Error-Feedback Model for Output Correction in Bilateral Control-Based Imitation Learning

Hiroshi Sato; Masashi Konosu; Sho Sakaino; Toshiaki Tsuji

REVIEW 3 major objections 5 minor 16 references

Error-Feedback Model for Output Correction in Bilateral Control-Based Imitation Learning

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Feeding predicted-state errors back into the lower-layer network improves a robot's ability to write characters it never trained on.

desk verdict Plausible error-feedback idea for hierarchical imitation learning, but the main tracking metric is a signed sum that can cancel out, so the central claim is not yet supported. read the letter →

arxiv 2411.12255 v1 pith:E2CCYRQT submitted 2024-11-19 cs.RO cs.AIcs.LG

Hiroshi Sato , Masashi Konosu , Sho Sakaino , Toshiaki Tsuji This is my paper · ORCID

classification cs.ROcs.AIcs.LG

keywords errorfeedbackimitationlearningbilateralcontrolhierarchicalneuralnetworkstatelessMLPLSTMcharacterwriting

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

In bilateral control-based imitation learning, a neural network predicts the robot's next command from its current state, but a feedforward network has no way to correct its own output errors during autonomous operation. The paper proposes a hierarchical structure in which an upper layer supplies long-horizon state predictions and a lower layer predicts the next state, with the difference between the lower output and the upper one-step prediction fed back into the lower layer's input. The authors show that this error-feedback model reduces angular tracking error and, for one unlearned character, improves the drawn shape's overlap (IoU). They also find that a stateless MLP benefits more from feedback than an LSTM, because it has no internal memory to carry old errors forward. The work is a step toward treating the lower layer as a controllable plant rather than a fixed feedforward mapping.

What carries the argument

The central mechanism is the error-feedback model: the upper layer outputs a one-step predicted state $f^{upper}_{k+1}$ and a ten-step target $f^{upper}_{k+10}$; the lower layer outputs $\hat{f}_{k+1}$; the correction $e = f^{upper}_{k+1} - \hat{f}_{k+1}$ is added to the ten-step target, giving $f^{upper} = f^{upper}_{k+10} + e$, and this corrected value is fed to the lower layer as the goal to track. The lower layer is a four-layer MLP with no internal state, which keeps the loop Markovian and easy to control, and it is compared against a three-layer LSTM lower layer. The mechanism is applied only during autonomous operation, not during training.

What would settle it

Run the identical writing task with a learned upper-layer neural network (trained to predict states) instead of recorded data, and measure Angular Error and IoU for characters '4' and 'B'; if the MLP-with-feedback configuration no longer beats the no-feedback baseline, the claimed benefit is an artifact of using ground-truth reference commands.

Watch

Extended reading notes

Core claim

The central claim is that output errors in a hierarchical imitation-learning network can be corrected by adding a feedback term $f^{upper}_{k+1} - \hat{f}_{k+1}$ to the upper-layer command that the lower layer receives. With this feedback, the lower layer tracks the upper layer's predicted states more closely than in the conventional hierarchical model. On the learned character 'A', feedback did not raise IoU but did lower Angular Error; on the unlearned character '4', feedback with an MLP lower layer increased IoU and cut Angular Error roughly in half; on 'B', feedback again reduced Angular Error, with MLP best, while IoU stayed low because the pen lost contact with the board. The paper interprets the MLP advantage as a Markovian property: without an internal state, the lower layer responds to the current feedback rather than being influenced by past memories.

Load-bearing premise

The whole demonstration assumes the upper-layer outputs are already known and taken from pre-recorded bilateral control data, so the feedback loop has never been tested against errors produced by a learned upper-layer model.

Editorial extensions

If this is right

The error-feedback model can be applied to any hierarchical imitation-learning setup where an upper layer provides multi-step predictions, without retraining the lower layer.
Using a stateless MLP lower layer yields better tracking than an LSTM when feedback is present, because the correction is not diluted by internal memory.
The model suppresses errors from extrapolating to unlearned motions: on character '4', feedback with MLP raised IoU and halved angular error.
The feedback correction works even when the lower layer is fed with upper-layer outputs for characters never seen in training.
Tracking the upper layer more closely reduces joint-angle error while not always improving the drawn shape, indicating that shape quality also depends on contact with the writing surface.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's oracle assumption means the real benefit of feedback with a learned upper layer remains untested; a concrete next experiment is to close the loop with a trained upper-layer network and see whether the feedback still stabilizes tracking.
The same feedback idea could be applied to other hierarchical policy architectures with a slow planner and a fast executor, where a stateless executor with error correction behaves like a classical servo tracking a reference trajectory.
Because the correction is just a proportional error term, the framework invites connections to PID control: adding integral or derivative terms on the error $e$ may improve tracking on trajectories like 'B' where the lower layer must extrapolate far from its training distribution.
The MLP's advantage suggests that for feedback-based control, intentionally removing recurrency and trading it for a shorter sampling period can be a design choice rather than a limitation.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

