VLA Knows Its Limits: Adaptive Execution Horizons for Robot Policies¶

Conference: ECCV 2026
arXiv: 2602.21445
Code: Video demo available on the project page (GitHub link not directly provided in the paper)
Area: Robotics / Embodied AI
Keywords: VLA, Action Chunking, Execution Horizon, Attention Sinks, Test-Time Adaptation

TL;DR¶

This paper discovers that the execution horizon (the number of steps actually executed in each action chunk) of flow-based VLAs exhibits a "rise-then-fall" unimodal performance curve with a unique optimal point. It reveals that the "radial action sinks" at the start and end of the action self-attention encode the model's prediction limits. Based on this, the authors propose AutoHorizon, a training-free and virtually overhead-free test-time method to dynamically estimate the execution horizon for each action chunk.

Background & Motivation¶

Action chunking has become standard in imitation learning for training VLAs. Instead of step-by-step prediction, the policy predicts a continuous sequence of future actions (a chunk) at once. The robot then executes only the first few steps of this sequence, discards the rest, receives new observations, and predicts the next chunk. The total predicted length is termed the "prediction horizon" \(p\), while the length of the actually executed prefix is called the "execution horizon" \(e\). This closed-loop mechanism essentially trades off long-term consistency for reactivity: a longer execution horizon yields smoother and more coherent actions, whereas a shorter one makes the system more sensitive to environmental changes. However, almost all existing works treat \(e\) as a fixed hyperparameter determined empirically or via grid search. Few have seriously investigated how \(e\) should be systematically determined.

The authors' starting point is a striking empirical observation: when evaluating π0.5 on LIBERO, merely varying the execution horizon causes the success rate to swing drastically between "near-perfect success" and "frequent failure." Moreover, the performance curve exhibits a distinct unimodal shape—rising first and then falling as \(e\) increases, with the optimal value lying somewhere in the middle. This suggests that a fixed horizon is inherently suboptimal. Different stages of a policy rollout naturally prefer different trade-offs between consistency and reactivity. For instance, when reaching for a coffee pot, a longer horizon is preferred for smooth motion; whereas when pouring water into a cup, a shorter horizon is required for prompt error correction. Since the optimal point drifts over time, the execution horizon should ideally adapt on a chunk-by-chunk basis rather than being fixed throughout. Grid search is not only expensive but also fails to address the fundamental need for in-context adaptivity.

How can one determine "how long this chunk should be executed" at test time without retraining the model? Turning to the attention mechanism for clues, the authors analyze how flow-based VLAs allocate attention among vision, language, and action tokens during action generation. They uncover two key phenomena: first, different actions within the same chunk always attend to the same set of vision-language tokens with nearly identical weights. Consequently, later actions cannot adjust their perceptual context based on environmental changes, exposing the ceiling of the predicted chunk's adaptivity. Second, the predicted actions pay abnormally strong attention to the action tokens at both ends (start and finish), which the authors term "radial action sinks"; intermediate actions are organized around these two anchor points. Core Idea: Interpret the action self-attention weights as implicit indicators of the model's prediction limits. The inflection point where the attention propagation stops advancing and enters a plateau marks the natural boundary of the VLA's reliable prediction capability. A bidirectional soft-pointer mechanism can locate this point to determine the execution horizon for the current chunk.

Method¶

Overall Architecture¶

The proposed method focuses on a specific problem: automatically estimating an appropriate execution horizon \(e\) for each predicted action chunk at test time, enabling the robot to move smoothly during stable phases and correct errors promptly during interaction phases. The framework consists of two main parts: first, explaining the phenomenon (why performance is unimodal with respect to \(e\) and what patterns are hidden in the attention weights), and second, designing the algorithm (how AutoHorizon extracts the horizon from the attention matrix).

