1. Bibliographic Information

1.1. Title

VLA-4D: Embedding 4D Awareness into Vision-Language-Action Models for SpatioTemporally Coherent Robotic Manipulation

The title clearly states the paper's core subject: proposing a model named VLA-4D. The model's key innovation is embedding "4D awareness" (3D space + 1D time) into Vision-Language-Action (VLA) models. The ultimate goal is to achieve robotic manipulation that is "spatiotemporally coherent," meaning actions are both spatially smooth and temporally consistent.

1.2. Authors

The authors are Hanyu Zhou, Chuanhao Ma, and Gim Hee Lee.

• Hanyu Zhou and Gim Hee Lee are affiliated with the School of Computing, National University of Singapore (NUS).
• Chuanhao Ma is affiliated with the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology.
• Gim Hee Lee is a prominent researcher in the fields of 3D computer vision, robotics, and machine learning, leading the Computer Vision and Robotic Perception (CVRP) Lab at NUS. Hanyu Zhou is a student in this lab, with a focus on 4D vision and multimodal learning.

1.3. Journal/Conference

The paper is available as a preprint on arXiv. The metadata indicates a future publication date of November 21, 2025, suggesting it has been submitted or is being prepared for submission to a major conference in computer vision or robotics (e.g., CVPR, ICCV, CoRL, ICRA). As a preprint, it has not yet undergone formal peer review.

1.4. Publication Year

The paper was submitted to arXiv with a 2025 date, which likely serves as a placeholder for a future conference publication. The content reflects research conducted in 2024.

1.5. Abstract

The abstract introduces the problem that existing Vision-Language-Action (VLA) models, while promising for general robotics, struggle with tasks requiring spatiotemporally coherent manipulation. Current methods often enhance spatial precision by embedding 3D positions but fail to achieve temporally coherent control. To address this, the authors propose VLA-4D, a model built on two key designs. First, a 4D-aware visual representation is created by embedding time into 3D positions and fusing these 4D embeddings with visual features using cross-attention. Second, a spatiotemporal action representation extends conventional spatial actions with temporal information, enabling the model to plan and predict actions in both space and time. The authors also extended a VLA dataset with temporal annotations to train their model. Experiments demonstrate that VLA-4D outperforms existing methods in robotic manipulation tasks.

1.6. Original Source Link

• Original Source Link: https://arxiv.org/abs/2511.17199
• PDF Link: https://arxiv.org/pdf/2511.17199v1.pdf
• Publication Status: This is a preprint and has not yet been peer-reviewed or officially published in a conference or journal.

2. Executive Summary

2.1. Background & Motivation

The core problem addressed by this paper is the lack of spatiotemporal coherence in robotic manipulation performed by modern Vision-Language-Action (VLA) models. While these models can interpret high-level language commands and visual scenes to generate actions, their control is often imprecise.

• Existing Challenges:

  1. 2D VLA Models: Models that rely solely on 2D images suffer from a mismatch between the 2D pixel space and the 3D robot workspace. This leads to coarse visual reasoning and spatially imprecise actions.
  2. 3D VLA Models: To improve spatial precision, many models incorporate 3D positional information (e.g., point clouds) into their visual representations. This helps generate spatially smooth trajectories. However, they lack an explicit understanding of time, often resulting in temporally incoherent behaviors like unnatural pauses, jittery movements, or inconsistent speeds.

• Gap in Prior Research: Previous works, even those labeled "4D," primarily focused on embedding temporal information into the visual representation to help the model better understand scene dynamics. However, they did not explicitly equip the model with the ability to control the temporal dimension of the action itself. Action planning remained largely spatial.

• Paper's Entry Point: The innovative idea of VLA-4D is to embed 4D awareness into the VLA framework dually:

  1. In Perception: Enhance the visual representation with both 3D spatial and 1D temporal information for a richer understanding of the scene.

  2. In Action: Enhance the action representation itself to include an explicit temporal control parameter, allowing the model to decide not just where to move but also how long each movement step should take.

