arXiv:2605.13548v1 [cs.RO] 13 May 2026
AttenA+: Rectifying Action Inequality in Robotic Foundation Models Daojie Peng1∗ Fulong Ma1∗ Jiahang Cao2∗ Qiang Zhang1,3,6 Xupeng Xie1 Jian Guo4 Ping Luo2 Andrew F. Luo2 Boyu Zhou5 Jun Ma1† 1 HKUST(GZ) 2 HKU 3 USTC 4 IDEA Research 5 SUSTech 6 X-Humaniod
Abstract Existing robotic foundation models, while powerful, are predicated on an implicit assumption of temporal homogeneity: treating all actions as equally informative during optimization. This "flat" training paradigm, inherited from language modeling, remains indifferent to the underlying physical hierarchy of manipulation. In reality, robot trajectories are fundamentally heterogeneous, where low-velocity segments often dictate task success through precision-demanding interactions, while high-velocity motions serve as error-tolerant transitions. Such a misalignment between uniform loss weighting and physical criticality fundamentally limits the performance of current Vision-Language-Action (VLA) models and World-Action Models (WAM) in complex, long-horizon tasks. To rectify this, we introduce AttenA+, an architecture-agnostic framework that prioritizes kinematically critical segments via velocity-driven action attention. By reweighting the training objective based on the inverse velocity field, AttenA+ naturally aligns the model’s learning capacity with the physical demands of manipulation. As a plug-and-play enhancement, AttenA+ can be integrated into existing backbones without structural modifications or additional parameters. Extensive experiments demonstrate that AttenA+ significantly elevates the ceilings of current state-of-the-art models. Specifically, it improves OpenVLA-OFT to 98.6% (+1.5%) on the L IBERO benchmark and pushes FastWAM to 92.4% (+0.6%) on RoboTwin 2.0. Real-world validation on a Franka manipulator further showcases its robustness and cross-task generalization. Our work suggests that mining the intrinsic structural priors of action sequences offers a highly efficient, physics-aware complement to standard scaling laws, paving a new path for general-purpose robotic control.
1
Introduction
Vision-Language-Action (VLA) and World-Action Models (WAM) have recently emerged as a powerful paradigm for end-to-end robotic control, enabling robots to interpret multimodal instructions and execute complex physical manipulation tasks [1, 2, 3]. However, this success masks a fundamental misalignment: while all linguistic tokens are assumed to be equally informative in standard NLP training, robotic actions are inherently heterogeneous in their physical significance. In a typical manipulation trajectory, not all action steps are created equal. Consider the task of picking up a fragile object: the rapid motion of the arm toward the object is transitional and error-tolerant, whereas the final, slow-speed adjustment of the gripper is precision-demanding and task-critical. Currently, dominant training frameworks adopt a "flat" optimization objective, assigning identical learning weights to every timestep regardless of its physical role [4, 5, 6]. ∗ †
Equal contribution. Corresponding author: [email protected]
Preprint. Under review.
Figure 1: Overview of AttenA+. AttenA+ is a paradigm-agnostic enhancement framework for action robotic foundation models, introducing velocity-field-based action attention to prioritize slow, critical manipulation steps. It seamlessly plugs into mainstream discriminative (e.g., OpenVLA-OFT) and generative (π0 , π0.5 , Diffusion Policy) architectures, as well as emerging World-Action Models (WAM). Without modifying core backbones or relying on data/model scaling, AttenA+ generalizes across diverse robotic datasets including L IBERO [15] and RoboTwin [16], and consistently improves task success rates over state-of-the-art baselines. This uniform treatment forces models to waste representational capacity on trivial transitional segments, while under-optimizing the slow, high-precision actions that actually determine task success [1, 7, 2, 8, 9, 10, 11]. Consequently, even the most advanced VLA models often struggle with last-centimeter precision in complex robotics tasks [12, 13, 14]. To bridge this gap, we argue that the physical properties of an action, specifically its velocity, should dictate its importance during training. We propose AttenA+, a universal framework that introduces velocity-driven action attention to reweight trajectory learning. Our key insight is simple yet effective: the end-effector’s velocity serves as a natural inverse proxy for precision demand. By assigning different optimization priorities to different actions, AttenA+ aligns model training with the intrinsic physics of manipulation. As an architecture-agnostic enhancement, AttenA+ can be seamlessly plugged into any existing robotic backbone without structural modifications or additional parameters. Our contributions are summarized as follows: 1) We identify and formalize the action inequality inherent in robotic trajectories, exposing a fundamental bias in current foundation models where the uniform treatment of all actions leads to suboptimal optimization of physically critical steps. 2) We introduce AttenA+, a plug-and-play optimization framework that utilizes the inverse velocity field as a physical prior to reweight trajectory learning, effectively aligning the model’s focus with kinematically demanding manipulation phases. 3) Extensive evaluations on L IBERO and RoboTwin benchmarks show that AttenA+ significantly elevates the performance ceilings of current state-ofthe-art models. Furthermore, real-world experiments on a Franka manipulator demonstrate that our method provides superior robustness and success rates specifically during precision-critical motions where standard baselines frequently fail.