The input is the action self-attention matrix \(\mathbf{S}_t \in \mathbb{R}^{p\times p}\) at a certain sampling step of the VLA (averaged across all transformer blocks and attention heads, and row-normalized). The output is the execution horizon \(N\) for this chunk. The intermediate workflow is as follows: first, filter out rows with high entropy (diffuse attention) to retain only the rows with clear, structured attention. Next, a forward soft pointer moves along the attention trajectory to find the inflection point where quality stops advancing, yielding the forward horizon \(N_f\). The same operation is applied to the flipped attention matrix to obtain the backward horizon \(N_b\). Finally, \(N_f\) and \(N_b\) are fused based on whether their sum covers the entire chunk to decide the final horizon. The entire process requires no additional training or parameter fitting, is executed only once at the 1st or 3rd sampling step, and incurs negligible overhead.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Action Self-Attention Matrix<br/>Averaged across blocks/heads + Row-normalized"] --> B["Actions in chunk view same perception<br/>+ Radial action sinks<br/>Self-attn as prediction limit indicator"]
    B --> C["Low-Entropy Row Filtering<br/>Keep only highly structured rows"]
    C --> D["Bidirectional Soft Pointer for Plateau Detection<br/>Forward Nf + Backward Nb"]
    D -->|"Nf+Nb≥p Full Course N=p<br/>Else N=Nf"| E["Execution Horizon N per Chunk"]

Key Designs¶

1. Existence of a Unique Optimal Execution Horizon: Modeling Cumulative Rollout Error as a Unimodal Function

The authors theoretically prove that "the optimal execution horizon indeed exists and is unique," establishing the foundation for their method. The core challenge is that if performance exhibits no predictable structure with respect to \(e\), estimating it becomes impossible. The authors decompose the expected error of a full rollout into two parts: the execution cost incurred at each boundary transition \(\delta^c\) (independent of \(e\)), and the divergence loss of each executed chunk relative to the expert trajectory \(\delta^d_j(e)\) (monotonically increasing with \(e\), modeled as \(\delta^d_j(e)=ke\log e\)). Letting \(L\) be the total number of low-level actions, and \(m=\lceil L/e\rceil\) be the number of chunks, the total error is defined as:

\[\mathcal{L}(e)=\sum_{i=0}^{m-1}\delta^{c}+\sum_{j=0}^{m}\delta^{d}_{j}(e)\]

Differentiating with respect to a continuous \(e\) yields a unique stationary point \(\hat e=\delta^c/k\), where the second derivative is positive. Thus, \(\mathcal{L}\) is strictly decreasing on \((0,\hat e)\) and strictly increasing on \((\hat e,\infty)\)—precisely reflecting the empirically observed unimodal curve. The intuitive meaning is clear: when the transition cost \(\delta^c\) is large (the policy learns a diverse action distribution), a longer horizon is favored for consistency; when the intra-chunk divergence \(\delta^d\) dominates (the policy struggles to model environmental dynamics), a shorter horizon is preferred for reactivity. This analysis generalizes the conclusions of Liu et al. (BID) into an explicit "consistency vs. reactivity" trade-off. The authors emphasize that this formulation only proves existence and does not directly guide the method design—the actual estimation relies on attention.

2. VLA Knows Its Limits: In-Chunk Attention Invariance and Radial Action Sinks

This observation forms the core of the paper, answering "where the unimodal curve comes from and how to locate the boundary." Visually analyzing the cross-attention at the final sampling step of π0.5 (\(p=50\)), the authors discover a surprising invariance: all actions within the same chunk attend to the exact same set of vision-language tokens with nearly identical weights. In other words, although the model predicts a long sequence of future actions, the later actions fail to adjust their perceptual context based on environmental changes. Instead, they repeatedly reuse static features that were useful for early actions but become increasingly outdated or even misleading for later ones. Executing these late actions is thus redundant or harmful, leading to "overconfident, poorly reactive" rollouts. (As a side note, the authors also observe an anomalously high weight on the first language token, similar to "attention sinks" in LLMs. However, masking all language tokens only slightly degrades the success rate, suggesting that the strong vision-language pre-training of the backbone has already absorbed semantic meaning into the visual representations.)