     This dual enhancement of both "what the robot sees" and "what the robot does" is the key to achieving actions that are both spatially smooth and temporally fluid.

2.2. Main Contributions / Findings

The paper presents four main contributions:

1. A Novel VLA-4D Framework: The authors propose VLA-4D, a general VLA model designed specifically for spatiotemporally coherent robotic manipulation. It uniquely embeds spatiotemporal information into both visual perception and action planning modules.

2. 4D-Aware Visual Representation: A new visual representation is designed that explicitly fuses 3D geometric positions and 1D temporal information (timestamps) into standard visual features. This is achieved via a cross-attention mechanism, enabling the model to perform fine-grained spatiotemporal reasoning about the scene.

3. Spatiotemporal Action Representation: The paper introduces a novel action representation that augments conventional spatial control parameters (translation, rotation, gripper state) with an additional temporal control variable ($Δt$). This allows the Large Language Model (LLM) core to plan actions that are coherent in both space and time, improving smoothness and efficiency.

4. Dataset Extension and SOTA Performance: The authors extended the existing LIBERO robotics dataset with temporal action annotations to facilitate the training of their model. Extensive experiments show that VLA-4D achieves state-of-the-art performance, outperforming 2D, 3D, and prior 4D VLA models in both task success rate and completion time.

3. Prerequisite Knowledge & Related Work

3.1. Foundational Concepts

3.1.1. Vision-Language Models (VLMs)

A Vision-Language Model (VLM) is a type of AI model designed to understand and process information from both visual (images, videos) and textual modalities simultaneously. A typical VLM architecture consists of:

• A vision encoder (e.g., a Vision Transformer or ViT) that converts an image into a set of numerical feature vectors (embeddings).
• A text encoder (part of the LLM) that converts a text prompt into embeddings.
• A Large Language Model (LLM) backbone (e.g., LLaMA, GPT) that processes the combined visual and text embeddings to perform tasks like visual question answering, image captioning, or object detection based on text queries. The key is aligning the visual and language feature spaces so the LLM can "see."

3.1.2. Vision-Language-Action (VLA) Models

A Vision-Language-Action (VLA) model is a specialized VLM adapted for robotics. It extends the VLM paradigm by adding an "action" component.

• Input: A VLA takes visual input from the robot's cameras (e.g., images, video), a language command (e.g., "pick up the red block"), and often the robot's own state (proprioception, like joint angles).

• Output: It generates a sequence of actions for the robot to execute. These actions are typically represented as a series of numerical values (e.g., end-effector displacement, rotation, gripper state), which are often discretized and "tokenized" so the LLM can predict them like text.

• Goal: To ground language commands in visual reality and translate them into physical manipulation. The following figure from the paper illustrates the evolution of VLA architectures.

  该图像是示意图，展示了3种不同的VLA模型架构：2D VLA（图a）、3D VLA（图b）和4D VLA（图c）。这些模型通过不同的编码方式实现机器人的时空一致性操作。4D VLA模型提取了视频数据，增强了时序信息，使得操作更加流畅和连贯。

3.1.3. Cross-Attention

Cross-attention is a mechanism, central to Transformer architectures, that allows a model to weigh the importance of different parts of one sequence when processing another. In this paper, it is used to fuse the 4D spatiotemporal embeddings into the visual features.

• Mechanism: It involves three vectors: Query (Q), Key (K), and Value (V). The Query sequence "asks" for relevant information from the Key-Value pair sequence. The relevance is calculated as the dot product between a Query and all Keys.
• Formula: The core attention calculation is: $ \mathrm{Attention}(Q, K, V) = \mathrm{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V $
• Symbol Explanation:
  • $Q$: The Query matrix, representing the sequence that is seeking information. In this paper, this is derived from the visual features $f_v$.
  • $K$: The Key matrix, representing the sequence that provides information. Here, it is derived from the 4D spatiotemporal embeddings $\hat{f}_{4D}$.
  • $V$: The Value matrix, also derived from the 4D spatiotemporal embeddings $\hat{f}_{4D}$. This is the information that gets aggregated.
  • $d_k$: The dimension of the key vectors. The division by $\sqrt{d_k}$ is a scaling factor to stabilize gradients during training.
  • softmax: A function that converts the attention scores (the dot products) into a probability distribution, ensuring the weights sum to 1.

