Chain-of-Action: Trajectory Autoregressive Modeling for Robotic Manipulation
Authors: Wenbo Zhang
Tianrun Hu
Hanbo Zhang
Yanyuan Qiao
Yuchu Qin
Yang Li
Jiajun Liu
Tao Kong
Lingqiao Liu
Xiao Ma
Venue: NeurIPS 2025 poster ()
Keywords: Robotic Manipulation
Primary area: applications

Abstract: We present Chain-of-Action (CoA), a novel visuomotor policy paradigm built upon Trajectory Autoregressive Modeling. Unlike conventional approaches that predict next step action(s) forward, CoA generates an entire trajectory by explicit backward reasoning with task-specific goals through an action-level Chain-of-Thought (CoT) process. This process is unified within a single autoregressive structure: (1) the first token corresponds to a stable keyframe action that encodes the task-specific goals;  and (2) subsequent action tokens are generated autoregressively, conditioned on the initial keyframe and previously predicted actions. This backward action reasoning enforces a global-to-local structure, allowing each local action to be tightly constrained by the final goal. To further realize the action reasoning structure, CoA incorporates four complementary designs: continuous action token representation; dynamic stopping for variable-length trajectory generation; reverse temporal ensemble; and multi-token prediction to balance action chunk modeling  with global structure. As a result, CoA gives strong spatial generalization capabilities while preserving the flexibility and simplicity of a visuomotor policy. Empirically, we observe that CoA outperforms representative imitation learning algorithms such as ACT and Diffusion Policy across 60 RLBench tasks and 8 real-world tasks.

Chain-of-Action: Trajectory Autoregressive Modeling for Robotic Manipulation
Wenbo Zhang 1.2
Tianrun Hu
Hanbo Zhang
Yanyuan Qiao² Yuchu Qin
Yang Li
Jiajun Liu
Tao Kong'
Lingqiao Liu
Xiao Ma
BaneeDance Seed
The University of Adelaide
National University of Singapore
Chhnese Academy of Sciences
SCSIRO
Thhe University of Queensland
wenbo wwwaghhaannnaaaaane www.aaaewaaedee..aeaeeeeeeeeeeee edu.au, au, xiaoma@bytedance com, lingqiao. liušadelaide edu. au
*Corresponding authors
Project pagerhhttpps//chhiiiooo-aaaioooo git.ub..ittubioo
Code: http::/s///ghhh.....oo//tooooaee Seehheea--eeeeeCnnineneee Action
Abstract
We present Chain-of-Action (CoA), novel visuomotor policy paradigm built upon Trajectory Autoregressive Modeling. Unlike conventional approaches that predict next step action(s) forward, CoA generates an entire trajectory by explicit backward reasoning with task-specific goals through action-level Chain-of- Thought (CoT) process. This process unified within a single autoregressive structure: (1) the first token corresponds to stable keyframe action that encodes the task-speeific goals; and (2) subsequent action tokens are generated autoregres- sively, conditioned on the initial keyframe and previously predicted actions. This backward action reasoning enforces a global-to-local structure, allowing each local action to be tightly constrained by the final goal. To further realize the action rea- soning structure, CoA incorporates four complementary designs; continuous action token representation; dynamic stopping for variable-length trajectory generation; reverse temporal ensemble; and multi-token prediction to balance action chunk modeling with global structure. As result, CoA gives strong spatial generalization capabilities while preserving the flexibility and simplicity of visuomotor policy. Empirically, we observe that CoA outperforms representative imitation learning algorithms such as ACT and Diffusion Policy across 60 RLBench tasks and 8 real-world tasks.
Introduction
visuomotor policies have made substantial progress in enabling robots to perform complex manipu- lation tasks from raw sensory observations. With the rise of large-scale demonstrations [5] 19 37
and powerful neural architectures [36] [ recent methods have increasingly focused on end-to-end
learning from visual inputs to low-level control 2).
To better model multi-modal action distributions and mitigate compounding errors, various modeling paradigms have been proposed 3 45 For instance, ACT 45 employs a conditional variational autoencoder learn action distributions and introduces action chunking to reduce compounding errors. Diffusion Policy 3 formulates action generation as a denoising process, capturing complex, multi- modal behaviors more effectively. Many subsequent developments have explored enhancements in multiple directions, including enriched sensory inputs [4] [0], improved network architecture 4 (24), expanded datasets (5) and scaled model capacity, represented by trend of VLA (vision-language- action) model 21
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Despite a wide range of these improvements, most of methods still follow a forward prediction paradigm, as illustrated in Figure [] While this formulation intuitive and widely adopted, it suffers from a critical limitation: the accumulation of compounding errors 32
30 during execution. The root cause lies in the training objective: these models are optimized to predict the next-step action based on current observation, rather than to ensure successful completion of tasks with long- horizon [32] While techniques such as action chunking and image goal conditioned behavioral cloning 228 37 have been introduced to alleviate compounding errors, they primarily address the symptoms rather than the root cause, which lies in the inherently myopic nature of forward prediction.
18
We approach the problem from the opposite end, both conceptually and practically, by reversing the action generation process. While the change in direction may appear simple, it reflects a funda- mental shift in how we conceptualize action gen- eration. Instead of predicting actions in a forward, step-wise manner, we propose to construct action sequences in reverse, forming a chain of actions that starts from the a keyframe action [13 34 9
forward glora sonurettion ettinn
bockward
generatron fio
Training
training
objective
dbjecting
devicte from gool compounding errer
géal-conditioned Prajectory
train
Rest
Tron
TEST
and backward towards the initial state. Our in- sight is that the keyframe action encodes the task- specific goal, which provides a strong structural prior to guide the entire action sequence. By explicitly generating actions from the goal back- ward, our method enforces a global-to-loca con- sistency [26 39 that significantly mitigates com- pounding errors and enhances generalization un- der distribution shifts.
Figure 1: Comparison between a conventional visuomotor policy (left) and our proposed Chain- of-Action (right). The former is optimized to predict step-wise actions based current observations, rather than long-term goals, often leading misaligned behav- iors during exccution. In contrast, Chain-of-Action adopts a backward generation paradigm, producing goal-conditioned trajectories that reliably execute to- ward the intended target.
To realize this backward reasoning paradigm while maintaining scalability potential [16, 35| for end-to-end training, we unify the entire reverse genera- tion process into single autoregressive framework. While the formulation is theoretically effective, its practical viability depends on four extra specific designs. These are not optional improvements, but necessary for stable training and reliable closed-loop execution. (1) Continuous action represen-
tation: Discretizing actions into finite bins introduces resolution loss (20) 31 23], which becomes particularly problematic in long-horizon autoregressive generation. In our backward generation setup, even small quantization errors can accumulate from the goal backward, leading to significant deviations in earlier steps. To preserve fine-grained structure and trajectory fidelity, we adopt continuous action representation. (2) Local action modeling: While the backward autoregressive structure effectively propagates high-level intent from the goal, it does not explicitly model local 3 within a sub-trajectory. To address this, we adopt multi-token prediction strategy 7 43 during training, which encourages the model to jointly predict short action chunks. This enhances local coherence and stabilizes training. (3) Dynamic stop: Closed-loog
action dependencies 220
45
execution (27) requires our generation stop at right point. However, in continuous action spaces, there is no discrete end-of-sequence (EOS) token to indicate termination (43). We thus design a distance-bart based stop mechanism that enables the model determine when to stop based on proximity to the goal, reducing over-generation and improving execution efficiency. (4) Reverse temporal
ensemble: Original ensemble strategies [45). used in ACT, are designed under forward temporal assumptions and are not directly applicable to our backward generation setting. To address this, we develop a evvese-comppttblee variant that ensembles multiple backward rollouts, mitigating temporal misalignment and reducing variance during closed- loop execution.
Chain-of-A (CoA), which integrates these four essential components into a single autoregressive framework, achieves strong performance in both simulation and real-world settings. CoA outper- forms ACT by 16% and Diffusion Policy by 23% across 60 RLBench tasks, the most comprehensive evaluation conducted on this benchmark to date, and surpasses ACT by 15% in real-world robotic manipulation. Crucially, CoA adopts comparable architectures and training setups to ACT, underscor- ing that the performance gains stem from a principled shift in the modeling paradigm. These results position our trajectory autoregressive modeling as a competitive alternative for visuomotor policy learning.
2

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Trajectory autoregressive modeling
Execution: Dynamic stop mechanism Reverse temporal ensemble
ar
@y-
ar-4
Ducode
Autoregressive
Transformer encoder
Transformer decoder causal
dy
dy dy-2
Until close to gripper state
140
Froode
Ensemble
CNN Posshily
2
Sub trajectory
d
Front
Left
Right
Writ
Figure 2: Chain-of-Action built on trajectory autoregressive modeling, The left part illustrates the network architecture where notation is for the training stage, and the right part illustrates the execution process. The model encodes visual and proprioceptive observations and generates actions in reverse order from predicted keyframe action by an autoregressive decoder. For clarity, the keyframe action ar is shown in green, and subsequent steps are visualized with gradual color transition.
2 Related work
Hierarchical modeling in robotic manipulation A widely adopted strategy in robotic manipulation first identify bigh-level keyframes, and then rely on predefined controllers to handle the low-level execution. This paradigm is exemplified by C2F-ARM [13 and extended by methods such Per-
Act [34], RVT 19. RVT-2 2 [8. Recent works like ChainedDiffuser [39] and HDP (26] propose neural planners replace traditional optimization-biss based planners. Despite these advances, such methods still operate in an open-loop manner [39 26 between keyframes and struggle to adapt to dynamic environments. Our method also builds the notion of keyframes, but differs fundamentally in its formulation. By unifying keyframe detection and trajectory generation within a single autoregressive framework, it enables efficient environment-awwe aware action prediction and closed-loop execution, where the model can continuously refines its actions based on feedback. As result, our method no longer relies on figh-fidelity 3D inputs for one-shot accurate predictions, which commonly required by those hierarchical approaches.
CoT-style methods in robotic manipulation A separate line of research explores CoT-style VLA agents [44] 6 38 [46), which introduce intermediate semantic representations- such as imagined im- age goal, visual trace, bounding boxes, gripper pose, guidance for subsequent action generation. Orthogonal to these directions, our work focuses on modeling the reasoning process directly between actions without relying extra modalities intermediate representations. This design makes method broadly compatible with different sensory inputs and policy architectures.
3 Chain-of-Action for robotic manipulation
Formulation The core idea of Chain-of- Action is to model trajectory generation in reverse: starting from task-specific goal and predicting actions backward in autoregressive manner. This reverse formulation imposes a global-to-local structure, anchoring the rollout to the final intent and mitigating compounding errors. An overview of the CoA pipeline is shown on the left of Figure We adopt the definition of keyframe originally from C2F-ARM (13), where keyframe is identified as a time step which the gripper state changes the joint velocities approach zero. This simple yet effective heuristic captures transitions between semantically meaningful phases, such grasp completion or object placement, and can interpreted as a sask-specific goal. Representing the goal an action allows it to share the same embedding space with all other actions, enabling seamless backward generation. For each training sample, CoA learns to model action sequence in reverse order using an autoregressive decoder. This formulation enforces reverse causal dependency among actions, yielding a coal-conditioned reasoning chain. Such backward chaining lies at the heart of the our framework, which models the trajectory distribution as:
3