The second phenomenon is the radial action sinks: when visualizing the action self-attention, attention is strongly concentrated on the start and end action tokens. The relative strength remains high at close distances and decays sharply to a low plateau as the temporal distance increases. The authors infer that the first action, having the lowest accumulated error, serves as a natural anchor, while the first and last actions jointly maintain consistency across boundaries (arising from random start-timestamp sampling during training). These two sinks define the implicit centers around which intermediate actions are organized. Consequently, the authors offer a crucial interpretation: as long as the attention on the radial sinks remains high, the model is confident that the predicted actions align with the anchors and remain valid under the current observation; once the attention decays, the model shifts to relying on its own previously generated actions rather than true perceptual inputs. This self-referential dependency amplifies cumulative errors, degrading performance in long rollouts. Therefore, the position where the "attention decays and plateaus" marks the boundary of the VLA's reliable predictions.

3. AutoHorizon: Low-Entropy Row Filtering and Bidirectional Soft Pointers to Locate Plateau Inflection Points

With the understanding that "the inflection point is the boundary", the remaining task is to robustly extract it from the matrix. The first step is to filter noisy rows: not all rows of attention are reliable, as uniformly diffused rows do not provide structural clues. The authors use row entropy to measure this and retain only the rows with entropy below the \(q\)-quantile,

\[H_t[i]=-\frac{1}{\log p}\sum_j \mathbf{S}_t[i,j]\log \mathbf{S}_t[i,j],\qquad R_t=\{\,i\mid H_t[i]\le Q_q(H_t)\,\}\]

This leaves rows with sharper, more confident attention as reliable bases. The second step is to locate the plateau using bidirectional soft pointers. For the forward pointer, the "expected prediction horizon" of each row is first calculated as \(\mu_t[i]=\max(\sum_j j\,\mathbf{S}_t[i,j],\ \max_{k\le i}\mu_t[k])\)—which weights the column index \(j\) by attention to quantify "how far forward" the model is looking, while applying a non-decreasing constraint to prevent backtracking. Next, the increment of adjacent rows is analyzed: \(\Delta\mu_t[i]=\mu_t[i]-\mu_t[i-1]\). A sudden spike in \(\Delta\mu\) indicates a rapid shift in the attention focus, signaling the start of the plateau. Thus, the set of actions before the plateau is defined as \(P_t=\{i\mid \Delta\mu_t[i]<\tau\}\), and the forward horizon is determined as \(N_f=\lfloor \mu_t[\min(R_t\cap P_t)]\rfloor+1\). Applying the exact same operations to the flipped matrix \(\tilde{\mathbf{S}}_t\) yields the backward horizon \(N_b\) (corresponding to the boundary viewed from the tail sink).

The bidirectional formulation is necessary because the start and end sinks each define a reliable boundary. The fusion rule is as follows: if \(N_f+N_b\ge p\) (the forward and backward coverage overlaps to cover the entire chunk), the entire chunk is deemed reliable, and the full horizon is set directly to \(N=p\); otherwise, only the prefix is executed, setting \(N=N_f\). Empirically, the former scenario typically occurs when the prediction horizon \(p\) is small and the model fits short trajectories very well, whereas the latter dominates when \(p\) is large. The entire pipeline is training-free, uses fixed hyperparameters (\(q=0.9,\tau=0.3\)), and is run only once per sampling step, incurring negligible computational overhead. It naturally generalizes to any flow-based VLA.

A Complete Example¶

Take the task "putting a Rubik's cube into a bowl" executed by π0.5 (\(p=50\)) as a concrete example: first, the robot needs to reach the cube. During this phase, the environment is stable and reactivity is less critical. The forward pointer in the attention matrix propagates far before encountering a plateau, yielding a large \(N_f\). When combined with the backward \(N_b\), \(N_f+N_b\ge 50\) is satisfied, and AutoHorizon triggers full-course execution, extending the horizon to guide the robot smoothly and rapidly toward the target. When the robot begins grasping and placing (intensive physical interactions), the perceptual context changes rapidly, causing the attention to decay into a plateau early. Consequently, the forward pointer hits the inflection point at a small step count, resulting in a small \(N_f\) and \(N_f+N_b<50\). The horizon is thus shortened, forcing the policy to re-observe the environment every few steps for timely error correction. The estimated horizons over the rollout naturally adapt dynamically, fluctuating between "long-short-long-short," which a fixed horizon can never achieve.