2
Related Works
2.1
Robotic Foundation Models
Vision-Language-Action (VLA) and World-Action Models (WAM) enable end-to-end robotic manipulation by grounding language in visual observations to generate continuous action sequences. A wide range of VLA frameworks have been proposed to advance robotic manipulation performance, including foundational models and their variants, as well as specialized optimizations. OpenVLA [1] 2
serves as a core foundational framework unifying visual perception, language understanding, and action generation, with its variant OpenVLA-OFT [17] further optimizing via orthogonal fine-tuning to push state-of-the-art (SOTA) performance on L IBERO tasks. The π model series, including π0 [2], π0 + FAST [18], and π0.5 [10], advances generative VLA capabilities through flow matching for strong generalization. Other representative VLA models and optimizations include UniVLA [7], VLA-ADP [19], CogACT [20], SmolVLA [21], NORA and NORA-Long [22], WorldVLA and WorldVLA* [8], SP-VLA [23], FlashVLA [24], VLA-Cache [25], FastV and FastV(+OFT) [26], SparseVLM [27], and CSP [28]. Parallel efforts emerging as WAMs include Motus [13], LingBot-VA [14], and Fast-WAM [29]. Despite consistent progress across benchmarks, nearly all existing action models share a core limitation: treating all action timesteps equally during training, neglecting the intrinsic physical hierarchy and heterogeneous importance of different motion phases. 2.2
Action Sequence Modeling for Robotics
Modeling sequential robotic actions is a core research direction, with early efforts focusing on trajectory optimization and inverse reinforcement learning (IRL). Recent data-driven approaches include Action Chunking with Transformers (ACT) [30], which uses transformers to model temporal dependencies in action sequences, and Diffusion Policy [31], which leverages diffusion models for smooth, feasible trajectory generation—though these prioritize action quality over critical action prioritization based on physical characteristics (e.g., velocity). Prior works have explored importance weighting for imitation learning: some weight entire trajectories by demonstration quality [32, 33], while others focus on per-timestep weighting (e.g., IRIS [34] for informative offline data, uncertaintybased weighting for critical states [35]). However, these are limited to single-task learning or require extra overhead, unlike our velocity-based approach that needs no additional training and is compatible with arbitrary VLA frameworks. A small number of VLA works explore action weighting (e.g., VLA-ADP [19] prunes redundant fast actions for efficiency), but none explicitly link velocity to learning priority. Different from all prior arts, AttenA+ introduces a plug-and-play velocity-field weighting principle that emphasizes learning on critical action phases, requiring no extra supervision and universally compatible with mainstream robotic foundation models. 2.3
Attention Mechanisms in Robotic Learning
Attention has become a standard component in modern robotic foundation models, yet its usage remains largely confined to input modalities. Visual attention focuses on task-relevant spatial regions for manipulation [36]; language attention aligns linguistic instructions with visual observations [37]; cross-modal attention further fuses vision and language features to predict actionable policies [1, 7]. Remarkably, almost all prior attention designs operate exclusively on input vision-language streams, while output action trajectories are treated as plain unweighted regression targets. Our work breaks this convention by proposing action attention: we apply attention weighting directly to output action sequences, guided by physical velocity priors to emphasize precision-demanding motion segments. This extends attention design from input feature alignment to physical-aware action trajectory modeling, mirroring the hierarchical nature of human motor control.
3
Methodology
3.1
The Homogeneity Bias in Robot Learning
Current robotic foundation models, regardless of their underlying architectures, typically formulate expert trajectory as a sequence modeled via either independent single-step forecasting or autoregressive generation, with uniform optimization weight across all time steps. This uniform weighting strategy is prevalent across both discriminative and generative paradigms. Formally, given a dataset D of expert trajectories, the general optimization objective can be expressed as: " T # X ∗ θ = arg min Eτ ∼D Lt (πθ (st ), at ) , (1) θ
t=1
where Lt is the per-step loss function. In discriminative models [1, 7], Lt often takes the form of a regression loss (e.g., L1 or L2 ); in generative models such as diffusion policy [31, 38, 39] or flow matching models (π0 [2]), it corresponds to a score-matching or vector-field objective. 3
Figure 2: Analysis of velocity fields revealing the inherent action inequality. We observe that the informational density of the robot dataset is non-uniformly distributed: rapid motions are often redundant transitions, while slow-motion phases dominate task success or failure. The discovery of this kinematic hierarchy motivates the development of AttenA+, a plug-and-play mechanism designed to rectify the uniform weighting bias in current robotic foundation models.
Despite the diversity in loss formulations, these paradigms share an implicit assumption of temporal homogeneity: every action token at contributes identically to the overall gradient. However, this assumption is physically misaligned with the reality of robotic manipulation. By reducing complex physical interactions to a flat sequence of undifferentiated control signals, existing models inadvertently waste representational capacity on redundant transitional motions while under-optimizing the high-stakes, precision-demanding segments that truly govern task success. 3.2