3.1.4. Fourier Features for Positional Encoding

Neural networks, especially Transformers, do not inherently understand the order or position of elements in a sequence. Positional encodings are added to input embeddings to provide this information. When dealing with continuous coordinates like 3D positions or time, sinusoidal functions (sines and cosines) of different frequencies are a powerful way to create unique positional signatures. This paper uses a learnable version known as Fourier features. The model learns to map a continuous input coordinate to a high-dimensional feature vector that represents its position uniquely and allows the model to easily reason about relative positions.

3.2. Previous Works

The paper categorizes related VLA models into three groups:

• 2D VLA Models (OpenVLA, Octo, DiffusionPolicy): These models use standard 2D images as their primary visual input. While effective for some tasks, they struggle with spatial precision because they have to implicitly learn the 3D structure of the world from 2D projections, which is difficult and can lead to inaccurate actions.

• 3D VLA Models (TraceVLA, SpatialVLA): These models improve upon 2D VLAs by explicitly incorporating 3D information. They typically take 3D data (like point clouds from depth sensors) as input and embed 3D positional information directly into the visual features. This helps align the visual understanding with the robot's 3D action space, leading to spatially smoother trajectories. However, they lack a notion of time, which can cause them to execute actions with inconsistent timing, resulting in jerky movements or idle pauses.

• 4D VLA Models (4D-VLA [Zhang et al., 2025]): These are the most closely related works. They recognize the need for temporal information and integrate it into the visual representation. For example, they might encode frame indices or learn 4D point trajectories from videos. While this improves the model's ability to reason about scene dynamics and temporal states (e.g., understanding which state comes before another), the authors of VLA-4D argue that this is insufficient. These models still output purely spatial actions, lacking direct control over the temporal execution of the action plan.

3.3. Technological Evolution

The evolution of VLA models reflects a progressive effort to provide more comprehensive world representations for robotic control:

1. 2D VLA: Grounding language in 2D images.
2. 3D VLA: Adding explicit 3D spatial awareness to improve action precision.
3. Prior 4D VLA: Adding explicit 1D temporal awareness to the visual input to improve understanding of dynamics.
4. VLA-4D (This paper): The proposed next step, which not only adds 4D awareness to the visual input but also adds temporal control to the action output, creating a fully spatiotemporal perception-action loop.

3.4. Differentiation Analysis

The core difference between VLA-4D and all previous works, including other 4D models, lies in its dual spatiotemporal enhancement:

• Previous 4D Models: Enhance perception only. They create a 4D visual representation but still command a 3D (spatial) action space. The model learns to act in response to temporal dynamics but cannot plan its own temporal dynamics.
• VLA-4D: Enhances perception AND action. It creates a 4D visual representation and explicitly adds a temporal dimension ($Δt$) to the action space. This allows the LLM to decide not just the what and where of an action, but also the how long, enabling true spatiotemporally coherent planning.

4. Methodology

The VLA-4D model is designed to achieve spatiotemporally coherent robotic manipulation. Its architecture, shown in the figure below, is guided by two key stages: 1) creating a 4D-Aware Visual Representation and 2) formulating a Spatiotemporal Action Representation.

该图像是一个示意图，展示了VLA-4D模型的架构。模型通过提取视觉特征并使用交叉注意机制融合4D嵌入，以实现时空一致的机器人操控。左侧显示了机器人平台及其感知信息的编码过程，右侧则呈现了将输入语言指令转化为动作令牌的流程。

4.1. Principles

The guiding principle of VLA-4D is that to achieve coherent manipulation, a robot needs to reason about and act in a 4D (3D space + 1D time) world. This requires enriching both the model's perceptual understanding and its action planning capabilities with spatiotemporal information.