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p(ar:r ()
p(ar O0)
p(ar-1 or, .)...p((as 13.T, 0)
p(a1
02:77
(I)
Keyframe Action
Reverse Reasoning Actions
Exccused Action
where ar denotes the keyframe action, and O denotes the observation context, including visual imput I and proprioceptive state S. To make the meaning of a explicit, we clarify how each training sample is constructed. A sub-trajectory is sampled from an expert demonstration by selecting a segment that starts at a random time step and ends at the next first keyframe action. The observation O is taken from the initial step, and a denotes the sequence of actions from the current step up to (and including) the keyframe. Each pair (O, a1.T) forms an independent training example.
Algorithm 1: Training Phase
Algorithm 2: Inference Phase
Inputs: datasct D
2 Modules:
Inputs: image I, proprioceptive state S Modules:
Action encoder fau: 0r ++ ae
Action decoder Jazsi 2i + dt
Action encoder senc: 1
Transformer Fa: encodcr-dccoder model Parameters: learned token 2ros,, loss weight X for iteration n = 1.
Action decnder fas: 2t + az
Transformer Fg: encoder-decoder model
Parameters: learned token aisos, max length Tiax
Sample S1, (a1,-.., or)) from D based keymrame heuristic
Initialize H < [arsos] for = to Timas do
T1T REVERSE ().:r))
H +- CONCAT (1sos, .1.7
8e f- Fo(H I,S)
ž + Fo(H L,S)
Append break
H STOP fax (2x); S) then
01.r < (aEVERSE(Saactaa
Lig + Ely Cunna(dr, ar)
Remove Jsos: If' 1
Livenlite, (ite, seno(ae)) Liad Lng Breaat
Linen f-
ā1.7 <- REVERSH (H'))
Return:
action sequence âi.r
Update 2sos backprop on Liuua
Continuous action token representation CoA adopts continuous action token representation. However, directly training with continuous latent tokens introduces its own challenge. Unlike discrete token embeddings [21] that are fixed indices supervised by softmax classifier, our latent actions generated through a learned encoder. In this setting, imposing loss directly on the action space fails to constrain the latent space to exhibit temporal consistency during autoregressive decoding. As result, the latent space lacks meaningful regularization, allowing encoding errors to propagate and amplify through the autoregressive process. To address this, we introduce latent consistency loss to regularize latent action space: Connsistnccy = || - fenc (a.)ll. where (a.) = Wen + bene- Here, dt, denotes the predicted latent from the previous timestep, and senc (a.) is the encoded latent of the ground-truth action. This loss acts as an inductive bias to align the latent space with temporal dynamics, improving the quality of autoregressive generation.
Locality modeling Multi token prediction (MTP) 7 can serve as a regularization for action locality modeling. We assign the last K layers of the transformer decoder to produce predictions for different future steps. Concretely, layer is predicts token fe+k. where = 1,... K, making the model aware of the mutual dependencies across the next K steps in single forward pass. This design introduces temporal locality into the decoding process, enhancing stability in nong-horizon generation while maintaining our -locallto-local chain-like structure. Importantly, this regularization is applied only during training and is removed at inference.
Dynamic stop To enable flexible-length trajectory generation in continuous action space, we in- troduce a distance-basee stop criterion. The core idea is to terminate decoding once the predicted action sufficiently approximates the current execution state, indicating that the backward-geeeraan trajectory has successfully reached the present, as shown in bottom-righ in Figure 2 This stop mechanism is agnostic to the specific action representation and can be readily applied to delta actions or joint-space control by adjusting the reference point accordingly.
Reverse temporal ensemble We introduce a reverse temporal ensembling strategy tailored for CoA. As shown in the bottom-right corner of Figure our approach aligns multiple reversed sub- trajectories by their predicted keyframe action ar, which serves as the anchor point for autoregressive decoding. This design offers unique advantage in CoA: since each trajectory decoded in reverse from the keyframe, the compounding error is inherently constrained by the accuracy of the keyframe

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Stack tap
Open
Push button
up
Take
Press switch
Reach target
Sweep cuutt
Open box
Figure 3: Visualization of predicted sub-trajectorics across 10 widely used tasks. Detail refers to Table [ Red waypoints represent ground-truth trajectories, and green waypoints denote model predictions. Each predicted trajectory is generated backward from a keyframe action to the current gripper state, enabling consistent coal-conditioned trajectory generation. The model successfully handles both straight and curved motion patterns.
action. By further improving the accuracy of the keyframe action through ensembling, we tighten this constraint even more.
4 Implementation details
Network architecture Our network follows similar overall architecture to ACT [45], consisting of a 4-layer Transformer encoder and a 7-layer Transformer decoder. However, unlike ACT, our model does not include the conditional variational autoencoder (CVAE) module. The final decoder layer contains multiple parallel heads for multi-token prediction (MTP), which are only used during training. The observations consist of multi-view RGB images and corresponding robot states, which encoded follows: each image view is processed by ResNet-18 vision encoder extract visual tokens. The gripper state is projected via learnable linear layer into token representation. All tokens concatenated and passed through the Transformer encoder to produce contextual features for decoding. Autoregressive action generation performed by the Transformer decoder, which is initialized with learnable saut-of--equence (SOS) token. This token serves query for the first prediction, corresponding to the keyframe action. The decoder iteratively predicts previous actions until the generated action becomes sufficiently close to the current gripper state, where the dynamic stopping criterion is applied. Actions are encoded and decoded into a shared latent embedding space via linear projection layers, which are regularized by the latent consistency loss described earlier. Additionally, sinusoidal positional embeddings are added to the action tokens to preserve temporal ordering cues.
Training For each training sample, we apply two loss terms: a regression loss in the action space and consistency loss in the latent space. Both are computed with the MTP regularization, where the model predicts a chunk of K actions at each decoding step. The total loss is defined as:
K
Liotal
|a
actk-1ll + A || Senc (Bc+6-1)))
where a/$a-1 and ditn-1 are the predicted action and its latent embedding from k-th head of MTP layer at step t, and (.)e(.) (.) is the action encoder network. Note that for decoding steps where t+ T, the corresponding terms are masked out and do not contribute to the loss. This ensures that predictions beyond the trajectory horizon are excluded from supervision. For parallel training with batch of samples, set Tmax the maximum sub-trajee uu-trrajcttory length (practically the longest in the dataset), and zero-pad all shorter sequences accordingly. The loss for padded steps is masked out avoid affecting gradient updates.
Execution For each inference, CoA generates an entire trajectory segment, which can executed in either open-loop closed-loop mode. We generally adopt closed-loop control, as it allows
5

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reverse temporal ensembling to continuously refine the predicted actions during execution. Under the dynamic stopping setting, we compute the Euclidean distance between the predicted action and the current end-effector pose. This termination criterion is well-suited for our continuous end-effector pose action space.
5 Experiments
In Sec. 5.1 we introduce our experiment settings, includ- ing simulation environment, train, evaluation settings and metrics. Then we show detailed results of the overall comparison Section 5.2 To dive into the spatial gen- eralization and obtain better understanding of how CoA work, more specific evaluation is shown Section [53 Ablation studies of each components in CoA are shown in Section 5.4 Finally, the real-world robot evaluations are shown Section 5.5
Sec.5.1
Table 1: Success rate across 10 widely-used tasks RI.Bench.
Task
CoA
ACT
DP
Octo
Stack Wine
0.80
0.56
0.56
0.52
Turn Tap
0.56
0.36
0.32
0.28
Open Drawer
0.88
0.52
0.44
0.84
Push Button
0.76
0.08
0.12
0.76
Pick Up Cup
0.80
0.20
0.00
0.44
Take
0.80
0.40
0.60
0.76
5.1 Simulation experiment settings
Press Switch
0.44
0.52
0.56
0.44
Reach Target
0.84
0.88
0.08
0.60
Simulation setup We conduct simulation experiments using RLBench [14,, a widely-used benchmark built on CoppeliaSim and interfaced via PyRep. The robot is 7-DoF Franka Emika Panda mounted behind a tabletop
Sweep Dust
0.92
1.00
1.00
0.80
Open Box
0.76
0.36
0.48
0.96
Avg.
0.756
0.488
0.416
0.644
workspace. Observations are collected from four RGB cameras (front, left shoulder, right shoulder,
and wrist). Images are rendered at a resolution of 128 x 128.
Baseline We compare our method against representative approaches from three categories: (I) training visuomotor policies from scratch, including ACT and Diffusion Policy (DP); (2) finetuned generalist robotic policies, represented by Octo [28]: (3) 3D-based hierarchical methods, including PerAct [34) 3D Diffuser Actor [17], and RVT-2 B). We note 3D-based hierarchical methods fundamentally differ from our approach by relying on 3D inputs and motion planners to generate trajectories. We provide additional discussion on these differences in Appendix[A]
Training and evaluation protocol To ensure broad and representative evaluation, our main bench- mark is conducted on a tailored set of 60 RLBench tasks, where CoA compared with ACT and DP, Each method is trained on 100 demonstrations and evaluated on 25 demonstrations and DP, we follow the RLBench training protocol introduced in [33] which is detailed in Appendix D To better demonstrate the effectiveness of our modeling paradigm, we align our base architecture with ACT and introduce modifications primarily in the transformer decoder, as detailed in Section 4 The strong performance of these baselines suceessscchh perfect success rates tasks like Sweep Dust and competitive results on others (Table - that all reference models are properly trained. For comparison with Octo, we adopt the evaluation subset RLBench- 10 proposed in [42] and use the reported results. This subset is also used for our ablation studies for convenience. To facilitate comparison with 3D-based hierarchical methods, reported results from prior work [ Note that our RL.Bench-18 18 setup is not strictly identical to the PerAct protocol: we train single-task policies and use only variation 0 for both training and evaluation. Hence, the RLBench- 18 results are reported as contextual reference rather than a fully protocol-matched comparison.
task. For ACT
evaluate on the RLBBecc--18 split [34], using
5.2 Overall comparisons
The overall results are presented in Figure with task-wise averages summarized in the accompany- ing wrapped table. To better assess the effectiveness of our method, we report task- improvements over both ACT and DP. Compared to ACT, our method achieves higher success rates on 81.7% of the tasks, with an average improvement of 16.3%. Relative to DP, our method improves performance on 80.0% of the tasks, with an average gain of 23.2%. These improvements are especially pronounced in tasks involving significant variation in object position and pose, indicating stronger spatial gener- alization. As ACT and CoA share a consistent Transformer encoder-decoder architecture and are trained on the same setting, the observed gains highlight the effectiveness of our modeling paradigm.