Quantifying Action Inequality via Velocity Fields
To rectify this misalignment, we propose a shift from uniform optimization toward Kinematic Criticality. Our approach is rooted in the empirical discovery of Action Inequality: the observation that the informational density of a manipulation sequence is non-uniformly distributed and is intrinsically linked to the movement velocity. As visualized in Figure 2, we analyze the velocity distribution across diverse task datasets. The results reveal a clear physical hierarchy within action sequences. High-velocity regions (highlighted in warm colors) typically correspond to "approach" or "transitional" phases—motions that occur in free space and are highly error-tolerant. In contrast, low-velocity regions (cold colors) consistently align with "interaction-rich" phases, such as precise alignment, grasping, or delicate placement. In these slow-motion segments, even a minor prediction error ϵ can lead to catastrophic task failure due to tight environmental constraints or contact dynamics. We formalize this relationship by defining the instantaneous velocity magnitude vt of the ground-truth action agt t at each timestep: v uDpos uX gt 2 vt = ∥at ∥2 = t (agt t,d ) ,
(2)
d=1
where Dpos denotes the translational and/or rotational degrees of freedom. This metric vt serves as a natural, unsupervised proxy for task importance: lower velocity signifies higher precision demand. This discovery motivates a re-weighting of the optimization landscape to prioritize these low-velocity, high-criticality actions. In the following section, we introduce the AttenA+ framework, which leverages this velocity-based prior to adaptively rescale the loss contribution of individual action tokens across different learning paradigms. 4
Figure 3: Overview of AttenA+. Given visual and language observations from datasets, we derive a velocity field. With attention weighting function FA , this field assigns higher attention weights to slow, critical manipulation steps and lower weights to fast transitional motions, prioritizing learning on error-sensitive actions while training the models. 3.3
Velocity-Field Attention (AttenA+)
To rectify the uniform weighting bias identified in current paradigms, we introduce AttenA+, a velocity-aware weighting mechanism designed to align model optimization with the physical criticality of robotic manipulation. As illustrated in Figure 3, AttenA+ functions as a "plug-and-play" enhancer that re-scales the loss manifold across diverse learning objectives without requiring architectural modifications. 3.3.1
Weight Construction and Mapping
The core of AttenA+ lies in translating the kinematic properties of expert demonstrations into an optimization priority. For a given dataset D, we derive the instantaneous velocity magnitude vt following Equation 2. Taking the L IBERO benchmark (D = 7) as a representative case, we compute the velocity magnitude using the first 6 dimensions (joint velocities) of the ground-truth action sequence Agt , omitting the binary gripper state to focus on continuous motion dynamics. This approach ensures that the resulting weight matrix W ∈ RT ×1 captures the intrinsic difficulty of the maneuver: low-speed segments, which consistently align with task-critical phases such as object grasping or precision placement, are assigned higher learning priorities, while high-speed transitional movements are downweighted. We define the attention weighting function FA to map velocity to its corresponding importance weight: wt = FA (vt ). (3) To accommodate varying task dynamics and noise profiles, we design four configurable mapping strategies: inverse, inverse squared, exponential decay, and logarithmic. These functions provide varying degrees of non-linear amplification for low-velocity actions, with detailed mathematical formulations provided in Appendix C. 3.3.2
Regularization for Training Stability
Directly applying raw inverse velocity weights can lead to numerical instability or gradient dominance by near-static timesteps. To ensure robust convergence, AttenA+ incorporates two essential regularization steps: • Weight Clipping: We constrain the weights to a predefined range [1/clipmax , clipmax ]. This prevents individual precision-critical steps from overwhelming the overall gradient and mitigates the impact of potential noise in expert demonstrations. PT • Loss Normalization: We optionally normalize the weight vector such that T1 t=1 wt ≃ 1. This ensures that the global learning rate remains consistent with standard unweighted baselines, facilitating stable integration into existing training pipelines. 5
3.3.3
Paradigm-Agnostic Optimization Objectives
A defining advantage of AttenA+ is its paradigm agnosticism. It can be seamlessly integrated into diverse action models by augmenting the existing loss function. Discriminative Models (AttenA+Disc): For standard regression-based VLAs, we transform the vanilla objective into a velocity-weighted L1 loss: " # T D 1 XX pred gt ∗ θ = arg min E(I,L,Agt )∼D wt · |at,d − at,d | , (4) θ T · D t=1 d=1
where θ denotes the model parameters and wt represents the velocity-derived weight. Flow Matching Models (AttenA+FM): For generative frameworks such as π0 or π0.5 , we revise the flow-matching objective to guide the model toward learning more accurate flow fields specifically for high-criticality segments: " # T D 1 XX gt ∗ 2 ϕ = arg min E(I,L,Agt )∼D wt · ∥ut (ϵ; I, L) − (at,d − ϵd )∥2 , (5) ϕ T · D t=1 ϵ∼N (0,I) d=1
