles that data with source-dependent flow-time admission: low-precision target-task data contributes at high noise, and high-precision task-mismatched data contributes at low noise. The method changes only flow-time sampling — not the policy architecture or objective.
High-quality, task-specific teleoperation is scarce. Low-precision target-task demonstrations and precise demonstrations from other tasks are far easier to obtain — but native co-training makes both sources supervise the entire flow trajectory, including regions where their mismatch is harmful.
At low flow times, prediction is action-dominant. At high flow times, task context becomes more influential. ε4P uses this transition as an axis for deciding when each source should contribute.
ε4P assigns each imperfect source to the region where its useful information remains while the effect of its mismatch is limited.
Dpt supervises the full trajectory. Dtm is restricted to the low-flow-time action-dominant regime, while Dpm is restricted to high flow times after its precision mismatch becomes indistinguishable. The latest action-context analysis shows a single crossover at t* = 0.4327.
At low flow time, the policy relies more strongly on the noised action input. Precise demonstrations from a mismatched task can transfer low-level execution skill with limited influence from the mismatched context.
Best source: high-precision, task-mismatched Dtm.
At high flow time, target-task context remains valuable even when demonstrated actions are less precise. A classifier identifies when noised actions from Dpm and Dpt can no longer be reliably separated.
Best source: target-task, precision-mismatched Dpm.
ε4P is a drop-in training change. Everything stays standard — only source-dependent flow-time sampling changes.
Find tpm with a flow-time-conditioned source classifier and find ttm with action/context intervention probes on the final post-trained policy.
High precision. ε4P is evaluated on ATX 24-pin connector insertion (about 0.2 mm nominal clearance) and two-stage cable plugging (about 0.3 mm lateral clearance).
Generality. Bolt–nut sorting tests whether the method also helps on a coarse-grained manipulation task. All policies use the same architecture, checkpoint, optimizer, source probabilities, and training budget.
RB-Y1 platform · 60 trials per target task
Native co-training with both imperfect sources achieves 38.3%. ε4P routes the same sources to complementary windows and improves success to 80.0%.
Compared with 78.3% using target-task data alone and 33.3% under native co-training with both imperfect sources.
The result shows that source-dependent admission is not limited to sub-millimeter insertion tasks.
Representative real-world executions from the three target tasks. Media remains intentionally blank for double-blind internal review.
Training vision-language-action (VLA) models for high-precision manipulation typically requires task-specific, high-quality data, which is slow and expensive to collect. To reduce this burden without compromising manipulation precision, we propose ε4P (Imperfection for Precision), a simple yet effective method that upcycles two otherwise discarded data sources: low-precision data from the target task and high-precision data from mismatched tasks.
Rather than naively mixing these imperfect data sources throughout co-training, ε4P controls where each source contributes along the flow-matching trajectory. Specifically, low-precision target-task data is used at high noise to preserve high-level task context, and high-precision task-mismatched data is used at low noise to transfer low-level action precision.
Through real-robot experiments on both sub-millimeter high-precision tasks and coarse-grained tasks, ε4P improves policy performance by up to 31.7 percentage points and can replace an equal amount of task-specific high-quality data with an average performance drop of only 4.2 percentage points. Overall, ε4P points toward a scalable paradigm in which heterogeneous imperfect data can be systematically repurposed to reduce reliance on costly task-specific high-quality data.
Use this anonymous citation during double-blind review. Venue and identifying details are intentionally omitted.
@misc{anonymous2027varepsilon4p,
title = {Imperfection for Precision: Upcycling Imperfect Data
for High-Precision Robotic Manipulation},
author = {Anonymous Authors},
year = {2027},
url = {https://varepsilon4p.github.io/}
}Supplementary material will expand the diagnostics, boundary validation, and implementation details. Visual media remains represented by placeholders during review.
Additional source-classifier and action-context reliance analyses across flow time.
content placeholderDense boundary sweeps, local perturbations, opposite-window controls, and loss reweighting comparisons.
content placeholderRobot setup, dataset composition, training protocol, and evaluation details.
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