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CoA improvement over ACT DP
Got Al
Method
Avg. SK
Oak 30
ACT
0.389
DP
0.326
CoA
0.552
Suace NMCC200-mm
60
and Ton
at
Figure 4: Success improvement on RLBench-60, sorted by improvement from high to low. The average success rate over all tasks is shown in the inset on the right.
Table 2: Comparison on the RLBench- 18. 3D-based hierarchical methods use 3D point clouds and motion planners, while image-based visuomotor policies operate directly RGB inputs.
3D based hierarchical methods
Image based visummotor policies
PerAct
3D Diffuser Actor
RVT-2
Image-BC (CNN)
Image-BC (ViT)
Close
55.2 + 4.7
96.0
2.5
100.0
0
Drag Stick
89.6 1 4.1
100.0 0.0
99.0 1 1.7
Insert Peg
5.6 +.1
65.6 4.1
40.0 + 0.0
Meat off Grill
70.4 1. 2.0
96.8
99.0 1.7
Open Drawer
88.0 5.7
89.6 4.1
74.0 11.8
4
Place Cups
2.4
24.0 7.6
38.0
0
Place Wine
7.8
93.6=
95.0 3.3
Push Buttons
9.88
98.4220 2.0
100.0:00
O
32
28
Put in Cuphoard
28.0 4.4
8,16=411
4.5
Put in Drawer
4.7
96.0=36
96.0
8
40
60
88
Put in Safe
3.6
97
96.0 2.8
Screw Bulb
1..6
82
88.0 4.9
Slide Block
13.0
97,6=3.2
92.0 2.8
Sort Shape
16.8
44.0=44
35.0 1.0+10
Stack Blocks
Stack Cups
2.4
47.2
69.0 5.9
Sweep Dustpan
Turn Tap
8..0
99.2 1.6
99.0 + 1.7
16
32
36
56
Average
48.7
81.3
$1.4
1.33
17.33
37.33
The results suggest that principled change in how action sequences are represented and generated can lead to substantially better performance under distribution shifts. The detailed per-task results in Appendix B In addition, the comparison with Octo and detailed results with ACT and DP over 10 selected tasks are shown in Table I Results the RLBench-18 benchmark are reported in Tab We observe that, in these settings, CoA outperforms the finetuned generalist robot policy Octo, while substantial performance gap remains compared the 3D-based hierarchical methods.
5.3
Dive into spatial generalization
Although CoA significantly outperforms ACT and DP on the overall benchmark, it remains crucial to understand why such improvements emerge. To this end, we investigate the spatial generalization behavior of our model from three complementary perspectives.
First, in the Interpolation vs. Extrapolation case study, we analyze CoA's performance under controlled spatial distributions within single representative task. This study reveals that CoA not only achieves higher success rates under in-distribution (interpolation) configurations, but also demonstrates substantially larger advantage in out-of-distribution (extrapolation) settings, indicating stronger spatial generalization.

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Rate Spat Veriance
Con vs Sontial lediace
Conl Spatal Var enca
MethodMGap
Pearson (r)
CoA
-0.1679
ACT
-0.2471
-0.2455
CoA ACC
0.1311
CoA-DP DP
0.1028
Figure 5: Correlation between success and spatial variance. Left image: Overall success decreases as object spatial variance increases, Middle and right image: CoA consistently outperforms ACT and DP across varying spatial generalization levels, with larger advantages in more challenging (higher variance) settings. Table: Pearson correlations highlight CoA's robustness to spatial perturbations.
Inter.
CoA
0.94/0.48
ACT
0.54/0.08
DP
0.18/0004
Figure 6: Interpolate vs, extrapolate performance. Success rate comparison on interpolation (in-distribution) and extrapolation ofut-of-distriuute subsets for the Push Button task. CoA maintains stronger performance across both regimes, with a notably smaller degradation under extrapolation. The gray dashed line denotes the 2D convex hull computed from the training samples. Cross markers represent training data, while circular markers denote evaluation samples, where green circles indicate successful executions and red circles indicate failures.
Second, in Correlation with sputial distribution, we quantitatively examine how task performance correlates with spatial variation difficulty across the 60 RLBench tasks. The results show that CoA consistently improves over ACT and DP across all spatial variance levels, and that the performance gap widens as spatial generalization becomes more challenging.
Finally, in Attention--ased analysis of action chain, we visualize the attention maps between action tokens the Transformer decoder. The attention patterns clearly reveal structured dependencies along the predicted action sequence, supporting the hypothesis that CoA performs chain-like global-to-loce reasoning throughout the trajectory generation process.
Interpolation vs. Extrapolation case study We conduct qualitative analyses on Push butlon task to contrast model behavior under interpolated (in-distribution) versus extrapolated -oistr--distiiuution) spatial configurations. For this analysis, we choose the Push Button task due to its large spatial variation and its frequent use in prior works. Unlike the standard benchmark setting, we randomly sample 200 demonstrations from the full dataset and project the button target positions onto the (x, y) workspace plane. We then compute the centroid of all sampled positions and select the 150 samples closest to this centroid based on Euclidean distance, which are used to form 2D convex hull. Within this convex hull, we randomly assign 100 samples for training and 50 samples for interpolation testing, while the remaining 50 samples lying outside the convex hull are used as extrapolation testing data. This protocol ensures a controlled and reproducible evaluation of spatial generalization, where extrapolation explicitly corresponds to goal configurations beyond the spatial support of the training distribution.
Correlation with spatial distribution We examine the relationship between success rate and the spatial distribution of objects in the evaluation set, aiming quantify each model's spatial generalization ability. We use the variance of object coordinates to measure how widely objects are spread in the workspace. As shown in the left plot of Figure [5] all methods exhibit clear trend: success rate decreases spatial variance increases. This indicates that there spatial generalization becomes more difficult when object placement more diverse. The improvement plots the Figure reveal more details. Compared to ACT and DP, our method consistently outperforms across all levels of spatial variance, and its advantage becomes more pronounced as task difficulty increases. This trend is further supported by quantitative Pearson correlation.

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Liger1
Lver Layer
Liver
Laper
Liver
Layer
18
36
Figure 7: Attention- bhased analysis of action chains. Self-attention maps reveal two key patterns: (1) chain-like dependencies, where each action token attends to recent predecessors, and (2) long-range dependencies (highlighted in the red box in Layer 1), where some tokens directly attend to the initial keyframe action.
method outperforms both ACT and DP under both interpolation and extrapolation conditions. Interestingly, while the success rate of CoA in extrapolated settings about half of that in interpolation, ACT and DP suffer from significantly steeper drops. This highlights the particular difficulty of spatial extrapolation for forward modeling approaches, and suggests that the reverse autoregressive modeling in CoA provides more robust generalization under spatial distribution shifts.
As shown in Figure 6
Attention- based analysis of action chain Figure 7 presents the self-attention maps among action tokens across all decoder layers in our model. The horizontal and vertical indices correspond to the autoregressive decoding order of action tokens, where index 0 denotes keyframe action. We observe two distinct attention patterns: (1) a dominant local chain-like structure, where each action token primarily attends to recent window of preceding tokens, directly reflecting modeling of CoA; and (2) occasional long-range dependencies (e.g., red box in layer and most of tokens in layer 6), where later tokens exhibit strong attention initial tokens. This behavior suggests the model leverages the goal-conditioned actions to anchor and guide the full trajectory generation.
5.4
Ablation on architectural components
We summarize how each architectural com- ponent contributes to performance across 10 representative RLBench tasks (selected con- sistently with Table I The average success rate of each variants are provided in Table 3
Table 3: Ablation study on individual components by replacing them with alternative settings. The bold
indicates the best setting adopted by our final model.
Modeling paradigm. CoA's modeling in- designs: (1) chain-style autoregressive generation, and (2) goal anchor- ing via keyframe action. To assess the neces- sity of each component, we compare Reverse ordering of CoA against two ablated variants:
Components
Setting
Avg. SR
corporates
Reverse
0.756
Modeling Paradigm
Forward
0.668
Hybrid
0.600
Action consisteney
0.212
Embedding Loss
Latent consistency
0.756
Forward ordering retains the autoregressive structure but removes goal anchoring, start- ing from the current state and predicting ac- tions forward. Compared to CoA, its lower success rate (0.668 vs. 0.756) highlights the importance of reverse ordering, the core of our proposed modeling. On the other hand, it sig- nificantly outperforms ACT (0.668 0.488), which also uses a autoregressive architecture but predicts fixed-length action chunks. This contrast underscores the advantage of modeling the joint distribution over the entire trajectory, rather than treating it as separated chunks.
Non-ensemble
0.66
Exccution
Reverse ensemble
0.756
0.710
0.704
0.720
Num. of MTP head
0.756
0.672
10
0.660
Hybrid ordering retains goal anchoring but drops chain-style reasoning. It initializes from the keyframe action but switches to forward action generation, removing backward generation process between actions. As result, the local continuity of autoregressive is lost, and performance drops greatly to 0.600.
These results confirm that trajectory autoregressive modeling is essential for effective robotic manipu- lation. Furthermore, reverse autoregressive ordering further enhances performance by anchoring the generation process to the task-specific goal, providing global guidance throughout the rollout.