where ut is the predicted flow field. By prioritizing these segments, AttenA+ enables generative models to capture the subtle nuances of precision-demanding actions that are often "washed out" in uniform training paradigms.
4
Experiment
We evaluate AttenA+ using four metrics: (1) Success Rate (SR) (%): percentage of successfully completed tasks. (2) Average Success Rate (SR) (%): mean success rate across tasks. (3) Average Error Rate (ER) (%): mean error rate across tasks. (4) Average Success Rate Improvement (SR-I) (%): absolute gain in average success rate. (5) Average Relative Error Rate Reduction (RER-R) (%): relative error reduction computed by ERAttenA+ RER-R = 1 − × 100. (6) ERother 4.1
L IBERO and RoboTwin 2.0 Benchmark
We build AttenA+OFT upon the official OpenVLA-OFT framework, and benchmark our approach on L IBERO dataset (Figure 5-I-(a)) against representative state-of-the-art VLA and WAM models across all four task subsets of the L IBERO dataset. We select the best-performing checkpoint from training, then conduct evaluation across 4 random seeds to report the mean and standard deviation of success rates. Additional training configurations are provided in Appendix E.1. As summarized in Table 1, AttenA+OFT obtains an overall average success rate of 98.6%, surpassing the prior SOTA OpenVLA-OFT by 1.5%. Consistent performance gains are observed across all task categories. In particular, our method achieves a 2.1% improvement on long-horizon manipulation tasks, verifying that our action attention mechanism effectively enhances robustness and precision for complex, extended sequential behaviors. We further validate our method on the RoboTwin benchmark (Figure 5-I-(b)), implementing AttenA+WAM based on the Fast-WAM framework. As shown in Table 2, AttenA+WAM achieves a new state-of-the-art average success rate of 92.46%, improving the base model Fast-WAM by 0.6% and outperforming the prior best LingBot-VA by 0.3%, without requiring any embodied pre-training. This confirms that our action attention mechanism can effectively boost performance even on larger, more diverse real-world benchmarks. 4.2
Improvement of Different Models with Action Attention
As shown in Table 3, we validate the effectiveness and generality of our velocity-field-based action attention by integrating it into both discriminative and generative models. Figure 4 provides a qualitative comparison: the original baseline fails due to accumulated errors in slow, critical manipulation 6
Table 1: Performance on L IBERO Compared with SOTA Methods. SR(%): Average Success Rate; ER(%): Average Error Rate; SR-I(%): Average Success Rate Improvement; RER-R(%): Average Relative Error Rate Reduction (Compared with AttenA+OFT using Equation 6). Method
Spatial
Object
Goal
10
SR ↑
ER ↓
SR-I
RER-R
OpenVLA [1] SparseVLM [27] FastV [26] VLA-Cache [25] FlashVLA [24] SP-VLA [23] WorldVLA [8] NORA-Long [22] SmolVLA [21] CogACT [20] CSP [28] π0 + FAST [18] π0 [2] π0.5 [10] UniVLA [7] VLA-ADP [19] OpenVLA-OFT [17]
84.7 79.8 83.4 83.8 84.2 75.4 85.6 92.2 93.0 97.2 84.7 96.4 96.8 98.8 96.5 99.0 97.6
88.4 67.0 84.0 85.8 86.4 85.6 89.0 95.4 94.0 98.0 82.2 96.8 98.8 98.2 96.8 98.2 98.4
79.2 72.6 74.2 76.4 75.4 84.4 82.6 89.4 91.0 90.2 77.1 88.6 95.8 98.0 95.6 96.8 97.9
53.7 39.4 51.6 52.8 51.4 54.2 59.0 74.6 77.0 88.8 74.3 60.2 85.2 92.4 92.0 91.2 94.5
76.50 64.70 73.30 74.70 74.35 74.90 79.05 87.90 88.75 93.55 79.58 85.50 94.15 96.85 95.23 96.30 97.10
23.50 35.30 26.70 25.30 25.65 25.10 20.95 12.10 11.25 6.45 20.42 14.50 5.85 3.15 4.77 3.70 2.90
+22.1 +33.9 +25.3 +23.9 +24.3 +23.7 +19.6 +10.7 +9.9 +5.1 +19.1 +13.1 +4.6 +1.8 +3.4 +2.3 +1.5
-94.0 -96.0 -94.8 -94.5 -94.5 -94.4 -93.3 -88.4 -87.6 -78.3 -93.1 -90.3 -76.1 -55.6 -70.7 -62.2 -51.7
AttenA+OFT (ours)
99.0 ± 0.16
100 ± 0.00
98.8 ± 0.28
96.6 ± 0.30
98.60
1.40
-
-
Table 2: Performance on RoboTwin 2.0 Compared with SOTA Methods. Embodied PT.
Clean
Rand.
SR ↑
ER ↓
SR-I
RER-R
π0 [2] π0.5 [10] X-VLA [40] Motus [13] LingBot-VA [14] Fast-WAM [29]
✓ ✓ ✓ ✓ ✓ ✗
65.92 82.74 72.90 88.66 92.90 91.88
58.40 76.76 72.80 87.02 91.50 91.78
62.20 79.75 72.85 87.80 92.2 91.80
37.80 20.25 27.15 12.20 7.80 8.20
+30.3 +12.7 +19.6 +4.6 +0.3 +0.6
-80.1 -62.8 -72.2 -38.0 -3.3 -7.7
AttenA+WAM (ours)
✗
93.06
91.86
92.46
7.54
-
-
Method
steps (clip, align, release), where precision is essential but receives equal loss weight to fast transitional motions. In contrast, AttenA+ prioritizes these high-precision segments with larger attention weights, leading to stable task completion. For the discriminative framework, we apply our method to OpenVLA-OFT, a strong baseline already achieving high performance on the L IBERO benchmark. Equipped with action attention, AttenA+OFT yields consistent gains across all task categories: Spatial (+1.4%), Object (+1.6%), Goal (+0.9%), and Long-horizon tasks (+2.1%). The overall average success rate improves by +1.5% (from 97.1% to 98.6%), with a corresponding -1.5% reduction in error rate. For the generative framework, we adopt π0.5 as the backbone and construct AttenA+π0.5 . Similarly, consistent improvements are observed across all task types, with an average success rate increase of +1.10%. These results demonstrate that our velocity-field action attention is paradigm-agnostic and can serve as a universal plug-and-play enhancement for both discriminative and generative models. Notably, the performance gain is most pronounced on long-horizon tasks, where distinguishing critical actions from transitional movements is essential for maintaining execution success.