• For Vision: Simply seeing a static image is not enough. The model needs to understand the 3D geometry of the scene and how it changes over time.
• For Action: Simply deciding the next position is not enough. The model needs to decide how quickly or slowly to execute the movement to that position to ensure fluid motion.

4.2. Core Methodology In-depth (Layer by Layer)

The overall workflow starts with a video sequence and a language instruction. These are processed to generate a sequence of spatiotemporal actions.

4.2.1. 4D-Aware Visual Representation (Sec 3.1)

This stage enhances the model's visual perception with 4D awareness. It involves two main steps: spatiotemporal embedding and cross-attention fusion. The figure below illustrates the benefit of using 4D representation over 2D or 3D.

该图像是示意图，展示了在机器人操控任务中，2D、3D和4D视觉语言模型的视觉推理和动作规划过程。不同维度的视觉信息影响机器人的动作执行，3D空间信息增强场景几何理解，而1D时间信息确保动态感知和时间状态的协调。

4.2.1.1. 4D SpatioTemporal Embedding

The goal here is to create a feature representation that captures the geometry and timing of the scene.

1. Geometric Projection (3D Position Extraction): To overcome the 2D-3D coordinate mismatch, the model first projects 2D pixel coordinates into the 3D world (or robot) coordinate system. For a given pixel $p_{2D}$ at a timestamp $t$, the model uses a geometry encoder (VGGT) to obtain the camera's extrinsic pose $P$ and the depth map $D$. Using the camera's intrinsic parameters $K$, the 3D position $p_{3D}$ is calculated as: $ p_{3D} = P^{-1} (D K^{-1} p_{2D}) $

   • Symbol Explanation:
     • $p_{2D}$: The 2D coordinate of a pixel in the image.
     • $K^{-1}$: The inverse of the camera intrinsic matrix, which maps pixel coordinates to camera-space rays.
     • $D$: The depth value at that pixel, obtained from a depth sensor or estimated.
     • $P^{-1}$: The inverse of the camera pose matrix (extrinsic parameters), which transforms coordinates from the camera's frame to the world's frame.

2. Spatiotemporal Encoding (STE): After obtaining 3D positions for points across all video frames, the model integrates this with temporal information. It uses a learnable Fourier-based encoding strategy to convert the continuous 3D position vectors $p_{3D}$ and 1D timestamps $t$ into high-dimensional embeddings. The encoding function for a continuous value $x$ is: $ \psi ( x ) = 1 / \sqrt { d } \ [ cos ( x W _ { r } ^ { \top } ) \ | | \ sin ( x W _ { r } ^ { \top } ) ] $

   • Symbol Explanation:

     • $x$: The input coordinate (either a position $p_{3D}$ or a time $t$).

     • $W_r$: A learnable frequency matrix. This allows the model to learn the most effective frequencies for encoding position and time.

     • $d$: The dimension of the output features.

     • ||: Concatenation operation.

       The final 4D embedding $f_{4D}$ is created by encoding both position and time and then projecting them with a linear layer: $ f_{4D} = w_p \cdot \left[ \psi ( p_{3D} ) \parallel \psi ( t ) \right] $

   • Symbol Explanation:
     • $\psi(p_{3D})$: The Fourier features for the 3D position.
     • $\psi(t)$: The Fourier features for the timestamp.
     • $w_p$: A learnable weight matrix for the final linear projection.

4.2.1.2. Cross-Attention Fusion

Now, the semantic visual features must be fused with the 4D spatiotemporal geometric features.

1. Visual Feature Extraction: A vision encoder (a ViT variant from Qwen2.5-VL-7B) processes the input video frames to extract high-level semantic visual features, denoted as $f_v$.