Key Experimental Results¶

Main Results¶

Evaluations are conducted in LIBERO (single-arm) and RoboTwin (dual-arm) simulations, as well as on a real Franka robot, using π0.5 and GR00T N1.5 as backbones. The core baselines include Static Oracle (fixed horizon), Static Oracle+ (a strong but expensive baseline that performs grid searches over fixed horizons, requiring \(p\) rollouts per task), and Random (random horizon).

Dataset / Backbone	Metric	AutoHorizon	Best Fixed Horizon Baseline	Description
LIBERO-10 / π0.5 (\(p=50\))	Success Rate	92.1	91.9 (Oracle+)	The optimal point of the fixed horizon is achieved only via grid search
LIBERO-10 / π0.5 (\(p=50\))	Success Rate	92.1	68.6 (Oracle @ \(e=p\))	Errant horizon choices cause performance to drop by 23+ points
LIBERO-Object / π0.5 (\(p=50\))	Success Rate	98.0	97.6 (Oracle+)	Consistently outperforms or matches
LIBERO-10 / GR00T N1.5 (\(p=16\))	Success Rate	92.7	90.0 (Oracle+)	Cross-architecture generalization
RoboTwin·Adjust Bottle / π0.5	Success Rate	100.0	98.7 (Oracle+)	Clear advantage in horizon-sensitive tasks
Real·Cube Bowl / π0.5 (\(p=50\))	Stage Completion Rate	99.0	97.5 (Oracle+)	Comprehensive lead on real robot across three tasks

The key conclusion is that AutoHorizon consistently matches or outperforms the "grid-searched optimal fixed horizon" (Oracle+) across two backbones and three evaluation environments, without requiring the substantial rollout budget needed by the latter. When \(p=50\), Static Oracle exhibits the classic rise-then-fall unimodal curve and is frequently surpassed even by Random, underscoring the critical importance of selecting the correct horizon; in contrast, AutoHorizon consistently secures the top spot through dynamic adjustment.

Ablation Study¶

Configuration	LIBERO-10 Success Rate	Description
AutoHorizon (Full)	92.1	Dynamic chunk-by-chunk estimation
Static Oracle (\(e=\lfloor m\rfloor\))	89.1	Fixed to the floored mean of AutoHorizon's estimates
Static Oracle (\(e=\lceil m\rceil\))	91.9	Fixed to the ceiled mean, still slightly inferior
Random	83.3	Random horizon, proving structured adaptivity is effective
Action Trigger (Best \(\tau_a\))	79.6	Replanning triggered by action differences, highly sensitive to hyperparameters
Uncertainty Proxy (Best \(\tau_u\))	79.2	Sampling 4 chunks to estimate uncertainty, high computational overhead

Key Findings¶

Even when the fixed horizon is set to the mean of AutoHorizon's estimated distribution (resembling the nearest Static Oracle), the success rate is still lower than that of AutoHorizon. This demonstrates that the value lies not in merely picking a "good average horizon," but in adapting chunk-by-chunk to extreme situations during long rollouts (e.g., occasionally requiring much longer or shorter horizons), which a single fixed value cannot provide.
When the execution horizon exceeds the prediction horizon (\(e>p\)), performance drops sharply. The authors attribute this to train-test mismatch (the model has never seen trajectories longer than \(p\)), which naturally provides the upper bound \(1\le e\le p\).
High robustness to hyperparameters: across a wide range of values for attention layers \(L\), entropy quantile \(q\), and threshold \(\tau\), the success rate remains stable around 90+. The defaults \(q=0.9\) and \(\tau=0.3\) generalize well without requiring per-task tuning. In contrast, the two trigger-based replanning baselines are highly sensitive to their thresholds.
Intuitive physical behaviors are observed on the real robot: with a short horizon (\(e\in[1,5]\)), the robot frequently hesitates and pauses (due to small initial action magnitudes and insufficient progress); with a medium horizon (\(e\in[20,40]\)), it is prone to overshooting or colliding with the workbench; with a very long horizon (\(e>40\)), it struggles to maintain object alignment, leading to frequent object drops.