Table 3: Performance Improvement with Velocity-Field-Based Action Attention on L IBERO dataset. Model
Spatial
Object
Goal
10
SR
ER
Generative
π0.5 AttenA+π0.5
98.8 99.2 (+0.4)
98.2 99.6 (+1.4)
98.0 98.8 (+0.8)
92.4 94.2 (+1.8)
96.85 97.95 (+1.10)
3.15 2.05 (-1.10)
Discriminative
OpenVLA-OFT AttenA+OFT
97.6 99.0 (+1.4)
98.4 100 (+1.6)
97.9 98.8 (+0.9)
94.5 96.6 (+2.1)
97.1 98.6 (+1.50)
2.9 1.4 (-1.50)
7
Figure 4: Qualitative comparison of task execution with/without AttenA+. (a) The original baseline fails due to accumulated errors in slow, critical manipulation steps (clip, align, release), which receive equal loss weight to fast transitional motions. (b) AttenA+ prioritizes these highprecision segments with larger attention weights, leading to stable task completion. Table 4: Ablation study on different velocity weighting strategies and weight clipping thresholds clipmax . We report task success rate (%) on the L IBERO benchmarks. Baseline is OpenVLA-OFT. Libero-Spatial 2.0 SR ∆SR
Strategy / Clipmax
Libero-Object 2.0 SR ∆SR
Libero-10 2.0 SR ∆SR
2.0 SR ∆SR
Libero-Goal 3.0 SR ∆SR
SR
5.0 ∆SR
baseline
97.6
-
98.4
-
94.5
-
97.9
-
97.9
-
97.9
-
exp_decay (wb,t = e−α·vb,t ) inverse_squared (wb,t = v21 )
99.2 99.4
+1.6 +1.8
99.8 99.8
+1.4 +1.4
96.8 94.2
+2.3 -0.3
99.0 98.8
+1.1 +0.9
95.4 97.9
-2.5 0.0
97.4 97.6
-0.5 -0.3
1 inverse (wb,t = vb,t ) 1 log (wb,t = log(1+vb,t ) )
98.6 98.2
+1.0 +0.6
100.0 99.6
+1.6 +1.2
95.8 88.8
+1.3 -5.7
98.0 99.0
+0.1 +1.1
98.2 97.8
+0.3 -0.1
95.6 97.8
-2.3 -0.1
4.3
b,t
Ablation Study on Weighting Strategies and Clipping Thresholds
We conduct an ablation study to validate the effectiveness of our proposed velocity-based weighting strategies and the criticality of the weight clipping threshold clipmax , with OpenVLA-OFT as our baseline model. Results on the L IBERO benchmark are reported in Table 4. First, we observe that no single weighting strategy universally dominates all task categories, which aligns with the distinct motion characteristics of different robotic manipulation tasks. Specifically, inverse_squared achieves the best performance on L IBERO -S PATIAL, inverse performs optimally on L IBERO -O BJECT and clipmax =3.0 settings of L IBERO -G OAL, while exp_decay and log show strong advantages on L IBERO -10 and clipmax =2.0 settings of L IBERO -G OAL. This demonstrates that different velocity-aware weighting functions adapt to task-specific motion patterns. Second, the clipping threshold clipmax plays a vital role in balancing weight emphasis and training stability. When clipmax =1.0, all weighted loss terms degenerate to the uniform baseline, yielding identical performance to the original OpenVLA-OFT. As clipmax increases to 2.0 or 3.0, our AttenA+ mechanism consistently improves the task success rates. However, an overlarge threshold (clipmax =5.0) tends to degrade performance, as extreme weights introduce training instability and over-emphasize noisy low-velocity actions. These results confirm that appropriate weight clipping is essential for maintaining the effectiveness of our velocity-field attention mechanism. 4.4
Real-World Robot Experiments
As shown in Figure 5, we design 4 kinds of task for validation using the Franka manipulator: (a) Close the open drawer, (b) Put the Green Cube into Green Bowl, (c) Put Object-A into Green Bowl, (d) Put Object-A into XXX and then put Object-B into XXX. For the easy tasks (a) and (b), we collect 50 trajectories for demonstration. For harder tasks (c) and (d), we collect 100 trajectories for 8
Figure 5: Overview of experimental tasks. I. Simulation: (a) Four L IBERO benchmark tasks; (b) 50 diverse RoboTwin tasks, including clean and randomized environments. II. Real-world experiments on Franka Panda: (a)–(d) Four representative tasks (drawer opening, pick-and-place, multi-objects, and sequential manipulation), showing AttenA+ enhanced policy execution. Model
Close Draw
Put Cube
Multi-object
Long
OpenVLA-OFT AttenA+OFT Improvement
50/50 50/50 0%
48/50 50/50 4% ↑
45/50 49/50 8% ↑
42/50 45/50 6% ↑
Figure 6: Real robot experimental results on Franka (Each task is tested over 50 trials): (a) Quantitative success rates (%); (b) Qualitative performance visualization.
demonstration. Notably, during demonstration data collection, we use different speed for different phase: at the beginning, we use the baseline speed for approaching the object for grasping, then we change the speed to be 1/3 of the baseline to fine align and operate the object which indicates critical actions. Then after grasping the object we change the speed to baseline and fastly move to the bowl. When approaching the bowl, the speed is again reduced to 1/3 of the baseline for fine align to the bowl and finally release the object. After collection, we clean the trajectory by removing the no action waiting frames and do action smoothing for efficient training and action attention. We then finetune and test the task following the OpenVLA-OFT recipe with 2 Nvidia H800 GPUs. In the testing phase, we deploy the model on a RTX-4090 GPU, evaluate each task for 50 times and compute the SR. The results are shown in Figure 6. We can see that AttenA+OFT consistently outperforms the baseline OpenVLA-OFT across all real-world tasks, improving the average success rate from 92.5% to 97.0%, with the largest gains on the more complex multi-object and long-horizon tasks, further validating the effectiveness of our method in real-world scenarios.
5
Conclusion
This work presents AttenA+, a generic enhancement framework for robotic foundation models. It introduces velocity-field-based action attention to prioritize critical, low-speed manipulation steps during training, aligning model optimization with real-world manipulation physics without modifying core architectures. Evaluated on L IBERO and RoboTwin 2.0 benchmarks, AttenA+ consistently improves success rates and reduces errors across both discriminative and generative paradigms (including VLA and WAM), and is readily extendable to other architectures such as diffusion policies. We also note two main limitations. First, our velocity-weighted attention relies on a hand-crafted heuristic, which assumes critical manipulation steps are inherently slow. This does not generalize to dynamic tasks (e.g., high-speed grasping, table tennis) where critical actions may instead be fast and 9
ballistic. Second, the mechanism only leverages velocity information, ignoring other physical cues such as force or torque that can signal action importance. Future work will move beyond fixed heuristics toward physically grounded, learnable action attention that integrates multi-modal physical signals and adapts dynamically to task semantics. By respecting the structure of robotic actions rather than treating all timesteps equally, we can build more efficient, robust, and generalizable robotic foundation systems.
