The practical consequence: you can run this checkpoint faster without retraining it.
The policy outputs a curve, so executing a(n·t) replays the same trajectory geometry
n times faster. Speed-up is an inference flag, and it is exact — verified to
0.000e+00 deviation at 2× and 4×.
This supersedes cupstack_bspline_act. Two things changed: idle frames were trimmed
from the demonstrations, and 5 episodes were held out for validation, so for the
first time there are held-out numbers for this task.
[!IMPORTANT]
Read the Evaluation section before trusting any number here.
Held-out error is ~19°, against 2.1° on training data. The policy is clearly
reading the scene — it beats the inter-demonstration spread by 42% — but it has
never been run on hardware, and task success rate is unknown. Keep the e-stop
within reach.
The repository root holds the recommended checkpoint, so --policy.path also accepts
the repo id directly. Individual checkpoints live under checkpoints/<step>/.
--policy.path takes either a Hub repo id (namespace/name) or a local directory
containing config.json — which is the pretrained_model/ subdirectory, not the
step directory above it. There is no --policy.subfolder flag.
To try the speed-up, raise --policy.speed_up to 2.0 or 4.0. Start at 1.0 and step up
only once the task succeeds. Retiming does not make the arm stronger — past the
low-level controller's tracking limit it overshoots rather than stopping. The paper
reaches 4× on cube picking but only 2× on speed stacking, and cup stacking is the same
precise-placement regime.
If the control loop can't keep up, drop --display_data (Rerun can saturate its
channel at two 640×480 streams) rather than assuming the policy is too slow — a
B-spline policy runs the network only when a segment is exhausted, roughly every
0.76 s, so most control ticks are just spline evaluation.
Camera naming is not optional
The --robot.cameras dict keys must be front and gripper, lowercase:
Key
Shape
observation.images.front
(3, 480, 640)
observation.images.gripper
(3, 480, 640)
observation.state
(6,)
Joint order is shoulder_pan, shoulder_lift, elbow_flex, wrist_flex, wrist_roll, gripper,
in degrees. Swapping the two cameras produces confident but wrong behaviour rather
than an error.
Requirements
This policy type is not in upstream LeRobot. You need a checkout containing the
bspline_act policy, installed with the scipy extra:
uv pip install -e ".[feetech,bspline]"
scipy>=1.15 is required for interpolate.generate_knots.
Unnormalization statistics are stored as buffers inside model.safetensors, so each
checkpoint is self-contained — you do not need the training dataset on the robot machine.
Checkpoints
Step
Epoch
Train error
Held-out error
Eval loss
10000
17
6.56°
19.20°
0.3074
20000
33
4.95°
19.36°
0.3072
30000
50
3.89°
19.33°
0.3060
40000
67
2.63°
19.06°
0.3084
recommended
45000
75
2.49°
18.72°
0.3005
best, within noise of 40k
50000
83
2.28°
19.05°
0.3088
60000
100
2.08°
19.22°
0.3121
final
All twelve checkpoints of the run span 18.72–19.36° held-out (mean 19.03, sd 0.22), so
every checkpoint here performs the same on unseen data. 45000 is nominally best and
is included for that reason, but its margin over 40000 is a quarter of the run's own
noise. Pick 40000 unless you have a reason not to.
Error is mean absolute joint error in degrees, worst joint, over each predicted
segment's horizon (~0.76 s), measured by decoding the spline and comparing against
ground-truth actions.
Leading and trailing motionless frames were removed from every episode — 77 s of
lead-in and 26 s of trailing idle across 50 episodes. Interior pauses were kept
(only 0.3% of frames, and they are real behaviour).
Motion is measured as peak-to-peak joint range over a ±0.5 s window rather than
frame-to-frame delta. A single jittery sample inside a dead stretch defeats a delta
test, which silently leaves the idle in.
Leading idle matters more than it looks: it maps the opening observation to
"don't move", and since executing a stay-still segment doesn't change the scene, the
policy can re-predict it indefinitely and never start.