---

Tesk- realoverdd experiment
1.0
0.8
Sucreesrae
0.6
:lose hidge lowe
pacce obbiret
oee sbinet
disse nirge Laper
cless cabiret
close frigge townr
0.0
dlose fyelge upper
open catinee
open triége lower
open micressv
piace in cabinet
place frida
lower
place
Figure 8: Real-world experiments on 8 kitchen tasks.
Figure 9: Real-world experimental results.
Number of MTP heads Multi-token prediction regularization enables the model to capture local action chunks while preserving global causality. Allocating too few heads underutilizes this local context, whereas allocating too many heads disrupts the causal structure. A moderate configuration of 5 heads strikes an effective balance, achieving the highest overall score 0.752.
Latent consistency loss We ablate the latent consistency loss by replacing it with a direct action reconstruction loss, which supervises the action encoder and action decoder to reproduce the input action. This substitution leads to a significant performance drop from 0.752 to 0.212, and results in unstable trajectories with unnatural curling. In contrast, enforcing latent consistency yields well-structured representation and substantially improves task success.
Reverse temporal ensemble We evaluate the impact of reverse temporal ensemble by comparing with a non-ensemble baseline. Without ensembling, the model achieves 0.660. Applying our reverse-compatible ensemble strategy improves performance to 0.756, highlighting the benefit of aggregating multiple backward rollouts during inference.
5.5 Real-world experiments
We deploy our method on Fetch robot featuring a 7-DoF arm and mobile base for real-world validation. For each task, the robot navigates to predefined location using its built-in 2D LiDAR- based localization system. Observations are captured from a single RGB camera at 640 x 480. resolution and resized to 224 224. for policy input. Execution is command by absolute end effector poses. To execute commands, we implement a PD controller that calculates the difference between current and desired end effector poses, projects this error into joint space via the Jacobian, and sends velocity commands to the robot. The neural policy operates at 10Hz while the PD controller runs locally on the robot 1000Hz, with communication handled through ROS for both image data and control commands. As shown in Figure & we evaluated CoA and ACT on 8 kitchen tasks, with the number of expert demonstrations ranging from 35 to 81 per task. Each task was evaluated over 10 trials. The results, summarized in Figure 9 show that CoA achieves an average success rate of 0.613, outperforming ACT, which achieves 0,463, by a margin of 15%. The detailed results are in Appendix
laptop with 4070 GPU,
Conclusion
We present Chain-of-Action, an action-level reasoning model built upon trajectory autoregressive modeling. By decomposing the joint distribution of the trajectory in reverse, starting from a keyframe and progressing backward the initial gripper state, our formulation imposes a global-to-locet structure that enforces consistency between local actions and global task goal. To enable stable training and execution under this backward autoregressive framework, we introduce four necessary design components. Overall, our proposed visuomotor modeling paradigm significantly improves spatial generalization, and we hope offers compelling alternative for future visuomotor policy design. However, the current modeling paradigm relies on keyframe heuristics to split the trajectory, which may not generalize well to diverse task types. Future work can explore learning keyframe structures in unsupervised manner.
10

---

7 Acknowledgements
We thank the Adaptive Computing Laboratory at National University of Singapore for facilitating the real-robot experiments in this project. Jiajun Liu was partially supported by the Responsible Al Research Center the University of Adelaide.

---

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A Comparison on RLBench-18
The RLBench-18 18 subset was originally introduced by PerAct (34 and later became the standard comparison benchmark for 3D hierarchical methods. The results detailed in Table To clarify the fundamental difference between these two categories of approaches, Table 4 summarizes their methodological distinctions. 3D-based hierarchical methods typically rely on 3D perception and motion planning, whereas image-based visuomotor policies operate directly on raw RGB observations and learn end-to-end trajectory generation without explicit planners. We observe that, for RGB- only policies, several tasks in RLBench- 18 are challenging and frequently result in zero success rates, which limits their discriminative power. This observation motivates our use of the proposed RLBench- evaluation split.
Table 4: Key differences between 3D-based hierarchical methods and image-basee based visuomotor policies.
Aspect
3D-based Hierarchical Methods
Image-based Visuomotor Policies
Typical Methods
PerAct, RVT. RVT-2, 3D Diffuser Actor
ACT, Diffusion Policy, CoA
Input Modality
point RGB-D
RGB only
Pipeline
Two-stage: keyframe action detection motion planning
End-to-end trajectory prediction without explicit planning
Execution Mode
Open-loop execution between keyframes
Closed-loop prodiction and control
B Per-task success rates on RLBench-60
To complement the summary figure in the main paper, which visualizes the performance gap between CoA and baseline methods, we provide the full success rates on all 60 RLBench tasks in Table This table lists the per-task success rate of CoA, ACT, and DP, along with the gap of baselines over CoA. Tasks are ordered by the maximum improvement CoA achieves over either baseline, highlighting where our method provides the most substantial gains.
Table 5: Detailed results of the overall comparison on RLBench. The simplified names used in Figure are matched with their corresponding original task names. The success gap between ACT, DP and CoA is shown as superscripts.
Simplified name
Original name
CoA
ACT
DP
pick up cup phone on base
pick_up-cup phone_on_base
0.80
0.20 0.60
0.00 -0.00
0.80
0.04
-0.76
0..6
0.04
reach target
reach_target
0.84
0.88
0.08 0.76
remove meat
meat_off_grin
0.88
0.32 0.56
0,16 0.72
0.16
push button
push_buttor
0.76
0.08
0.08-0.68
0.68
0.12 0.64
put money in safe
put_money_in_set
0.80
0.36-0.44
0.24
move hanger
move_hanger
0.88
0.68
0.32 0.56
slide block
slide_ [Lide_block_tor to target
0.52
0.32 0.22 0.20
0.00 0.52 -.522
remove toilet roll
roll stand
0.56
0.40
0.08-0.48 -048
lamp off
lamp_off
0.68
0.68-0.00
0.20-0.18
lamp on
lamp_on
0.48
0.04
0..4 0.48
open door
open_door
0.92
0.44-0.48
0.60 0.32
open drawer
open_drawer
0.88
0.52 -.36
0.44 0.44
remove frame
take_frame off. hanger
0.64
0.44 0.20
0.20
0.24 0.40
Continued on next page
14

---

Simplified name
Original name
CoA
ACT
DP
open washer
wren_washing_macae
0.76
0.44 0.32
0.10-0.16
remove pan lid
take_lid_owe offfoofffe_e
0.80
0.40
0.40-0.40
0.40
0.60-0.20
unplug charger
unplug- charger
0.60
0.56 0.04
0.20-0.40
buzz game remove umbrella
beat_the_bele
0.36
0.12 0.24
0.00-0.36
sexe__mbrella__ee
0.52
0.16
0,20 0.32
umbrella_stand
drag to target
reach_and_drees
0.64
0.36 0.36-0.25
0.28
0,28 0.28-0.36 0.36
get ice
get_icee_from_friee
0.60
0.32
0.24 0.24-0.30 0.36
open box
open_box
0.32
0.16 0.16
0.32 0.00
place knife
place_knife_ong _on wtw.k//fe_eooocoopinngggggg
0.04
0.04-0.00
0.00-0.01 0.04
board
play jenga
play-jenga
1.00
1.00
0.72-0.25
place plate
put.plaate_in_colored.
0.32
0.12 0.20
0.04-0.28
rack
put bottle in fridge remove plate
put_
put_bottle_in_fridde
0.28
0.00
0.28
0.00-0.25 0.28
take liee_plate_offcollll
0.40
0.40 00.00
0.12 0.12-0.28 0.28
dish_rack
turn tap
turn_tap
0.56
0.36-0.20 0.20
0.32-0.24 0.224
remove from scale
0.84
0.44-0.40
0.64-0..
stack wine
stack_wine
0.80
0.56-0.2
0.56 -0.24 0.24
close drawer
close_drawer
1.00
0.96-0.01
0.76-0.25 -0.24
close box
box
1.00
0.96-0.01
0.76
set clock
change_clock
0.40
0.28
0.20-0.22
hang frame
hang_frame_on,
Setrame__o_walll
0.16
0.08-0.08
0.00-0.16 0..16
open microwave
open_microwave
0.44
0.40-0.04
0.40-0.0L
close fridge
close_fride
0.92
0.84-0.08
0.76 0.76-0.10 0.16
remove USB
0.60
0.48 0.12
0.72 +0.12
change channel
change_channed
0.12
0.00 0.00-0.12
0.00 0.12
insert USB
insert_usbbin_ccoppteee
0.92
0.80
0.88 0.88-0.04
seat down
toilet_seat_dom
1.00
0.96 0.04
0.88 0.88-0.12
close grill
close_grill
0.56
0.48-0.05
0.68+0.12
lift block
lift__umberedd_ble block
0.08
0.00
0.08-0.00
seat up
toilet_seat_u
0.84
0.76-0.06
0.88+0.00
take shoes
take_shoes_oute _ox box
0.08
0.00
0.16+0.08
take out money
take_money_out_saff
0.76
0.80+
0.68-0.08
screw nail
screw_nail
0.08
0.12+0.04
0.00-0.08
water plants
water_plants
0.48
0.40
0.56+0.08
hockey
hockey
0.08
0.04
0.00
open wine
son__win_bbottll
0.36
0.28 0.28-0.08
0.40+0.04
hit ball
hit_ball_with_co
0.08
0.00 0.00
0.00
put groceries
gto_groceries_ihccupbaae
0.08
0.04
0.00
turn on oven
turn_oven_on
0.36
0.32-0.04
0.28
set checkers
setup_checkers
0.04
0.00
0.04-0.00
basketball
booketbball_in_howe
0.76
0.72
0.72 0..2 0.04
hang hanger
place_hange
place_hanger_on_racc
0.32
0.04-0.28
0.00-0.32 -0332
open grill
open_grill
0.24
0.00
0.00-0.24
straighten rope
straighten_rope
0.00
0.04+0.04
0.00
sweep dust
sweep_to_dustpan
0.92
1.00
1.00
press switch close microwave
press_switch
0.44
0.52
0.56
close_microwaw
0.72
+.80
0.80
15