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A
Preliminary Concepts
A.1
Unified Task Definition and Notation
We unify the formulation for robotic foundation models (including VLA and WAM) across discriminative and generative paradigms using consistent notation, focusing on the core mapping from multimodal inputs to task-compliant action sequences: • I = {i1 , i2 , ..., iT }: Sequence of visual observations (RGB images) at timesteps 1 ≤ t ≤ T , where it ∈ RH×W ×3 in most cases. • L: Natural language instruction (e.g., "stack the blue block on the red block"), tokenized to L = [l1 , l2 , ..., lN ] via standard tokenizers (e.g., CLIP [41], Bert [42]). • A = {a1 , a2 , ..., aT }: Robotic action sequence, with at ∈ RD and D denoting action dimensions (e.g., D = 7 for L IBERO benchmarks). • Agt : Ground-truth action sequence from expert demonstrations, serving as the target for model learning. A.2
Discriminative Robotic Foundation Models
Discriminative paradigms [1, 17, 7] cast robotic action learning as a deterministic regression task. Given visual observations I and language instructions L, a discriminative model fθ (parameters θ) directly predicts a deterministic action sequence: Apred = fθ (I, L)
(7)
Training minimizes the discrepancy between predicted and ground-truth actions via a regression loss over the dataset D (tuples of I, L, Agt ). Most existing works adopt an unweighted ℓ1 loss as the optimization objective: " # T D 1 X X pred gt ∗ θ = arg min E(I,L,Agt )∼D at,d − at,d (8) θ T · D t=1 d=1
12
A.3
Generative Robotic Foundation Models via Flow Matching
The π-series models (π0 [2], π0.5 [10]) are representative generative frameworks based on flow matching. Instead of direct regression, these models learn a continuous vector field to transform Gaussian random noise ϵ ∼ N (0, I) into task-aligned action sequences. Specifically, the learnable network gϕ predicts a time-dependent flow field conditioned on I and L, denoising random inputs toward Agt . The standard unweighted flow matching objective is: # " T D 2 1 XX gt ∗ ut (ϵ; I, L) − at,d − ϵd (9) ϕ = arg min E(I,L,Agt )∼D ϕ T · D t=1 2 ϵ∼N (0,I) d=1
gt Here, agt t,d is the d-th dimension of A at timestep t, with T and D denoting action sequence length
and dimensionality, respectively. While π0.5 introduces hierarchical reasoning for complex tasks, it retains the original flow matching objective. Related diffusion policy frameworks are discussed in Appendix B.
B
Action Attention Formulation of Generative VLA: Diffusion Policy
B.1
Generative VLA: Diffusion Model (Diffusion Policy)
Diffusion Policy (DP) represents an independent line of generative work, distinct from π0 /π0.5 . It models action generation as a iterative denoising process. Given K diffusion steps, the model hψ predicts the noise ϵpred added to the action state at step k. The standard unweighted L2 diffusion k optimization objective is: # " D T 2 1 X X pred ∗ (10) ϵk − ϵk ψ = arg min E (I,L,Agt )∼D ψ T · D t=1 2 k∼Uniform(1,K) d=1
ϵk ∼N (0,I) (k)
where at,d = αk agt t,d + βk ϵk is the noisy action, and αk , βk are pre-defined diffusion schedule coefficients. B.2
Revised Optimization Objective for Diffusion Policy (AttenA+Diff)
For diffusion-based generative policies (Diffusion Policy), we apply the same velocity-based weighting to the denoising objective: # " D T 2 1 XX pred ∗ wt · ϵk − ϵk (11) ψ = arg min E (I,L,Agt )∼D ψ T · D t=1 2 k∼Uniform(1,K) d=1
ϵk ∼N (0,I)
where wt emphasizes denoising accuracy for slow, critical timesteps during the diffusion process.
C
Velocity-Based Action Attention Weighting Strategies
We detail the four handcrafted weighting strategies used to implement velocity-field-based action attention in AttenA+. These formulations serve as empirical, physics-inspired examples to demonstrate the core idea of prioritizing slow, critical actions during training, rather than definitive or exclusive solutions. All weighting rules assign higher importance to low-velocity timesteps, consistent with the intuition that precise manipulation phases require stricter optimization in our experiment datasets (L IBERO, RoboTwin 2.0). For the b-th sample at timestep t, the velocity-aware weight wb,t is defined as follows: 1. Inverse strategy 1 (12) vb,t This baseline scheme applies inverse weighting proportional to action speed, providing a mild but clear emphasis on slower movements. wb,t =
13
2. Inverse squared strategy (amplified weight difference) wb,t =
1 2 vb,t
(13)
By squaring the velocity term, this strategy strongly amplifies the contrast between slow and fast actions, making it the default choice in our main experiments. 3. Exponential decay strategy (fast attenuation) wb,t = e−α·vb,t
(14)
where α = 5.0 controls the decay rate. This method suppresses high-speed actions rapidly while maintaining soft weighting for slow segments. 4. Logarithmic strategy (smoothed weight) wb,t =
1 log(1 + vb,t )
(15)
The logarithmic transform yields gentle, stable weighting, reducing sensitivity to noise in velocity estimation. Notably, these four heuristic functions are example implementations chosen for simplicity, interpretability, and empirical effectiveness. They are not intended to limit the design space of action attention. In future work, action weighting can be naturally extended to broader families of parametric functions, task-adaptive formulations, or fully learnable attention mechanisms that infer importance end-to-end from data and physical constraints, rather than relying on fixed handcrafted rules.