Architecture
Standard ACT with one change: the decoder emits a B-spline parameter matrix rather
than an action chunk.
(n_knots, 1 + action_dim) = (16, 7) = 112 values per prediction
column 0 knot vector, in source-frame units, 0 = "now"
columns 1: control points, one per joint
Params
51.6 M
Vision backbone
ResNet18 (ImageNet init, fine-tuned)
dim_model / chunk_size
512 / 16
VAE
enabled, kl_weight 10.0
B-spline degree
3 (cubic, C² continuous)
bspline_chunk_size
10
Fitting tolerance ε
0.2 (degrees)
Max knot span
6 frames
Knot spacing is fitted adaptively, so a fixed 16 rows covers a variable time
horizon — 0.50 s to 1.03 s per segment, 0.76 s mean. The network runs only when a
segment is exhausted, which decouples policy rate from control rate.
On the fitting tolerance
ε = 0.2 is not the paper's value. The paper uses 0.002 for metre-scale end-effector
actions; SO-101 stores joint targets in degrees (~±120), roughly 100× larger.
At ε = 0.002 compression is 1.06× — one knot per frame, which defeats the
representation. At 0.2 the fit compresses 2.41× and reconstructs to 0.187° p99, well
below servo resolution.
max_knot_span caps how wide a single knot interval may be, bounding open-loop
exposure at chunk_size × 6 frames. On this dataset it is nearly a no-op (uncapped
p95 span is already 1.17 s); it matters on recordings with long pauses, where uncapped
fitting produced 18-second segments.
Evaluation
Offline only. No hardware evaluation has been performed.
Train (45 eps)
Held-out (5 eps)
Best checkpoint
2.49°
18.72°
Recommended (40k)
2.63°
19.06°
Two reference points for the held-out number:
Inter-demonstration spread: 32.27° — how far apart two different human
demonstrations of this task are, phase-aligned. At 18.7° the policy predicts an
unseen episode's trajectory substantially better than another demonstration would.
It is reading the scene, not replaying an average.
Hold-still baseline: 17.59° — emitting the current action for the next 0.76 s.
The policy scores near this, but the comparison flatters a do-nothing policy: over a
short horizon on a slow task, "don't move" is a decent predictor while being a
useless policy. Do not read this as "no better than nothing".
Held-out performance was fixed after step ~3,000. Across twelve checkpoints and
55,000 steps it moved 0.6°, while training error fell from 8.00° to 2.08°. Everything
after the first few thousand steps went into fitting the training episodes harder.
The predecessor model card reported "2.10° open-loop error at 100k" without a
validation split. This run reproduces that figure (2.08° at 60k) and shows the
held-out number underneath it is ~19°. That was a training-data measurement, not a
generalization result.
Temporal rescaling is exact: on a real predicted segment, a(2t) and a(4t)
reproduce the 1× samples to 0.000e+00, consuming the segment in 24 / 12 / 6 control
ticks.
Limitations
No hardware evaluation. Task success rate is unknown.
Held-out split is the last 5 episodes, not a random sample. Episodes were largely
cut from a continuous teleoperation stream (40 of 49 boundaries are contiguous to
under 1°), so adjacent episodes are correlated and an interleaved split would leak.
The tail split avoids leakage at the cost of possible session drift.
Single task, single scene. No robustness to lighting, camera placement, or cup
position changes should be assumed.
Speed-up has a hardware ceiling. Expect degradation near 2× on this task.
Camera assignment is silent when wrong. Swapped views degrade behaviour without
raising an error.
Citation
bibtex
1@article{han2026b,
2 title={B-spline Policy: Accelerating Manipulation Policies via B-spline Action Representations},
3 author={Han, Xiaoshen and Xiong, Haoyu and Chen, Haonan and Liu, Chaoqi and
4 Torralba, Antonio and Zhu, Yuke and Du, Yilun},
5 journal={arXiv preprint arXiv:2607.09648},
6 year={2026}
7}