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C
Supplementary real-world results
Table 6 reports the per-task success rates of CoA, ACT, and DP across real-world kitchen manipula- tion tasks. CoA consistently achieves the highest average performance.
Table 6: Per-task success rate in real-world experiments.
Task
CoA
ACT
DP
close cabinet
0.80
1.00
0.90
close fridge lower
0.20
0.50
0.60
close fridge upper
0.70
0.40
0.80
open cabinet
0.50
0.40
0.10
open fridge lower
0.70
0.40
0.00
open microwave
0.80
0.30
0.50
place in cabinet
0.70
0.10
0.00
place in fridge
0.50
0.60
0.00
Avg.
0.613
0.463
0.363
D Hyperparameters for RLBench
We provide the training and evaluation hyperparameters for CoA and all baseline methods used in the simulation experiments. To ensure fair comparison, the hyperparameters for ACT are largely aligned with those of CoA, allowing us to isolate and assess the impact of our proposed modeling paradigm. For DP, observe slower convergence relative to CoA and ACT, and thus extend its training duration to 100,000 iterations. In addition, we incorporate temporal ensembling into DP following the implementation in ACT. Octo converges substantially faster, and find that 2,000 training iterations are sufficient. Given that Octo primarily pretrained on single-camera data, we finetune it using only the front camera, while increasing the image resolution enhance visual fidelity. All models are trained on single NVIDIA H100 GPU per task.
Table 7: Hyperparameters for CoA
Backbone
ImageNet-trained ResNet18 [10
Action dimension
(3 position quaternion gripper) wrist, front, right shoulder, left shoulder
Cameras
Learning rate
le-
Weight decay
le
Image size
128 x 128
Execution horizon
Observation horizon
# encoder layers
4
# decoder layers
(6
multi-token prediction layer)
# heads
Feedforward dimension
3200
Hidden dimension
512
Dropout
0.1
Iteration
20000
Batch size
128
Temporal ensembling
true (reverse temporal ensemble)
Action normalization
[1,
16

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Table Hypperparameters for ACT
Backbone
ImageNet-trained ResNet18 10]
Action dimension
8 (3 position 4 quaternion + gripper) wrist, front, right shoulder, left shoulder 1e
Cameras
Learning rate
Weight decay
le
Image size
128 128
Action sequence
20
Execution horizon
1
Observation horizon
1
# encoder layers
4
decoder layers
heads
8
Feedforward dimension
3200
Hidden dimension
512
Dropout
0.1
Iteration
20000
Batch size
128
Temporal ensembling
true
Action normalization
1,
Table 9: Hyperparameters for DP
Backbone
ImageNet-trained ResNet18 10
Noise predictor
UNet [29]
Action dimension
8 (3 position 4 quaternion gripper) wrist, front, right shoulder, left shoulder 1e-4
Cameras
Learning rate
Weight decay
1e
Image size
128 x 128
Observation horizon
Action sequence
20
Execution horizon
Train, test diffusion steps
50,
Hidden dimension
512
Iteration
100000
Batch size
128
Temporal ensembling
true (following ACT's)
Scheduler
DDPM 12]
Action normalization
[-1, I]
17

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Table 10: Hyperparameters for Octo
Pretrained model
Octo-small 28
Action dimension
8 delta joints gripper)
Cameras
front
Learning rate
3e
Weight decay
le-2
Image size
256
Observation horizon
1
Action sequence
4
Execution horizon
1
Iteration
2000
Batch size
128
Temporal ensembling
false
Action normalization
std linear head
Finetuning head
Image augmentation
resized crop, brightness, contrast, saturation, hue
E ACT variant with keyframe action
To further examine the impact of keyframe action on action sequence modeling, we conduct an additional ablation by modifying the ACT baseline. Specifically, we introduce variant, ACT+KF, in which an extra keyframe action is appended to ACT's original action chunk.
As shown in Table II ACT+KF achieves higher average success rate (0.516) compared to the original ACT (0.488), indicating that injecting keyframe actions yields marginal improvements. However, the overall gain remains limited.
This result suggests that while keyframe actions may provide some global guidance, they do not substantially improve the final action quality when introduced in this manner. A similar trend is observed in the poor performance of Hybrid (Table 3), variant of CoA that incorporates both keyframe supervision and causal decoding but lacks trajectory continuity. The limited effectiveness of both ACT+KF and Hybrid underscores key insight: merely injecting keyframe signals and enforcing an autoregressive structure is not sufficient. Instead, it is crucial to model the entire trajectory holistically with temporal continuity, whch is explicitly realized in our CoA formulation.
Table 11: Comparison of ACT vs. ACT+KF (with keyframe action) on 10 RLBench tasks.
Task
ACT
ACT+KF
Stack Wine
0.56
0.56
Turn Tap
0.36
0.32
Open Drawer
0.52
0.76
Push Button
0.08
0.16
Pick Up Cup
0.20
0.36
Take Lid
0.40
0.40
Press Switch
0.52
0.28
Reach Target
0.88
0.72
Sweep Dust
1.00
0.96
Open Box
0.36
0.64
Avg.
0.488
0.516
18