2. Fusion: The 4D embeddings $f_{4D}$ are first projected by an MLP to match the dimension of the visual features: $\hat{f}_{4D} = \mathrm{MLP}(f_{4D})$. Then, a cross-attention mechanism fuses $\hat{f}_{4D}$ into $f_v$. Here, the visual features $f_v$ act as the query, seeking to enrich themselves with spatiotemporal context from the 4D embeddings $\hat{f}_{4D}$, which provide the keys and values. $ q = w_q f_v, \quad k = w_k \hat{f}{4D}, \quad v = w_v \hat{f}{4D} $ $ f_v^{4D} = f_v + \mathrm{softmax} ( \frac{q k^{\top}}{\sqrt{d}} ) v $

   • Symbol Explanation:
     • $f_v$: The original visual features (query).
     • $\hat{f}_{4D}$: The dimension-aligned 4D spatiotemporal embeddings (source for key and value).
     • $w_q, w_k, w_v$: Learnable weight matrices to project $f_v$ and $\hat{f}_{4D}$ into query, key, and value spaces.
     • $f_v^{4D}$: The final unified visual representation, now aware of 4D semantics and geometry. The addition represents a residual connection, which is standard in Transformer blocks.

4.2.2. SpatioTemporal Action Representation (Sec 3.2)

This stage extends action planning into the spatiotemporal domain to ensure coherent execution. The figure below illustrates the concept.

该图像是示意图，展示了时空动作表示的过程。左侧展示了机器人的操作环境，中心和右侧分别描绘了两种不同的动作轨迹，分别对应于"violent motion"和"smooth motion"，反映了空间参数与时间参数对动作规划及执行一致性的影响。

4.2.2.1. Spatiotemporal Action Definition

Conventional models only predict spatial actions. This paper argues that adding a temporal parameter is crucial for coherence.

• Conventional Spatial Action ($X$): $X = [\Delta x, \Delta \theta, Grip]$
  • $\Delta x$: The translational displacement of the robot's end-effector.
  • $\Delta \theta$: The rotational change in the end-effector's orientation.
  • Grip: A binary signal for opening or closing the gripper.
• Proposed Temporal Action ($T$): $T = \Delta t$
  • $\Delta t$: A continuous variable representing the duration for executing the current action step. This is not a fixed value but is predicted by the model based on the visual scene, language command, and robot state.
• Final Spatiotemporal Action ($A$): $A = [\Delta x, \Delta \theta, Grip, \Delta t]$

4.2.2.2. Multimodal Alignment and Optimization

To predict this spatiotemporal action, the model aligns all input modalities and learns a mapping function.

1. Multimodal Alignment: The 4D-aware visual features $f_v^{4D}$ and the robot's proprioceptive state features $f_p$ (e.g., joint angles, gripper velocity) are projected into the LLM's language embedding space using MLPs. This converts them into "visual tokens" $\tau_v^{4D}$ and "proprioceptive tokens" $\tau_p$. The language instruction is also tokenized into linguistic tokens $\tau_l$. $ \tau_v^{4D} = \mathrm{MLP}(f_v^{4D}), \quad \tau_p = \mathrm{MLP}(f_p) $

2. Task Optimization: The tokens are concatenated ($[\tau_v^{4D}, \tau_p, \tau_l]$) and fed into a pretrained LLM ($\mathcal{T}(\cdot)$), followed by an MLP-based action head ($\mathcal{H}(\cdot)$) that predicts the final spatiotemporal action vector. $ [\Delta x, \Delta \theta, Grip, \Delta t] = \mathcal{H}(\mathcal{T}([\tau_v^{4D}, \tau_p, \tau_l])) $

3. Loss Function: The model is trained to minimize the difference between its predicted actions and the ground-truth actions from the dataset. An L1-norm loss is used for this regression task. $ \mathcal{L}_{action} = \sum (\lvert \Delta x - \tilde{\Delta x} \rvert_1 + \lvert \Delta \theta - \tilde{\Delta \theta} \rvert_1 + \lvert Grip - G\tilde{r}ip \rvert_1 + \lvert \Delta t - \tilde{\Delta t} \rvert_1) $

   • Symbol Explanation:
     • Variables with a tilde ($\tilde{\cdot}$), such as $\tilde{\Delta x}$, denote the ground-truth values from the demonstration data.
     • $\lvert \cdot \rvert_1$ denotes the L1 norm (sum of absolute differences), which is less sensitive to outliers compared to the L2 norm (squared error).