Here is my read on arXiv:2411.12255. The core idea is simple and worth a look: add an error-feedback term to the lower layer of the hierarchical bilateral-control imitation learning model from Hayashi et al. [8]. The lower layer gets the upper layer's ten-step-ahead state plus the difference between the one-step-ahead prediction and its own output. The twist is using a stateless MLP instead of an LSTM, on the rationale that a Markovian lower layer is easier to control. That is a reasonable extension, and the observation that the MLP benefits more from feedback than the LSTM is genuinely interesting.

The paper does a few things well. It clearly separates the Markovian and non-Markovian parts of the task, it uses IoU of the drawn character as an independent metric, and it explicitly acknowledges that the upper-layer states are pre-recorded rather than produced by a learned upper model. The comparison framework between LSTM and MLP is clean.

The soft spot is load-bearing and it is in the evaluation. Equation (3) defines Angular Error as a signed cumulative sum of (θ_upper − θ_res) with no absolute value, no square, and no normalization. The section is titled 'MSE of Angles,' but the formula is not an MSE. Positive and negative deviations cancel, so a low Angular Error can mean the trajectory oscillates around the reference rather than tracking it. That is exactly what the results suggest. For character 'B', the MLP with feedback shows a big drop in Angular Error (3.31 vs 6.27) while IoU actually falls from 0.035 to 0.025. If the metric were a true MSE or MAE, the improvement would likely shrink or disappear. With only one untrained character showing an IoU gain (MLP for '4': 0.204 vs 0.127), the evidence for the paper's central claim is thin. There are also no significance tests over the five runs, and no code or data released.

Who should read this? Researchers working on bilateral-control imitation learning or hierarchical models with feedback might find the idea worth exploring. The paper deserves a serious referee, but as it stands it needs major revision: fix the metric, report per-time-step errors or an uncancelled statistic, and show that the IoU gains are consistent across more than one character and robust to reruns. If the authors can do that, the contribution becomes credible.

My recommendation: send to peer review with a request for heavy revision, not desk reject. The idea is not flawed; the evidence is.

Referee Report

3 major / 5 minor

Summary. This paper proposes an error-feedback mechanism for hierarchical bilateral-control-based imitation learning. The upper layer supplies future state plans, and the lower layer predicts the next state from the current state and the upper-layer plan. The difference between the lower-layer prediction and the one-step-ahead upper-layer output is added to the upper-layer input (Eq. (1)). The lower layer is implemented either as an LSTM or as a stateless MLP, and experiments are performed on a character-writing task with characters 'A', '4', and 'B', using pre-recorded upper-layer outputs. The authors report IoU and a quantity called Angular Error, and claim that the feedback model improves tracking of the upper-layer outputs and improves accuracy for untrained characters, particularly with the MLP lower layer.

Significance. If the claims were fully supported, the idea of deliberately using a stateless MLP as the low-level controller in a hierarchical network and closing a simple error-feedback loop is a useful step toward integrating neural networks with control-theoretic ideas. The authors are transparent about using pre-recorded upper-layer states and about the limitation that a learned upper layer is not tested. However, the current experimental evidence is not sufficient to establish the central claim: the main angular metric is mathematically flawed, the independent IoU evidence is positive for only one untrained character, and no statistical tests accompany the five-run comparisons. The contribution is therefore conditional on a corrected and more rigorous evaluation.

major comments (3)

[Section IV.D.2, Eq. (3).] The Angular Error metric as written is a signed cumulative sum, not a mean squared error despite the subsection title. Positive and negative deviations cancel over time and across joints, so a small or decreased value does not establish accurate tracking. This is load-bearing: in Fig. 9, character 'B' with the MLP shows IoU decreasing from 0.035 to 0.025 while Angular Error decreases from 6.27 to 3.31, the opposite of what improved tracking should produce. The authors should replace Eq. (3) with a per-sample absolute or squared error, normalize by sample count, and report per-joint or otherwise non-cancelling summary statistics before interpreting Angular Error decreases as evidence of improved tracking. In addition, because the feedback signal in Eq. (1) is the same one-step difference being measured in Eq. (3), a reduction in this metric is partly a check that the loop is doing what it was designed to do rather than an independent validation.
[Section V.B, Fig. 9.] The claim that the model improves accuracy for previously untrained characters is supported by only one clear IoU increase: the MLP on '4' (0.127 to 0.204). The LSTM on '4' improves only slightly (0.034 to 0.045), and for 'B' there is no IoU improvement; the MLP's IoU actually decreases from 0.035 to 0.025. With only five runs and overlapping standard deviations, and without significance tests, the evidence is too thin for the abstract's statement that the model demonstrated improved accuracy in writing previously untrained characters. The authors should add appropriate statistical testing or restrict the claim to the specific condition where the IoU evidence is positive.
[Section III.C and Section V.B.] The evaluation assumes that upper-layer outputs are known in advance from pre-recorded bilateral control, as the authors explicitly acknowledge. This tests only whether the lower layer can track a perfectly known reference; it does not test closed-loop behavior when the upper layer is a learned model whose predictions contain errors. The abstract's statement that 'Through autonomous control with error feedback, we confirmed that the lower layer could effectively track the output of the upper layer' should be qualified to this oracle-upper-layer setting, and the paper should not imply that the full autonomous hierarchical system has been validated.