D
Visualization of Action Speed and Velocity-Guided Action Attention
In this section, we provide detailed analysis of the action speed patterns and velocity-guided attention weights, which are briefly summarized in the main text. Figures 7–10 present comprehensive visualizations of raw action velocity profiles and the resulting velocity-field-based attention weights under four distinct clipping thresholds clipmax ∈ {1.0, 2.0, 5.0, 10.0} on the L IBERO - OBJECT manipulation benchmark. Each figure follows a consistent layout: Subplot 1 illustrates the temporal distribution of raw action speed magnitudes across multiple expert demonstration trajectories, revealing inherent speed variations within task execution. Subplots 2 through 5 display the attention weight distributions generated by the four velocity transformation rules (Equations 12–15): inverse weighting, inverse squared weighting, exponential decay weighting, and logarithmic weighting, respectively. Subplot 6 serves as the baseline, showing the original action trajectory under uniform, unweighted treatment without action attention. From the raw velocity visualizations, distinct slow–fast motion patterns emerge consistently across all task trajectories. Slow-motion segments consistently align with task-critical phases, including robot initialization, precise object approaching, fine manipulation, grasping, targeted placement, and task completion. These phases demand high positional accuracy and are highly sensitive to execution errors, making them decisive for overall task success. Conversely, fast-motion segments correspond to robust, error-tolerant transitional movements, such as free-space arm traversal, coarse positioning toward target objects, and post-grasp repositioning, where minor deviations rarely lead to task failure. The effect of the clipping threshold clipmax is clearly demonstrated across Figures 7–10. At clipmax = 1.0, all velocity-adaptive weighting schemes collapse to uniform values, reverting AttenA+ to a standard VLA model with equal emphasis on all timesteps. As clipmax increases sequentially from 1.0 to 2.0, 5.0, and 10.0, the discriminative power of action attention is progressively strengthened: slow critical actions receive increasingly prominent weights, while fast transitional actions are assigned relatively lower weights, widening the gap in learning priority. Moreover, the four velocity mapping functions exhibit distinctive attention characteristics. As clearly visible in the clipmax = 2.0 visualization, exponential decay weighting (Equation 14) produces highly localized emphasis: it strongly amplifies a small set of extremely slow actions while broadly suppressing fast actions across a wide range. In contrast, inverse (Equation 12), inverse squared (Equation 13), and logarithmic (Equation 15) schemes maintain widespread emphasis on slow 14
Figure 7: Visualization of Action Speed in L IBERO -O BJECT Task with Different clipmax = 1.0
Figure 8: Visualization of Action Speed in L IBERO -O BJECT Task with Different clipmax = 2.0 actions and exert mild, localized suppression on fast actions. Within this group, the intensity of low-speed amplification follows a clear hierarchy: inverse squared (Equation 13) yields the strongest enhancement, followed by logarithmic weighting (Equation 15), and then inverse weighting (Equation 12). This consistent trend is observable across all clipping thresholds in Figures 7–10, validating the design principles of velocity-field-based action attention and supporting the selection of inverse squared weighting as the default configuration in the main experiments.
E
Details about Model Training
This section presents comprehensive training and implementation details for AttenA+OFT (evaluated on LIBERO) and AttenA+WAM (evaluated on RoboTwin), covering architectural modifications, 15
Figure 9: Visualization of Action Speed in L IBERO -O BJECT Task with Different clipmax = 5.0
Figure 10: Visualization of Action Speed in L IBERO -O BJECT Task with Different clipmax = 10.0
16
optimization configurations, fine-tuning pipelines, checkpoint scheduling, and best-model selection criteria. All experiments in this work use the weight clipping settings clipmax = 2.0 and clipmax = 5.0, which are applied consistently across both model variants. E.1
AttenA+OFT
We build AttenA+OFT as a direct adaptation of the OpenVLA-OFT framework, with our core velocityfield action attention integrated as a weighted module without altering the backbone architecture. Following the standard OpenVLA-OFT fine-tuning protocol, we train separate models for each of the four LIBERO task categories (Spatial, Object, Goal, Long) to ensure fair comparison with prior work. All models are trained for a total of 200,000 steps, with checkpoints saved every 5,000 steps. The taining time of each model using single H800 GPU is about 35 hours. During training, we strictly retain the original optimizer configuration, learning rate schedule, batch size, and data preprocessing used in OpenVLA-OFT to isolate the improvement brought by action attention. After training, we evaluate over saved checkpoints on the corresponding LIBERO test split and select the checkpoint with the highest success rate as the final model for reporting results. E.2
AttenA+WAM
We implement AttenA+WAM on top of the Fast-WAM architecture, again integrating our velocityguided action attention as a plug-and-play weighting module. Since the official Fast-WAM repository does not release end-to-end fine-tuning code, we adopt a practical and fair adaptation protocol: we freeze all vision encoders and the pre-trained WAM backbone, and only fine-tune the final action head using our proposed action attention mechanism. This design ensures we only introduce our method while preserving the pre-trained knowledge of the original model. We fine-tune on the RoboTwin dataset for 1 epoch, saving checkpoints every 2,000 steps. The taining time of the model using two H800 GPUs is about 4 days. Consistent with AttenA+OFT, we evaluate over intermediate checkpoints and select the best-performing one based on validation success rate for final experimental comparisons.