4.2.3. Training Pipeline (Sec 4.2)

The model is trained in a two-stage process to leverage large-scale pretraining and specialized fine-tuning.

• Stage 1: 4D Vision-Language Alignment: The VLM component of the model is pretrained on several large-scale 3D and 4D vision-language datasets (e.g., Scan2Cap, Chat4D). The goal is to teach the model strong 4D spatiotemporal perception and reasoning capabilities before it ever sees a robotic task. In this stage, the vision and geometry encoders are frozen, and only the fusion modules and LLM (via LoRA adapters) are trained.

• Stage 2: Robotic Task Fine-Tuning: The entire VLA-4D architecture is fine-tuned on the custom-annotated LIBERO dataset. The model learns to map its 4D visual understanding to the spatiotemporal action space. The training uses the $\mathcal{L}_{action}$ loss. In this stage, most of the pretrained modules are frozen, and only the action head, projector, and LoRA adapters are updated.

5. Experimental Setup

5.1. Datasets

The primary dataset used for training and evaluation is LIBERO, an existing benchmark for lifelong robot learning.

• Source and Characteristics: LIBERO is a simulation suite containing tasks categorized into four benchmarks: LIBERO-Spatial (spatial reasoning), LIBERO-Object (object understanding), LIBERO-Goal (diverse goals), and LIBERO-Long (long-horizon tasks).
• Dataset Extension: The original LIBERO dataset was not suitable for training a 4D model out-of-the-box. The authors extended it by:
  1. Rendering the existing human-designed trajectories in a simulator to generate multi-view videos with timestamps, depth maps, and camera parameters.
  2. Manually annotating temporal actions ($Δt$). They identified "action chunks" with consistent motion trends and converted the number of simulation steps in each chunk into a continuous time duration $Δt$, based on the simulation's sampling frequency.
• Final Dataset Scale: After processing, the final dataset contains 40 subtasks and a total of 150,000 paired vision-language-action samples.
• Reason for Choice: LIBERO provides a diverse set of manipulation tasks, making it a comprehensive benchmark for evaluating the generalizability and coherence of robotic policies.

5.2. Evaluation Metrics

The performance of the models is evaluated using two primary metrics:

5.2.1. Task Success Rate (SR)

• Conceptual Definition: This metric measures the effectiveness of the policy. It is the percentage of trials where the robot successfully completes the task as defined by the benchmark's criteria. A higher success rate is better.
• Mathematical Formula: $ \text{SR} (%) = \frac{\text{Number of Successful Trials}}{\text{Total Number of Trials}} \times 100 $
• Symbol Explanation:
  • Number of Successful Trials: The count of runs where the task goal was achieved.
  • Total Number of Trials: The total number of attempts made for a given task.

5.2.2. Completion Time (CT)

• Conceptual Definition: This metric measures the efficiency and temporal coherence of the policy. It is the total time (in seconds) taken to complete a task successfully. A lower completion time is better, as it indicates a more direct and less hesitant (i.e., more coherent) execution.
• Mathematical Formula: This is a direct measurement, not a ratio. $ \text{CT} = T_{end} - T_{start} $
• Symbol Explanation:
  • $T_{start}$: The timestamp when the task execution begins.
  • $T_{end}$: The timestamp when the task is successfully completed.

5.3. Baselines

The proposed VLA-4D model is compared against a representative set of state-of-the-art VLA models, categorized by their visual input dimensionality:

• 2D VLA Models:
  • OpenVLA
  • Octo
  • CogACT
  • DiffusionPolicy
• 3D VLA Models:
  • TraceVLA
  • SpatialVLA
• 4D VLA Models:

  • 4D-VLA (Zhang et al., 2025)

    These baselines are representative because they cover the main paradigms in recent VLA research, allowing for a clear comparison of how adding spatial and temporal awareness at different levels impacts performance.