Highlights & Insights¶

Adapting the concept of "attention sinks"—originally used to optimize LLM inference—the authors ingeniously interpret it as a "prediction limit indicator" for VLA action sequences. The point where attention to the radial sinks decays corresponds exactly to the boundary where the model should stop execution and re-observe. This perspective of utilizing the model's own attention as a confidence measure without requiring auxiliary heads or retraining is highly elegant and transferable to any autoregressive or chunked generation task where predicting the boundary of reliability is essential.
The method is virtually cost-free: requiring no training, no model modifications, and only a single attention matrix read at one sampling step, it matches the performance of the best fixed horizon found via grid search. This provides a "free lunch" style test-time enhancement with an extremely low deployment barrier.
By first formulating a mathematically provable unimodal error model to explain "why an optimal horizon exists" and then utilizing attention profiling to explain "where the optimal point lies and how to find it," the work balances both theoretical and mechanistic insights, elevating "dynamic horizon" from an empirical trick to a well-grounded methodology.

Limitations & Future Work¶

The proposed method specifically targets the attention architecture of flow-based / diffusion-based VLAs (relying on action self-attention and radial sinks); its applicability to non-chunked or non-attention-based policies remains unverified.
Although the threshold \(\tau\) and quantile \(q\) in the bidirectional soft pointer are shown to be robust, they are still manually set hyperparameters. The heuristic "rapid change in attention increment indicates a plateau" lacks strict mathematical guarantees of optimality for the inflection point.
The upper bound \(e\le p\) stems from the train-test distribution mismatch, meaning the proposed method cannot bypass the constraints of the predicted horizon itself. To achieve longer smooth executions, one must still increase \(p\) during training.
The number of tasks (3 pick-and-place tasks) and trial counts on the real robot are relatively limited. The binary success metrics lead to high variance, and the system's robustness under more complex, long-horizon tasks warrants further investigation.

vs. BID (Bidirectional Decoding): BID demonstrates from a policy learning perspective that action chunking improves long-term consistency at the expense of short-term reactivity, utilizing rejection sampling to select the optimal chunk. This paper generalizes BID's analysis into an explicit unimodal model of cumulative rollout error. Furthermore, rather than modifying the sampling process, it estimates the horizon solely at test time, shifting the focus from "which chunk to select" to "how long to execute a chunk."
vs. RTC (Real-Time Chunking): RTC models chunk prediction as image inpainting under asynchronous execution. This work addresses the orthogonal dimension of "execution horizon" in synchronous execution, make them highly complementary.
vs. StreamingLLM / Visual Attention Sinks: StreamingLLM discovered attention sinks on initial tokens in LLMs for efficient long-text generation, while Kang et al. identified visual attention sinks on salient yet semantically irrelevant tokens in VLMs. This paper is the first to identify "radial" bidirectional sinks in VLA action sequences, attributing to them a novel functional semantic meaning as "prediction limits," rather than viewing them merely as structural tokens to be retained or redistributed.
vs. Traditional Fixed Horizon / Grid Search: Traditional VLAs rely on heuristics, control frequencies, or exhaustive grid searches to set the execution horizon. This paper uses training-free attention readings to adapt the horizon on a chunk-by-chunk basis, bypassing the cost of grid searches while acquiring a level of step-level flexibility that exceeds the theoretical limit of any fixed horizon.

Rating¶

Novelty: ⭐⭐⭐⭐⭐ This is the first work to systematically investigate the execution horizon in VLAs and interpret action self-attention sinks as prediction limits, offering a highly refreshing perspective.
Experimental Thoroughness: ⭐⭐⭐⭐ Covering two backbones, simulation and real-robot setups, diverse tasks, and comprehensive hyperparameter sensitivity analysis; real-robot tasks are somewhat limited in scale.
Writing Quality: ⭐⭐⭐⭐⭐ Clear progression from observations and theory to methodology, with excellent connections between attention visualizations and physical behaviors.
Value: ⭐⭐⭐⭐⭐ Training-free, zero-overhead, plug-and-play, and capable of matching grid-searched optimal horizons, offering high practical value for VLA deployment.