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Reviews:
[{"review_id": "CIhoByVQRL", "reviewer": "Reviewer_t6sS", "summary": "The paper presents Chain-of-Action (CoA), a novel visuo-motor policy architecture for robotic manipulation, built upon trajectory autoregressive modeling with a reverse generation paradigm.\nCoA generates the actions by reasoning backward from a goal-specific keyframe action to the initial state.\nThis backward generation enforces a global-to-local structure, ensuring that every local action remains tightly aligned with the task objective and significantly mitigating compounding errors.\nThe authors introduce four key design elements to realize the CoA framework:\n- Continuous action token representation to avoid quantization errors.\n- Multi-token prediction to improve local action coherence.\n- Dynamic stopping for flexible trajectory lengths.\n- Reverse temporal ensemble to aggregate multiple backward rollouts.\nExperimental results on the RLBench benchmark (60 simulation tasks and 10 representative tasks) demonstrate that CoA achieves state-of-the-art performance, outperforming strong baselines such as ACT and Diffusion Policy (DP), with average improvements of 16% and 23% respectively. Notably, CoA shows superior spatial generalization, maintaining higher success rates even as the spatial variance of the environment increases, and proves more robust in out-of-distribution scenarios. Ablation studies confirm the importance of each design component. Real-world experiments on a Fetch robot further validate CoA’s effectiveness, achieving a 15% higher average success rate than ACT on eight kitchen manipulation tasks.", "questions": "- I am curious whether there are truly no existing works that adopt a similar reverse-order trajectory generation approach. If your response (or further discussion among reviewers) can clarify the novelty of CoA relative to prior literature, I would be inclined to rate the paper more favorably.\n- I would also like to better understand why the proposed method achieves better performance than Diffusion Policy. As I understand, Diffusion Policy also considers future states by denoising current actions, which seems to have a similar effect to the reverse-order generation in CoA. Is there a specific reason for CoA’s superior performance? For example, could it be due to the action sequence length? According to Figure 7, CoA generates sequences of about 80 steps, whereas Diffusion Policy typically generates only around 20 steps per trajectory. Is it possible that DP does not fully account for the keyframe action or long-horizon dependencies as effectively due to this shorter sequence length?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths\n- The proposed algorithm is both simple and intuitive. By leveraging a backward, goal-conditioned trajectory generation paradigm, the approach is conceptually easy to understand and implement, yet powerful in practice.\n- The method achieves strong empirical performance, consistently outperforming existing baselines across a wide range of simulated and real-world robotic manipulation tasks.\n- The paper provides extensive experimental analysis, including comprehensive comparisons to widely-used methods, thorough ablation studies, and in-depth exploration of spatial generalization and robustness, which together offer convincing evidence for the effectiveness of the proposed approach.\n\nWeaknesses\n- The method is limited to manipulation tasks where actions correspond directly to end-effector poses. Both the keyframe extraction heuristic and the distance-based stopping mechanism rely on this correspondence, making it difficult to generalize the approach to broader classes of robotic tasks (e.g., locomotion, multi-agent coordination, or tasks with more abstract action spaces).\n- While the algorithm’s simplicity and intuitive design are strengths, it raises the question of whether reverse-order planning is truly novel, or if similar ideas have been explored in previous work. A more thorough review of related literature on backward or reverse-order trajectory generation would strengthen the paper.", "was_revised": true, "final_justification": "The authors demonstrated the novelty of their proposed method and its superiority over existing approaches through their rebuttal. Accordingly, I raised my rating.", "rebuttal": "We appreciate your insightful questions and suggestions. Below, we provide detailed responses to your concerns:\n\n## w1[Limitations in applicability]\nWe acknowledge that this limitation exists in our implementation in this paper. However, the core idea of CoA can be extended to other domains through domain-specific heuristics and design choices. For example, in quadruped locomotion, foot touchdown events can naturally serve as keyframes. Moreover, the dynamic stopping mechanism could also be learned depending on the specific scenario, rather than relying on a distance-based rule.\n\n## w2/q1[Regarding novelty]\nWhile backward planning has been extensively studied in the classical motion planning and optimization communities, to the best of our knowledge, it has not been explored within learning-based visuomotor policies prior to our work.\n\nHowever, we actually find a concurrent work titled “Efficient Robotic Policy Learning via Latent Space Backward Planning” (accepted to ICML 2025, released on arXiv on May 11, four days before the NeurIPS deadline) also adopts a backward planning strategy—but in the latent space, by predicting future latent states and sub latent goals from current observations and . **This approach is fundamentally different from ours: we perform backward planning directly in the action space, enabling explicit autoregressive generation of a whole trajectory. Our advantage is that: 1. the modeling of CoA can serve as a effective alternative to action chunking for it is highly compatible with other existing methods 2. CoA offers better interpretability, as its generated trajectories can be visualized to reveal the underlying decision-making logic.**\n\nAnother related work is “Chain of Thought Imitation with Procedure Cloning”(NIPS 2022), which proposes procedure cloning conditioned **only on the final goal pose. However, it does not involve backward prediction of the full trajectory.**\n\nIn summary, our method is the first manipulation imitation learning policy to perform backward prediction directly in the action space. \n\n\n## q2[Comparison with Diffusion Policy with longer action horizon]:\nThank you for raising this insightful point. To directly address your question, we conducted additional experiments to explicitly compare CoA with Diffusion Policy (DP) under longer action horizons. Specifically, we evaluated DP on 10 representative RLBench tasks (as previously used in Table 1's ablation studies) with extended action horizons of 100 and even 180 steps. Note that 180 exceeds the maximum full trajectory length observed across these 10 tasks (178.96 steps), as detailed below:\n\n**Full Trajectory Lengths (10 representative tasks):**\n\n| Task                   | Full Trajectory Length |\n|------------------------|------------------------|\n| turn_tap               | 146.48                 |\n| take_lid_off_saucepan  | 98.80                  |\n| sweep_to_dustpan       | 118.08                 |\n| stack_wine             | 178.96                 |\n| reach_target           | 43.88                  |\n| push_button            | 84.52                  |\n| press_switch           | 116.84                 |\n| pick_up_cup            | 97.28                  |\n| open_drawer            | 105.28                 |\n| open_box               | 152.36                 |\n\nThe resulting success rates for DP with extended action horizons are summarized below:\n\n| Action Horizon | Success Rate (%) |\n|----------------|------------------|\n| 20             | 41.6             |\n| 100            | 42.0             |\n| 180            | 42.0             |\n| 100 (w/ Goal)  | 44.8             |\n\nWe observed that extending DP’s action horizon from its original length of 20 steps to 100 or even 180 steps yielded minimal improvement (from 41.6% to only 42%), indicating that DP does not effectively leverage longer action horizons. This finding aligns with the original Diffusion Policy paper, which noted optimal performance at around 8-step horizons, beyond which performance deteriorates.\n\nThus, the superior performance of CoA compared to DP can be attributed to CoA's ability to effectively handle long-horizon trajectories and explicitly condition each local action sequence on the final goal via backward reasoning. In contrast, despite denoising steps implicitly considering future states, DP inherently struggles to capture long-horizon dependencies when the action horizon is significantly increased."}, {"review_id": "kmZZMdFoMC", "reviewer": "Reviewer_Nays", "summary": "This paper presents Chain-of-Action (CoA), a novel trajectory-level autoregressive modeling framework for robotic manipulation. Unlike conventional forward action generation, CoA introduces backward trajectory prediction, starting from a goal-anchored keyframe and generating actions in reverse. Empirical results show that CoA significantly outperforms prior methods such as ACT and Diffusion Policy on 60 RLBench tasks and 8 real-world kitchen tasks.", "questions": "1. What is the reason that the proposed model failed on Press Switch, Reach Target, Sweep Dust and Open Box?\n2. Does the learned token $x_{SOS}$ refers to the latent variable learnt from the encoder? If the proposed network follows the design of ACT, then what is the distribution of this latent variable? \n3. Can the proposed method generalize to other model architectures other than CVAE?", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "### Strength:\n1. Strong empirical results: CoA achieves strong performance across both simulation and real-world settings, outperforming several baselines.\n\n2. Comprehensive ablation and case studies: The reviewer appreciates the in-depth ablation study, which provides valuable insights to the contribution of each design choice. \n\n### Weakness:\n1. Motivation: It is unclear what the biggest motivation is for favoring the reverse autoregressive structure over the forward autoregressive structure. Is it because of the compounding error? If yes, it is worth investigating methods that tackle similar problems. \n\n2. Incremental novelty: This paper essentially proposes an improvement on top of the ACT paper, with goal-conditioning and reverse autoregressive. Goal-conditioning is a well-explored topic, and it is not surprising that it can improve the performance. The reverse autoregressive idea is interesting; however, I find the paper lacks theoretical grounding on the proposed idea, and insufficient discussion on the “chain-of-action”.\n\n3. Writing:  The writing can be improved. It would be helpful to explain the overall architecture and then dive deep into each component. Also, many terms are not properly defined. For example, what does the start-of-sequence (SOS) token and the final keyframe action refer to in line 166?\n\n4. Related work: It would be helpful to include more literature on goal-conditioned learning. \n\n5. Baseline: It would be interesting to see how the goal-conditioned forward autoregressive model and goal-conditioned diffusion model perform. These are important baselines to evaluate the contribution of this work.", "was_revised": true, "final_justification": "The authors provided high-quality responses during rebuttal and addressed most of my concerns. This work presents a novel approach to handling compounding error for autoregressive models, which is important for robotic manipulation tasks. I do think that 1) improving the writing of the manuscript and 2) providing a more comprehensive benchmark could strengthen the paper. However, given the responses provided during rebuttal, I would like to raise my score for this submission.", "rebuttal": "We appreciate your insightful questions and suggestions. Below, we provide detailed responses to your concerns:\n\n## w1[Motivation]\nTo clarify our motivation more precisely, we decompose it into two aspects:\n1. Goal conditioning helps mitigate compounding errors.\n2. Backward prediction can seamlessly incorporate goal-conditioned generation, whereas forward prediction cannot do so as naturally.\n\n### Evidence that goal conditioning reduces compounding errors:\n\nWaypoint-Based Imitation Learning for Robotic Manipulation (CoRL 2023) demonstrates that decomposing trajectories into intermediate waypoints effectively mitigates cumulative errors. Similarly, hierarchical modeling approaches discussed in related work support this idea. For example, Hierarchical Diffusion Policy for Kinematics-Aware Multi-Task Robotic Manipulation (CVPR 2024) leverages keyframes and a diffusion-based planner, achieving higher success rates than ACT and Diffusion Policy.\n\n### Why goal conditioning with backward prediction is better:\n\nBackward prediction can incorporate goal conditioning following the natural trajectory order, preserving the spatial dependencies between waypoints, which leads to better performance. Of course, forward prediction can also incorporate goal conditioning, as shown by the setting `Hybrid` in Table 2, where the goal is predicted first and then actions are generated in a forward manner. However, its performance is even worse than pure `Forward`. This is because backward prediction imposes a natural global-to-local constraint on the predicted actions. **In contrast, the hybrid approach directly jumps from the goal prediction to the current action, lacking spatial causal continuity.**\n\n## w2[Novelty]\nSince our technical approach has not been extensively explored before, there may be concerns about its rationale. To address this, we highlight two possibly related works that partially support our idea:\n1. There is a concurrent work titled Efficient Robotic Policy Learning via Latent Space Backward Planning (accepted to ICML 2025, posted on arXiv May 11, four days before NIPS DDL), which performs backward planning in the latent space by predicting future latent states from current observations. This is fundamentally different from our approach, as we conduct backward planning directly in the action space, enabling explicit autoregressive generation of action sequences from goal to start.