minor comments (5)

[Abstract.] The sentence 'In the character-writing task, this model demonstrated improved accuracy in writing previously untrained characters.' appears twice in the abstract and should be deduplicated.
[Section III.B, Eq. (1).] The notation f^{upper} is overloaded: the left side is a new input vector while the right side contains both f^{upper}_{k+10} and f^{upper}_{k+1}; the authors should define the dimension and timing of each quantity more explicitly.
[Section IV.D.2.] The heading 'MSE of Angles' is inconsistent with Eq. (3), which is neither a mean nor a squared error; if a mean squared error was intended, the equation should be corrected accordingly.
[Section VII.] There are grammatical errors in the future-work section, such as 'an lower-layer'; the manuscript should be proofread for articles and plural forms.
[Figures 8 and 9.] The results in Figs. 8 and 9 are presented in a compressed table-like format with small numeric values; a regular table with clear column headers would improve readability and reduce transcription errors.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the error-feedback law is an empirical control loop, and the main positive result for an untrained character is supported by an independent image-based metric.

full rationale

The proposed method is an explicit feedback control law (Eq. 1) that adds the upper/lower prediction difference to the lower-layer input; it does not define the lower-layer output to equal the upper-layer target, so tracking behavior is an empirical outcome, not an identity. The independent IoU metric (Eq. 2) grounds the key positive result for the untrained character '4'. The authors openly state that upper-layer states are pre-recorded (Section III.C), a stated scope limitation rather than a circular input. The prior hierarchical model [8] is self-citation by Sakaino and Tsuji, but is used as baseline/context, not to justify the new feedback mechanism. The angular-error metric in Eq. (3) is a signed cumulative sum and therefore not a proper error magnitude; this is a correctness/evaluation risk, not circularity because the feedback signal and metric are not equal by construction.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the assumption that the lower layer is Markovian and that the upper-layer states are available as pre-recorded data. The feedback gain is hand-chosen, and the upper-layer information set is selected via a validation experiment. No new physical entities are introduced.

free parameters (4)

Error-feedback gain α in Eq. (1) = 1 (implicit)
The feedback term is added with unity gain; the paper states 'the simple difference worked well', indicating it was chosen by hand without tuning.
Downsampling step for upper-layer output = 10 (20-ms interval)
Chosen to match previous work [8] and to increase data by a factor of 10; not optimized.
Upper-layer output information set = [θ, θ̇, τ] (angle, angular velocity, torque)
Selected in the preliminary experiment based on evaluation; this is model selection on the validation data.
Network architecture dimensions = 200 hidden units, 4 layers (MLP); 200-unit LSTM (3 layers + FC)
Architecture hyperparameters are standard but hand-chosen; no ablation is provided.

assumptions (4)

domain assumption Lower-layer dynamics are Markovian at the short sampling period, so a stateless MLP is sufficient.
Section III.A states the lower-layer is considered to exhibit high Markovian properties; this is an assumption about the system, not proven.
ad hoc to paper Upper-layer outputs are known a priori (pre-recorded via bilateral control) during evaluation.
Section III.C explicitly assumes the states predicted by the upper-layer are known; this simplifies the problem and limits the generalization of the results.
ad hoc to paper The simple difference error f^{upper}_{k+1} - \hat{f}_{k+1} is a suitable error signal and the feedback loop is stable.
Equation (1) defines the feedback with no stability analysis or justification; the authors themselves note that extending to various control mechanisms is future work.
domain assumption The 500 Hz position/force hybrid controller and the robot setup produce accurate torque estimation via a reaction force observer.
Standard control assumptions, not verified in this paper.