6. Results & Analysis

6.1. Core Results Analysis

The main results, comparing VLA-4D against baselines on the fine-tuned LIBERO benchmark, are presented in Table 1.

The following are the results from Table 1 of the original paper:

• Analysis:
  • Dimensionality Matters: There is a clear trend where performance improves with increased dimensionality. 3D models generally outperform 2D models, and 4D models significantly outperform both. For instance, the average success rate jumps from ~72-78% for 2D/3D models to 88.6% for 4D-VLA and an impressive 97.4% for VLA-4D.
  • VLA-4D Dominance: The proposed VLA-4D model is the undisputed top performer across all task categories. It achieves the highest success rates and, crucially, the lowest completion times. For example, in the LIBERO-Long benchmark, it achieves a 94.8% success rate, a massive improvement over the next best (4D-VLA at 79.1%) and more than 40 percentage points higher than some 2D models.
  • Efficiency Gain: The low completion times of VLA-4D (e.g., 5.8s on average vs. 6.8-8.7s for others) strongly support the paper's central claim: explicitly modeling and controlling temporal aspects of actions leads to more efficient and coherent manipulation.

6.2. Comparison on Zero-Shot Tasks

The following figure from the paper shows the generalization performance on unseen tasks.

该图像是一个图表，展示了不同 VLA 模型在零-shot 机器人操作任务中的成功率（SR）和完成时间（CT）的定量比较。模型包括 OpenVLA、Octo、CogACT、SpatialVLA 和 VLA-4D（我们的模型），结果表明 VLA-4D 在成功率和完成时间方面表现优异。

• Analysis: VLA-4D demonstrates superior zero-shot generalization. In all three unseen tasks shown, it achieves a significantly higher success rate and lower completion time compared to other representative models. This suggests that the learned spatiotemporal representations are robust and can be effectively applied to new manipulation scenarios without task-specific fine-tuning.

6.3. Qualitative Comparison on SpatioTemporal Planning

The following figure visualizes the robot arm trajectories and speeds predicted by different models.

该图像是一个插图，展示了不同 VLA 模型在时间空间动作规划上的视觉比较，包括 OpenVLA、SpatialVLA 和我们提出的 VLA-4D。图中呈现的路径和运动速度曲线显示了在相同机器人任务中，各模型之间在轨迹和动作控制上的差异。

• Analysis:
  • 2D VLA (OpenVLA): The trajectory is inefficient with redundant global motion, and the local motion speed fluctuates wildly, indicating a lack of coherence.
  • 3D VLA (SpatialVLA): The global trajectory is much smoother, demonstrating the benefit of 3D spatial awareness. However, the local motion speed is still unstable and jittery.
  • 4D VLA (VLA-4D): The model produces a trajectory that is both spatially smooth (globally) and temporally stable (locally). The motion speed is consistent, without the pronounced oscillations seen in other models. This visualization provides compelling qualitative evidence for the "spatiotemporal coherence" that VLA-4D achieves.

6.4. Ablation Studies / Parameter Analysis

6.4.1. Effect of Visual Representation Modules

The following are the results from Table 2 of the original paper:

• Analysis: This ablation clearly shows the contribution of each component of the 4D-aware visual representation.
  • Adding spatial embedding ($√, ×, ×$) provides a significant boost over the baseline (×, ×, ×).
  • Adding temporal embedding on top ($√, √, ×$) further improves both success rate and completion time.
  • Finally, using cross-attention for feature fusion ($√, √, √$) provides the last push to reach peak performance. Each component is essential.

6.4.2. Effect of Action Representation Components

The following are the results from Table 3 of the original paper:

• Analysis: This is a crucial ablation that validates the second key idea of the paper. Adding the temporal parameter $Δt$ to the action space results in a slight improvement in success rate but a dramatic reduction in completion time (e.g., from 5.0s to 4.1s in LIBERO-Spatial). This confirms that spatial parameters are foundational for what the robot does, while temporal parameters are key to improving the efficiency and coherence of how it does it.