\n2. Another related work is Chain of Thought Imitation with Procedure Cloning, which introduces procedure cloning and conditions action prediction only on goal poses. However, it does not incorporate backward trajectory prediction.\n\nIn summary, to the best of our knowledge, ours is the first method to perform explicit reverse-order prediction in the action space.\n\nOn the naming rationale of “chain-of-action”:\nWe believe the community widely accepts that “chain-of-…” terminology refers to the presence of an intermediate reasoning or procedural process between inputs and outputs, not necessarily limited to symbolic or language-based reasoning like in large language models (LLMs). For instance, recent work like CoT-VLA simply uses an image goal as a condition for action prediction, yet the naming convention is broadly accepted. This supports our use of “chain-of-action” to describe our method’s autoregressive backward action reasoning.\n\n## w3[Writing]\nWe apologize for the unclear description in the current manuscript and would like to update. To clarify, the start-of-sequence (SOS) token serves as a query input to the transformer decoder and then transferred to the keyframe action that initiates the autoregressive prediction sequence. \n\n## w4[Related work]\nWe would like to clarify that our work is specifically related to subgoal-conditioned policy learning in robotic manipulation, rather than the broader class of general goal-conditioned methods. Prior works that use goal poses as subgoals predominantly depend on explicit motion planners and 3D state observations, these methods have been comprehensively reviewed in “Hierarchical Modeling in Robotic Manipulation.”\n\nFor approaches utilizing alternative subgoal modalities—such as language, bounding boxes, or visual traces. We have already discussed relevant works in our review of CoT-style methods in robotic manipulation. \n\napart from these, we notice more works that employ subgoals for manipulation, including:\n 1. Waypoint-Based Imitation Learning for Robotic Manipulation\n 2. Hierarchical Foresight: Self-Supervised Learning of Long-Horizon Tasks via Visual Subgoal Generation\n 3. Subgoal Diffuser: Coarse-to-Fine Subgoal Generation to Guide Model Predictive Control for Robot Manipulation\n\n## w5[Baseline] \nWe will improve our writing for clearer expression. In fact, we have already presented results for goal-conditioned forward prediction (the Hybrid setting in Table 2), as well as for ACT with keyframe action conditioning. As mentioned in Appendix D, adding keyframe action conditioning improves ACT’s performance from 48.8% to 51.6%. Additionally, we conducted an experiment showing that Diffusion Policy improves from 42.0% to 44.8% with keyframe conditioning. We will update these results accordingly in the manuscript.\n\n## q1[Failure case]\nIn summary, we did not observe consistent failure patterns across specific categories of tasks (e.g., high-precision or deformable-object tasks). However, distinct failure modes can often be identified at the individual task level, suggesting that performance limitations are more task-specific than type-specific.\n\n### Regarding tasks where CoA shows lower performance compared to ACT, DP, or Octo:\n- Ocot with Pretrained model and different action space: CoA underperforms relative to Octo on this task. This is largely because Octo is a fine-tuned, pretrained model and operates in a delta joint action space, which is particularly advantageous for tasks requiring precise rotational control. Therefore, direct comparisons on such tasks remain limited in fairness.\n- Incidental fluctuations due to training variability: For individual tasks such as Reach Target, Press Switch, and Sweep Dust, the relatively small performance gaps (<12%) can be attributed to non-systematic factors such as optimization variability. That is, re-training the model with the same hyperparameters may yield slightly different results—sometimes even better—and we report results from batch training without any manual selection over individual tasks. Such variability is commonly observed in imitation learning, especially with behavior cloning, and may lead to minor performance shifts across runs. In some cases, CoA may even outperform other methods on the same task under different training seeds. To mitigate these fluctuations, we report average performance over a broad task set (10 tasks for ablations and 60 for overall evaluation), ensuring that our conclusions reflect stable, aggregated trends. Similar instability has also been discussed in prior work, such as \"What Matters in Learning from Offline Human Demonstrations for Robot Manipulation\".\n\n## q2/q3[About CVAE and latent token]\nWe would like to clarify a potential misunderstanding and modify the writing to better reflect our approach. As shown in Figure 1, we do not use the CVAE component from ACT, so there is no latent variable from CAVE. The SOS token actually indicates a start token for the autoregressive transformer decoder. \n\n### CoA only share identical number of layers of transformer encoder and decoder with ACT\nAs detailed in Section 4 (Implementation Details – Network Architecture), our model do share architectural similarity with ACT, as both employ a 4-layer Transformer encoder and a 7-layer Transformer decoder. However, we intentionally removed the CVAE module to maintain a minimalist design. We will further clarify this distinction explicitly in our manuscript to avoid confusion."}, {"review_id": "3hpxWz7cQ4", "reviewer": "Reviewer_8ry4", "summary": "This paper introduces Chain-of-Action (CoA), a trajectory autoregressive model for robotic manipulation, which generates action sequences backward from goal keyframes to initial states, aimed at mitigating compounding errors and improving spatial generalization. The method is empirically demonstrated to outperform several baselines on the RLBench benchmark and real-world tasks.", "questions": "- The abstract claims an \"action-level Chain-of-Thought (CoT) process,\" yet the method primarily predicts flexible-length action chunks without explicit or latent reasoning steps. Could the authors clarify this discrepancy or better justify the labeling of their approach as CoT?\n- One of the unique properties of CoA is the flexible execution segment prediction. However, there is no analysis of that part. The average length of the execution segments is not clearly stated. Given that longer segments could introduce larger accumulative errors, it would be helpful to see an analysis of how segment length affects success rates across tasks.\n- What kinds of RLBench tasks still fail (see tails of Fig 4)? Are there qualitative patterns (e.g., high-precision alignments, deformable objects)?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\n- The core idea of backward trajectory generation is interesting and potentially effective for addressing compounding errors in robotic manipulation tasks.\n- The authors demonstrate strong empirical results on extensive simulation benchmarks (60 RLBench tasks) and real-world tasks.\n- The approach is well-explained, with clearly presented visualizations.\n\nWeaknesses:\n- The integration-based stopping criterion appears effective for pick-and-place tasks but may be challenging for tasks involving frequent or prolonged contacts, such as locomotion or dexterous manipulation.\n- Previous works like ACT succeeded with only an L1 loss over actions. It is unclear why CoA specifically requires the temporal consistency loss to function effectively. Can the authors clarify why their method underperforms without this additional constraint, compared to existing methods?\n- Although the paper includes some ablation studies, it remains difficult to pinpoint which components of CoA are primarily responsible for its improved performance over baselines. Several elements (mtp, continuous actions, and temporal consistency loss) are known techniques. In my view, the truly novel aspects are the backward prediction and the use of variable-length action chunks. Table 2 partially addresses the backward prediction by comparing with a forward model, but it would be helpful to also include an ablation that combines forward prediction with fixed-length action chunks. This would better isolate the contribution of the reverse, variable-length modeling.\n- No statistical confidence / error bars. Results are means over 25 trials, but variance or CI is never reported.", "was_revised": true, "final_justification": "The idea of generating the chain of thought in reverse is intriguing, and the experimental results suggest it leads to improved performance. While some of the individual components have been explored in prior work, the specific combination presented here is novel and likely to be of interest to the community. That said, since all of the core ideas have been previously studied and the main contribution lies in how they are combined, I am keeping my score at \"borderline accept.\"", "rebuttal": "We sincerely appreciate your thoughtful questions and valuable suggestions. Below, we provide detailed responses to address your concerns:\n\n## w1[Limitation]\nWe thank the reviewer for the valuable suggestion. Indeed, the stopping critiria of CoA might face issues when generalize to other scenarios, e.g., dexterous manipulation. However, as a proof of concept, CoA focuses on quasi-static tasks and aims to boost the spatial generalization capabilities. We demonstrated its performance on 60 RLBench tasks. In our future work, we will extend this paradigm by learning the stopping signal.\n\n## w2 [Why latent consistency loss]\nOverall, our goal is to establish a robust representation for autoregressive modeling in continuous action spaces. While **ACT also uses a Transformer decoder, its action predictions are generated in parallel** rather than autoregressively. In contrast to **LLMs and VLMs, which operate over a fixed, discrete vocabulary**, our scenario involves continuous action prediction, where the output cannot be constrained to a predefined token set. As a result, **even small drifts in action embeddings can accumulate and amplify over autoregressive steps**. To address this, we introduce a latent consistency loss that explicitly enforces the stability of action embeddings across time steps.\n\n## w3[Ablation of keyframe action + forward action chunk]\nwait for the result\n\n## w4[statistical confidence]\nThis is a valuable question as it concerns whether the method truly works or merely reflects randomness. Variance is indeed reported in many prior works. We fully understand its importance and would like to clarify why we do not include it in our results. Our primary goal is to evaluate the generalization ability of the method across a diverse set of tasks. Therefore, we extend the evaluation to cover 60 different tasks and report the average performance. Conducting multiple training runs for all these tasks would be computationally expensive. To address variance, we perform ablation studies on 10 representative tasks, which can similarly help reduce the variance of the average success rate. In summary, this is a trade-off between computational cost and statistical rigor.\n\n## q1[The rationale of name]\nThank you for pointing this out. We agree that the classical notion of Chain-of-Thought (CoT) in language models typically refers to multi-step intermediate reasoning expressed in discrete text. However, the connotation of CoT has been evolving with technological advances, and recent works support our naming rationale.\n\nFor example, recent works such as CoT-VLA and Robotic Control via Embodied Chain-of-Thought Reasoning have extended the CoT concept beyond text, conditioning action prediction on image goals.\n\nSimilarly, another related work from NeurIPS 2022, Chain of Thought Imitation with Procedure Cloning, introduces procedure cloning without relying on intermediate discrete text reasoning.\n\nTherefore, we follow this broader community understanding and apply the term “chain-of-action” to denote multi-step, intermediate action-level reasoning in continuous action spaces, which we believe is a reasonable and natural extension of the CoT paradigm.\n\n## q2[Correlation between segment length and success rate]\nThe average segment length of CoA across the 60 RLBench tasks is approximately 72, with most trajectories consisting of 2 execution segments. The Pearson correlation between average segment length and task success rate coefficient is −0.27 (p ≈ 0.037), indicating a statistically significant negative correlation: tasks with longer execution segments tend to have lower success rates, likely due to accumulated prediction errors.\n\nThis is matched with similar observation in Figure 5:  we analyze task success rates under varying levels of spatial variance, which reflects the spread of object positions across demonstrations. Tasks with higher spatial variance generally require longer execution segments. The success rates of all methods decline as spatial variance increases, which is expected due to the increased difficulty and longer required trajectories. \n\n## q3[Failure case]\nIn summary, we did not observe consistent failure patterns across specific categories of tasks (e.g., high-precision or deformable-object tasks). However, distinct failure modes can often be identified at the individual task level, suggesting that performance limitations are more task-specific than type-specific.\n\n### Regarding tasks where CoA shows lower performance compared to ACT, DP, or Octo:\n- Ocot with Pretrained model and different action space: CoA underperforms relative to Octo on this task. This is largely because Octo is a fine-tuned, pretrained model and operates in a delta joint action space, which is particularly advantageous for tasks requiring precise rotational control. Therefore, direct comparisons on such tasks remain limited in fairness.