F
Detailed Evaluation Results on RoboTwin 2.0 and Real Franka Robot Experiments
F.1
Detailed Results on RoboTwin 2.0
17
Table 5: We present quantitative results on the RoboTwin 2.0 simulation benchmark, covering 50 bimanual manipulation tasks with two difficulty levels. RoboTwin 2.0 serves as a rigorous dual-arm manipulation testbed that demands precise bilateral coordination. The easy setting adopts fixed initial scene arrangements, whereas the hard setting introduces randomized object placements and scene configurations for higher generalization challenges. Model Task Type
AttenA+WAM(Ours)
Fast-WAM
LingBot
Pi_05
Pi_0
X-VLA
Motus
clean
random
clean
random
clean
random
clean
random
clean
random
clean
random
clean
random
Adjust Bottle Beat Block Hammer Blocks Ranking RGB Blocks Ranking Size Click Alarmclock Click Bell Dump Bin Big Binbin Grab Roller Handover Block Handover Mic Hanging Mug Lift Pot Move Can Pot Move Pillowbottle Pad Move Playingcard Away Move Stapler Pad Open Laptop Open Microwave Pick Diverse Bottles Pick Dual Bottles Place A2B Left Place A2B Right Place Bread Basket Place Bread Skillet Place Burger Fries Place Can Basket Place Cans Plasticbox Place Container Plate Place Dual Shoes Place Empty Cup Place Fan Place Mouse Pad Place Object Basket Place Object Scale Place Object Stand Place Phone Stand Place Shoe Press Stapler Put Bottles Dustbin Put Object Cabinet Rotate QRcode Scan Object Shake Bottle Horizontally Shake Bottle Stack Blocks Three Stack Blocks Two Stack Bowls Three Stack Bowls Two Stamp Seal Turn Switch
100 99 100 93 100 100 97 100 95 100 67 100 89 98 100 74 99 71 91 100 97 95 93 88 96 65 99 98 86 99 97 88 91 92 90 99 96 92 91 85 92 93 100 100 97 100 95 95 91 80
100 93 100 94 100 100 95 100 90 91 62 100 91 100 100 70 100 49 85 96 96 98 93 91 96 64 100 99 89 100 91 88 85 94 91 99 99 94 91 85 91 89 100 100 96 100 95 95 89 79
100 99 100 94 100 100 97 100 95 99 58 100 90 100 100 77 98 62 80 100 95 93 91 90 96 71 99 96 94 100 96 83 89 90 90 97 96 90 95 94 93 89 100 100 95 100 80 92 90 61
100 97 100 98 100 100 96 100 81 100 62 100 88 99 100 64 100 45 85 96 93 99 93 93 99 69 96 100 88 100 96 89 88 97 94 99 99 97 90 89 89 92 100 100 97 100 81 98 94 59
90 96 99 94 99 100 89 100 99 94 40 100 94 99 100 91 92 82 89 100 97 97 97 95 97 81 100 99 94 100 99 93 91 96 99 97 98 85 87 85 96 96 100 100 99 100 86 94 96 44
94 98 98 96 100 100 96 100 78 96 28 99 97 99 99 79 94 86 82 99 93 95 95 90 95 84 99 97 89 100 93 96 88 95 96 97 98 82 91 87 91 91 99 97 98 98 83 98 97 45
100 96 92 49 98 99 92 100 66 98 18 96 51 84 96 56 90 34 81 93 87 87 77 85 94 62 94 99 75 100 87 60 80 86 91 81 92 87 84 80 89 72 99 99 91 97 77 95 79 62
99 93 85 26 89 66 97 100 57 97 17 85 55 61 84 42 96 77 71 63 82 84 64 66 87 62 84 95 75 99 85 39 76 80 85 81 93 83 79 79 87 65 99 97 76 100 71 96 55 54
99 79 80 14 77 71 88 98 47 97 14 80 68 67 74 41 71 4 69 59 43 39 62 66 81 55 63 97 59 91 66 20 67 57 82 49 76 44 65 73 74 55 98 94 72 93 77 94 46 41
95 84 63 5 68 48 83 94 31 97 11 72 48 46 65 24 81 32 31 37 47 34 46 49 76 46 45 92 51 85 71 20 70 52 68 53 76 37 56 60 70 42 92 91 52 79 75 95 33 42
100 92 83 67 99 100 79 100 73 0 23 99 89 73 93 78 93 79 58 47 48 36 81 77 94 49 97 97 79 100 80 70 44 52 86 88 96 92 74 46 34 14 100 99 6 92 76 96 76 40
99 88 83 74 99 100 77 100 37 0 27 100 86 71 98 73 100 71 36 36 49 36 71 67 94 52 98 95 88 98 75 70 39 74 88 87 95 98 77 48 33 36 100 100 10 87 86 93 82 61
89 95 99 75 100 100 95 100 86 78 38 96 34 93 100 83 95 95 90 96 82 90 91 86 98 81 98 98 93 99 91 66 81 88 98 87 99 93 81 88 89 67 100 100 91 100 79 98 93 84
93 88 97 63 100 100 91 100 73 63 38 99 74 96 96 85 91 91 91 90 79 87 94 83 98 76 94 99 87 98 87 68 87 85 97 86 97 98 79 71 73 66 98 97 95 98 87 98 92 78
Average
93.06
91.86
91.88
91.78
92.9
91.5
82.74
76.76
65.92
58.4
72.88
72.84
88.52
87.02
18
Table 6: Detailed Evaluation Results on Real Franka Robot Experiments. We report the success rates (SR) across four manipulation tasks under the Baseline and our Attention-based method. Experiment
Baseline
AttenA+
Close Draw
Put Cube
Multi-object
Long
Close Draw
Put Cube
Multi-object
Long
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1
1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1
SR (%)
100
96
90
84
100
100
98
90
19
Figure 11: Third-person views of example L IBERO manipulation tasks. Frames labeled ‘critical’ highlight slow, high-precision actions (e.g., grasping, alignment) where AttenA+ applies increased attention weights to improve task success.
20
Figure 12: Third-person views of example RoboTwin tasks in both clean and randomized environments. The ‘critical’ labels mark slow, precision-sensitive steps, where AttenA+ prioritizes learning to boost performance across diverse conditions.
21
Figure 13: Third-person views of four representative real-world Franka tasks. The ‘critical’ labels identify slow, high-precision manipulation steps, demonstrating how AttenA+ prioritizes these phases to improve real-robot success rates. 22