6.4.3. Influence of Input Modality

The following are the results from Table 4 of the original paper:

• Analysis: The most significant performance jump occurs when 4D cues (the proposed spatiotemporal embeddings) are introduced. The success rate leaps from ~90% to ~97%. Using video over a single image provides a moderate benefit, and adding proprioceptive state feedback provides a final, small improvement. This shows that the proposed 4D visual representation is the primary driver of the model's high performance.

6.4.4. Impact of Training Strategy

The following are the results from Table 7 of the original paper:

• Analysis: The two-stage training strategy (Stage 1 + Stage 2) is vastly superior to directly fine-tuning on the robotics dataset (Only Stage 2). This demonstrates the value of pre-training the vision-language components on large-scale 4D datasets to build a strong foundation for spatiotemporal reasoning, which then transfers effectively to the downstream robotic manipulation task.

7. Conclusion & Reflections

7.1. Conclusion Summary

The paper successfully identifies and addresses a key limitation in existing VLA models: the lack of spatiotemporal coherence. The authors propose VLA-4D, a novel model that embeds 4D awareness into both its perceptual and planning modules. By designing a 4D-aware visual representation that fuses semantic and spatiotemporal geometric information, and a spatiotemporal action representation that gives the model explicit control over the timing of its actions, VLA-4D achieves a new level of performance. Supported by extensive experiments on a newly extended dataset, the paper demonstrates that this dual enhancement leads to robotic manipulation that is not only more successful but also significantly more efficient and fluid.

7.2. Limitations & Future Work

The authors acknowledge one primary limitation: the potential difficulty of deploying VLA-4D in unseen real-world environments. While the model performs well in simulation, the real world introduces unpredictable factors such as:

• Mechanical wear and calibration drift: Physical changes in the robot over time can introduce errors that the simulation model is not trained to handle.

• Domain gap: Differences in lighting, object textures, and physics between simulation and reality can degrade performance.

  As a direction for future work, the authors propose incorporating reinforcement learning (RL). An RL-based approach could be used to fine-tune the model online, allowing it to adapt to these real-world uncertainties and correct errors in its predicted spatiotemporal actions, leading to more robust and adaptive planning.

7.3. Personal Insights & Critique

This paper presents a clear, logical, and effective solution to a well-defined problem. Its strengths are numerous:

• Conceptual Clarity: The core idea of dually enhancing both perception and action with spatiotemporal information is intuitive and powerful. It addresses the problem holistically rather than focusing on just one part of the pipeline.

• Simplicity and Effectiveness: The introduction of a single temporal parameter $Δt$ into the action space is a simple yet highly effective modification that yields significant performance gains in temporal coherence.

• Rigorous Evaluation: The paper's strength is significantly boosted by its thorough experiments, including comparisons with a wide range of baselines, extensive ablation studies that validate each design choice, and insightful qualitative visualizations.

  Potential areas for reflection or critique include:

• Temporal Annotation Process: The paper states that the temporal action annotations ($Δt$) were created by "manually" selecting action chunks. This process could introduce human bias or result in suboptimal temporal segmentation. Future work could explore methods for automatically learning this segmentation from demonstration videos, perhaps using change-point detection or other unsupervised techniques.

• Nature of $Δt$: The paper successfully shows that controlling $Δt$ improves coherence. However, $Δt$ is a "step-level" duration. For truly fluid, human-like motion, a more continuous representation of velocity or acceleration profiles might be even more effective than a sequence of constant-velocity steps with varying durations.

• Sim-to-Real Gap: As the authors note, the sim-to-real gap is a major challenge. While RL is a promising direction, the sample inefficiency of many RL algorithms could make real-world training difficult. Combining the imitation learning approach of this paper with more sample-efficient RL techniques or advanced domain randomization methods will be crucial for practical deployment.

  Overall, VLA-4D represents a significant step forward in robotic manipulation. It convincingly argues for and demonstrates the importance of making VLA models not just spatially aware, but fully spatiotemporally aware in both perception and action. Its elegant methodology and strong results provide a solid foundation for future research in creating more intelligent and capable robots.