\n- Incidental fluctuations due to training variability: For individual tasks such as Reach Target, Press Switch, and Sweep Dust, the relatively small performance gaps (<12%) can be attributed to non-systematic factors such as optimization variability. That is, re-training the model with the same hyperparameters may yield slightly different results—sometimes even better—and we report results from batch training without any manual selection over individual tasks. Such variability is commonly observed in imitation learning, especially with behavior cloning, and may lead to minor performance shifts across runs. In some cases, CoA may even outperform other methods on the same task under different training seeds. To mitigate these fluctuations, we report average performance over a broad task set (10 tasks for ablations and 60 for overall evaluation), ensuring that our conclusions reflect stable, aggregated trends. Similar instability has also been discussed in prior work, such as \"What Matters in Learning from Offline Human Demonstrations for Robot Manipulation\"."}, {"review_id": "DG9V4hySsK", "reviewer": "Reviewer_2Ph3", "summary": "The paper proposes to using backward reasoning to generate/predict the action chunks intead of all maintream method using next token prediction in a forward manner, claiming that this will enforge a global-to-local structure and better relaize the final goal.", "questions": "First, please refer to weakness to discuss the 3 main weakness, besides that, i still have some small quesitons as follows:\n1. I would like to understanding the author's opinion on: only predicting the target keyframe insteading of predicting action chunks from keyframe to current state in a reverse manner, that is, the whole paper rely on claim that using keyframe centered goal conditioned backward reasoning can better lead the model focus on its short-horizon local goal, intead of gradual lose attention and goal in a foward manner, so in that sense, the accuracy whould highly depends on the prediction of the keyframe given the current state, so how about only perdict the keyframe and continouly call go to pose until it gets there, what is the advantages of CoA compared to it?\n\n2. For the inference, how the exact reverse ensemble is implemented? is it aggregate n steps prediction and smooth it? how many steps is actually executed for each prediction call?\n\n3. what is the computation burden of the autoregressive model, since it seems the model should be able to modeling the longest length of a keyframe segment, wonder what is the exact context length of the model.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The assumption that reasoning the model backward from the keyframe to the current state is intuitively rationale since in a foward manner, based on the characteristic of autoregressive model, the error will compound, leading to less and less accurate with increasing of the horizon.\n2. The shown results can support the claim that the proposed regularization of latent space, backward reasoning, reversal ensembling, multi-token prediction can all boost the performance to some extent.\n\nWeakness:\n1. The main simulation results shown in Table 1 seems not like a standard benchmark, as well as known, the standard 18 tasks shown in PerAct is well used for a standard reference for RLBench, why the author here using 10 self-selected tasks to eval the method, also the author mentioned it decrease the variation to 1, which is kind of suspicious compared with the standard benchmark in RLBench.\n\n2. The main results in Table 1 seems only compared with ACT and DP, which is kind of lack, how about it compared with the state-of-art method OpenVLA, which is a well known standard autoregressive method in forward reasonaing manner.\n\n3. The experiment and ablation parts use lots of space to explore the spatial distribution, which makes me confused, first the description for the experiment in Section 5.3 (the first two parts) is not clear what the author did, is that all about choosing and eval on different demonstrations? how you control the object distributions when generate the demos? what exact the interpolationa and extrapolation mean? Also, most impotant is I am confused and intuitively cannot relate the sptial properties of the policy and the proposed backward reasoning manner, seems the two does not have some casual relationship, i am not convinced by both the shown Figure 5,6 and the conceptual rationale.", "was_revised": true, "final_justification": "The author has addressed my major concern about the imcomplete results for sim and further explains the task design. I decide to raise my score as borderline accept.", "rebuttal": "We appreciate your insightful questions and suggestions. Below, we provide detailed responses to your concerns:\n\n## w1[Why using 60 tasks rather than 18 tasks]\nThank you for the valuable suggestion. We would like to kindly clarify a possible misunderstanding regarding our evaluation protocol.  Our full evaluation covers 60 diverse RLBench tasks rather than just the commonly used 18 standard tasks. While the 18 tasks are often used as a benchmark, they are neither the only nor a required standard for evaluation. **In fact, several recent works—including Point Cloud Matters (NeurIPS 2024), Conditional Flow Matching (CoRL 2024), and Generative Image as Action Models (CoRL 2024)—also adopt customized subsets of RLBench tasks tailored to their specific settings.**\n\nThe rationale behind this is that the standard 18 tasks are frequently employed to evaluate hierarchical policies that rely on high-precision 3D inputs and motion planners. Many of these tasks are quite challenging for RGB-only visuomotor policies, resulting in uniformly low success rates and limited discriminative power. For this reason, we excluded some of these tasks, although 7 out of the 18 standard tasks are still included in our larger 60-task set.\n\nMoreover, to directly address your concern, we now provide results on 18 standard tasks. The results highlight two key points:\n- A large performance gap exists between RGB-based imitation learning methods (CNN/ViT-BC, CoA, ACT) and 3D keypoint-based hierarchical models (RVT), which validates the difficulty of these tasks under 2D perception.\n- CoA still achieves the best performance among RGB-based imitation learning methods, demonstrating its advantage within this category.\n- The results for CNN-BC, ViT-BC, and RVT-2 are directly reported from the paper \"RVT-2: Learning Precise Manipulation from Few Demonstrations\", while the CoA and ACT results are reproduced by us.\n\n| Task               | CNN-BC (Image) | ViT-BC (Image) | RVT-2 (Point cloud, SOTA on this 18 task benchmark, goal pose prediction + motion planner)           | CoA (Image)    | ACT (Image)   |\n|--------------------|----------------|----------------|------------------|---------|--------|\n| Close Jar          | 0              | 0              | 100.0 ± 0.0      | 0       | 0      |\n| Drag Stick         | 0              | 0              | 99.0 ± 1.7       | 0       | 0      |\n| Insert Peg         | 0              | 0              | 40.0 ± 0.0       | 0       | 0      |\n| Meat off Grill     | 0              | 0              | 99.0 ± 1.7       | 88      | 32     |\n| Open Drawer        | 4              | 0              | 74.0 ± 11.8      | 88      | 52     |\n| Place Cups         | 0              | 0              | 38.0 ± 4.5       | 0       | 0      |\n| Place Wine         | 0              | 0              | 95.0 ± 3.3       | 80      | 56     |\n| Push Buttons       | 0              | 0              | 100.0 ± 0.0      | 28      | 32     |\n| Put in Cupboard    | 0              | 0              | 66.0 ± 4.5       | 8       | 0      |\n| Put in Drawer      | 8              | 0              | 96.0 ± 0.0       | 88      | 60     |\n| Put in Safe        | 4              | 0              | 96.0 ± 2.8       | 80      | 36     |\n| Screw Bulb         | 0              | 0              | 88.0 ± 4.9       | 0       | 0      |\n| Slide Block        | 0              | 0              | 92.0 ± 2.8       | 64      | 36     |\n| Sort Shape         | 0              | 0              | 35.0 ± 7.1       | 0       | 0      |\n| Stack Blocks       | 0              | 0              | 80.0 ± 2.8       | 0       | 0      |\n| Stack Cups         | 0              | 0              | 69.0 ± 5.9       | 0       | 0      |\n| Sweep to Dustpan   | 0              | 0              | 100.0 ± 0.0      | 92      | 1      |\n| Turn Tap           | 8              | 16             | 99.0 ± 1.7       | 56      | 36     |\n| **Average**        | **1.33**       | **0.89**       | **81.2**         | **37.33** | **18.94** |\n\n## w2 [Compare with OpenVLA]\nWhile it would be beneficial to include comparisons to OpenVLA if time and resources permit, it is important to note that OpenVLA targets a different problem setting. It is a large-scale Vision-Language-Action model (~7 billion parameters) pretrained on the extensive Open-XE dataset, requiring substantial computational resources and data.\n\nIn contrast, our work focuses on visuomotor policy learning with relatively small-scale models (under 0.5 billion parameters), without reliance on massive pretraining datasets. As such, a direct comparison to OpenVLA would largely reflect differences in model scale and data availability rather than algorithmic advances.\n\n## w3[Understanding of experiments]\nThank you for pointing this out. **Our goal in Section 5.3 is to evaluate how well CoA generalizes under spatial shifts in object positions. To this end, we evaluate the performance with respect to the object position. This way is also used in previous work like Generative Image as Action Models (CoRL2024), DemoGen: Synthetic Demonstration Generation for Data-Efficient Visuomotor Policy Learning (RSS2025).**\n\nIt is important to clarify that RLBench primarily varies object positions between training and test scenes, while other attributes such as texture, shape, and color remain fixed. As a result, task success rates serve as a direct indicator of a policy’s spatial generalization capability.\n\nIn our setup, we generate 150 object configurations per task. Among these, we select the 100 samples nearest to the center and compute their convex hull. We then randomly sample:\n- 50 configurations inside the hull as the training set,\n- another 50 configurations within the hull as the interpolation test set, and\n- the remaining 50 outside the hull as the extrapolation test set.\n\nSection 5.3 is dedicated to analyzing how well CoA generalizes across these spatial regimes. Specifically:\n- Interpolation refers to test object positions within the convex hull of the training distribution.\n- Extrapolation refers to positions outside this region, requiring out-of-distribution generalization.\n\nThe core insight is that backward reasoning allows the policy to anchor each local action on the final task goal. This global-to-local structure mitigates compounding errors in long-horizon tasks and enhances environment-aware decision-making, especially under spatial shifts. Figures 5 and 6 provide both quantitative and qualitative evidence to support this claim.\n\n## q1[Compare with goal+motion planner]\nThis is a great question. The strategy of first predicting a goal pose and then using a motion planner to reach it is a well-established approach, commonly adopted in hierarchical modeling. We review such methods in our Related Work section, including:\n“A Multi-Task Transformer for Robotic Manipulation”,\n“RVT: Robotic View Transformer for 3D Object Manipulation”,\n“RVT-2: Learning Precise Manipulation from Few Demonstrations”, and\n“Coarse-to-Fine Q-Attention with Learned Path Ranking.”\n\nCoA differs from these approaches in three key ways:\n1. Closed-loop execution: Rather than relying on an open-loop planner, CoA generates action chunks that are continually updated based on real-time observations.\n2. Context-aware control: Tasks with path constraints (e.g., sweeping dust or articulated object manipulation) often fail under naive go-to-pose strategies.\n3. All hierarchical modeling depends on 3D observation\n\nTo further investigate this, **we conducted a controlled study where we replaced CoA’s predicted trajectory with direct execution of its keyframe actions (i.e., the goal poses) via a motion planner**:\n- Open Box: Success rate drops from 72% to 0%, as the task requires executing a specific rotational trajectory to lift the hinged lid.\n- Sweep Dust: Success rate drops from 92% to 8%, since merely reaching the end pose fails to guarantee coverage along the intended sweeping path.\n\nWe note that some hierarchical models perform well on these tasks using motion planners. However, they often benefit from high-fidelity 3D inputs, intensive computation to accurately infer the goal pose, finer-grained trajectory decomposition, and curved trajectory generation through specific motion planners, all of which differ significantly from our integrated and lightweight design.\n\n## q2[Reverse temporal ensemble]\nOur reverse ensemble is conceptually similar to ACT’s temporal ensemble, but aligns predictions using the keyframe action as anchor, rather than forward time alignment.\n\nDuring inference, we generate the trajectory autoregressively from the keyframe backward. Each method—including CoA and baselines—executes one action per inference call, enabling closed-loop control.\n\n## q3[computation overhead]\nThe inference cost is proportional to the predicted trajectory length, which depends on the distance between the gripper and the goal. During training, we determine a maximum sequence length T_max (see Implementation Details and Algorithm 2). Most tasks have a sequence length of 50-100 steps, and for CoA is a single-task imitation learning method, the specific length is up to task."}]

Author rebuttal:

Meta-review: The paper introduces Chain-of-Action (CoA), a novel visuo-motor policy architecture for robotic manipulation based on trajectory autoregressive modeling with a reverse-generation paradigm. CoA generates actions by reasoning backward from a goal-specific keyframe action to the initial state.
The method outperforms standard 2D policies. All reviewers responded positively, citing its strong empirical performance and comprehensive evaluation and ablations. The paper is recommended for publication.
Decision: Accept (poster)