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Cite this review

Pith. "Pith review of Error-Feedback Model for Output Correction in Bilateral Control-Based Imitation Learning." pith.science (2026). https://pith.science/paper/E2CCYRQT

@misc{pith2026241112255,
  author       = {Pith},
  title        = {Pith review of: Error-Feedback Model for Output Correction in Bilateral Control-Based Imitation Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E2CCYRQT}},
  note         = {Machine review of arXiv:2411.12255}
}

read the original abstract

In recent years, imitation learning using neural networks has enabled robots to perform flexible tasks. However, since neural networks operate in a feedforward structure, they do not possess a mechanism to compensate for output errors. To address this limitation, we developed a feedback mechanism to correct these errors. By employing a hierarchical structure for neural networks comprising lower and upper layers, the lower layer was controlled to follow the upper layer. Additionally, using a multi-layer perceptron in the lower layer, which lacks an internal state, enhanced the error feedback. In the character-writing task, this model demonstrated improved accuracy in writing previously untrained characters. In the character-writing task, this model demonstrated improved accuracy in writing previously untrained characters. Through autonomous control with error feedback, we confirmed that the lower layer could effectively track the output of the upper layer. This study represents a promising step toward integrating neural networks with control theories.

Figures

Figures reproduced from arXiv: 2411.12255 by the authors.

**Figure 4.** The LSTM network is comprised of three layers of 200- dimensional LSTM units and a fully connected layer, resulting in a total of four layers. In this study, the states predicted by the upper-layer are assumed to be known. Specifically, time-series states of the follower are stored in advance through bilateral control, and this data is utilized. This allows for the comparison of different lower-layers using the same… view at source ↗

**Figure 7.** Characters drawn by [PITH_FULL_IMAGE:figures/full_fig_p004_7.png] view at source ↗

Figures from the paper (3 more)

**Figure 8.** Figure 8: The black line in the figure represents the drawing made [PITH_FULL_IMAGE:figures/full_fig_p004_8.png]

**Figure 8.** Figure 8: Performance comparison of autonomous robot operation based on [PITH_FULL_IMAGE:figures/full_fig_p005_8.png]

**Figure 9.** Figure 9: Comparison of Autonomous Performance: error-feedback model in Writing ’A,’ ’4,’ and ’B’ [PITH_FULL_IMAGE:figures/full_fig_p006_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [8]

An independently learnable hierar- chical model for bilateral control-based imitation learning applications,

K. Hayashi, S. Sakaino, and T. Tsuji, “An independently learnable hierar- chical model for bilateral control-based imitation learning applications,” IEEE Access, vol. 10, pp. 32 766–32 781, 2022

work page 2022

[2] [1]

Viola: Imitation learning for vision-based manipulation with object proposal priors,

Y . Zhu, A. Joshi, P. Stone, and Y . Zhu, “Viola: Imitation learning for vision-based manipulation with object proposal priors,” in Proceedings of The 6th Conference on Robot Learning , ser. Proceedings of Machine Learning Research, K. Liu, D. Kulic, and J. Ichnowski, Eds., vol

work page

[3] [2]

Mobile aloha: Learning bimanual mobile manipulation with low-cost whole-body teleoperation,

Z. Fu, T. Z. Zhao, and C. Finn, “Mobile aloha: Learning bimanual mobile manipulation with low-cost whole-body teleoperation,” arXiv preprint arXiv:2401.02117, 2024

arXiv 2024

[4] [3]

Learning fine-grained bimanual manipulation with low-cost hardware,

T. Z. Zhao, V . Kumar, S. Levine, and C. Finn, “Learning fine-grained bimanual manipulation with low-cost hardware,” 2023. [Online]. Available: https://arxiv.org/abs/2304.13705

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[5] [4]

Imitation learning for nonprehen- sile manipulation through self-supervised learning considering motion speed,

Y . Saigusa, S. Sakaino, and T. Tsuji, “Imitation learning for nonprehen- sile manipulation through self-supervised learning considering motion speed,” IEEE Access, vol. 10, pp. 68 291–68 306, 2022

work page 2022

[6] [5]

Autoregressive model considering low frequency errors in command for bilateral control-based imitation learn- ing,

T. Akagawa and S. Sakaino, “Autoregressive model considering low frequency errors in command for bilateral control-based imitation learn- ing,” IEEJ Journal of Industry Applications , vol. 12, no. 1, pp. 26–32, 2023

2023

[7] [6]

Soft and rigid object grasping with cross-structure hand using bilateral control-based imitation learning,

K. Yamane, Y . Saigusa, S. Sakaino, and T. Tsuji, “Soft and rigid object grasping with cross-structure hand using bilateral control-based imitation learning,” IEEE Robotics and Automation Letters , vol. 9, no. 2, pp. 1198–1205, 2024

work page 2024

[8] [7]

Bi-act: Bilateral control-based imitation learning via action chunking with transformer,

T. Buamanee, M. Kobayashi, Y . Uranishi, and H. Takemura, “Bi-act: Bilateral control-based imitation learning via action chunking with transformer,” 2024. [Online]. Available: https://arxiv.org/abs/2401.17698

arXiv 2024