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vla-4d-spatiotemporal Enhance VLA models with spatiotemporal awareness by embedding both 3D spatial coordinates and temporal sequences: predict actions that include temporal parameters (duration) alongside spatial movements, achieving 97.4% robotic manipulation success by grounding reasoning in coherent 4D representations.
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name vla-4d-spatiotemporal title VLA-4D: Embedding 4D Awareness into VLA Models version 0.0.2 engine skillxiv-v0.0.2-claude-opus-4.6 license MIT url https://arxiv.org/abs/2511.17199 keywords ["Vision-Language-Action","Robotics","Spatiotemporal Reasoning","4D Perception","Manipulation"] description Enhance VLA models with spatiotemporal awareness by embedding both 3D spatial coordinates and temporal sequences: predict actions that include temporal parameters (duration) alongside spatial movements, achieving 97.4% robotic manipulation success by grounding reasoning in coherent 4D representations.
VLA-4D: Spatiotemporal Aware Robotic Manipulation
Standard vision-language-action models predict spatial movements but lack temporal understanding, making robots execute incoherent sequences of actions with temporal discontinuities. This skill demonstrates how to extend VLAs with 4D awareness—explicitly reasoning about both 3D space and 1D time—enabling robots to perform spatiotemporally coherent manipulation requiring fine-grained timing and smooth motion trajectories.
The core innovation is augmenting action spaces to include temporal parameters and grounding visual representations in explicit 4D coordinates, enabling models to understand when actions should occur, not just where.
Core Concept
VLA-4D implements 4D awareness through:
4D Visual Representation : Encodes both 3D spatial positions and temporal sequences from videoSpatiotemporal Action Space : Actions include temporal parameters (duration) alongside spatial controlTemporal Grounding : Time-aware visual features enabling smooth action executionCross-Attention Fusion : Integrates spatial and temporal information via attention mechanisms
Architecture Overview
Video Encoder : Extracts spatiotemporal features from observation sequences4D Feature Embedding : Maps 3D coordinates + time into unified representation spaceSpatial Action Head : Predicts movement vectors (Δx, Δy, Δz), rotation (Δθ), gripper stateTemporal Action Head : Predicts action duration (Δt) and timingCoherence Decoder : Ensures temporal continuity between sequential actions
Implementation Steps
The system extends standard VLA architectures with temporal reasoning.
1. Build Video Encoder for Spatiotemporal Features
Extract both spatial and temporal information from observation sequences.
class SpatiotemporalVideoEncoder (torch.nn.Module):
"""
Encodes video sequences into spatiotemporal features.
Captures both spatial structure and temporal dynamics.
"""
def __init__ (self, hidden_dim=768 , num_frames=8 ):
super ().__init__()
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def
forward
self, video_frames
"""
Encode video into spatiotemporal features.
Args:
video_frames: (batch, num_frames, 3, height, width)
Returns:
spatiotemporal_features: (batch, num_frames, height, width, hidden_dim)
"""
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2. Implement 4D Feature Embedding
Embed 3D coordinates and temporal information into unified 4D representation space.
class FourDFeatureEmbedding (torch.nn.Module):
"""
Maps 3D spatial coordinates + time into 4D embedding space.
Enables spatiotemporal grounding of visual features.
"""
def __init__ (self, hidden_dim=768 , max_time=10.0 ):
super ().__init__()
self .hidden_dim = hidden_dim
self .max_time = max_time
self .spatial_pos_embed = torch.nn.Linear(3 , hidden_dim // 2 )
self .temporal_pos_embed = torch.nn.Linear(1 , hidden_dim // 2 )
self .fusion_layer = torch.nn.Linear(hidden_dim, hidden_dim)
def embed_4d_position (self, x, y, z, t ):
"""
Embed 3D position + time into 4D space.
Args:
x, y, z: Spatial coordinates (batch, seq_len)
t: Temporal coordinate (batch, seq_len)
Returns:
embedding: (batch, seq_len, hidden_dim) 4D embedding
"""
spatial_coords = torch.stack([x, y, z], dim=-1 )
spatial_embedding = self .spatial_pos_embed(spatial_coords)
t_normalized = t.unsqueeze(-1 ) / self .max_time
temporal_embedding = self .temporal_pos_embed(t_normalized)
combined = torch.cat([spatial_embedding, temporal_embedding], dim=-1 )
embedding = self .fusion_layer(combined)
return embedding
def forward (self, visual_features, spatial_coords, temporal_coords ):
"""
Integrate visual features with 4D positional information.
Args:
visual_features: (batch, height, width, hidden_dim)
spatial_coords: (batch, height, width, 3) 3D coordinates
temporal_coords: (batch, height, width) time values
Returns:
grounded_features: (batch, height, width, hidden_dim) 4D-grounded features
"""
batch, h, w, _ = visual_features.shape
spatial_flat = spatial_coords.reshape(batch, -1 , 3 )
temporal_flat = temporal_coords.reshape(batch, -1 )
pos_embedding = self .embed_4d_position(
spatial_flat[:, :, 0 ], spatial_flat[:, :, 1 ], spatial_flat[:, :, 2 ],
temporal_flat
)
pos_embedding = pos_embedding.reshape(batch, h, w, -1 )
grounded_features = visual_features + pos_embedding
return grounded_features
3. Implement Spatiotemporal Action Head
Predict 4D actions including spatial movements and temporal duration.
class SpatiotemporalActionHead (torch.nn.Module):
"""
Predicts robot actions in 4D: (Δx, Δy, Δz, Δθ, gripper, Δt)
Temporal parameter enables coherent action sequencing.
"""
def __init__ (self, hidden_dim=768 ):
super ().__init__()
self .action_backbone = torch.nn.Sequential(
torch.nn.Linear(hidden_dim, hidden_dim),
torch.nn.ReLU(),
torch.nn.Linear(hidden_dim, hidden_dim // 2 ),
torch.nn.ReLU()
)
self .spatial_head = torch.nn.Sequential(
torch.nn.Linear(hidden_dim // 2 , 4 ),
torch.nn.Tanh()
)
self .gripper_head = torch.nn.Sequential(
torch.nn.Linear(hidden_dim // 2 , 1 ),
torch.nn.Sigmoid()
)
self .temporal_head = torch.nn.Sequential(
torch.nn.Linear(hidden_dim // 2 , 1 ),
torch.nn.Softplus()
)
def forward (self, features ):
"""
Predict 4D action from visual features.
Args:
features: (batch, hidden_dim)
Returns:
actions: Dict with spatial, gripper, temporal components
"""
backbone_out = self .action_backbone(features)
spatial_action = self .spatial_head(backbone_out)
gripper_action = self .gripper_head(backbone_out)
temporal_action = self .temporal_head(backbone_out)
delta_xyz = spatial_action[:, :3 ] * 0.1
delta_theta = spatial_action[:, 3 ] * np.pi
actions = {
'position_delta' : delta_xyz,
'rotation_delta' : delta_theta,
'gripper' : gripper_action.squeeze(-1 ),
'duration' : temporal_action.squeeze(-1 )
}
return actions
4. Build Complete 4D VLA Model
Integrate video encoder, 4D grounding, and action heads.
class VLA4D (torch.nn.Module):
"""
Vision-Language-Action model with 4D spatiotemporal awareness.
Predicts robot actions with explicit temporal parameters.
"""
def __init__ (self, language_model_name='bert-base-uncased' , hidden_dim=768 ):
super ().__init__()
self .hidden_dim = hidden_dim
self .video_encoder = SpatiotemporalVideoEncoder(hidden_dim=hidden_dim)
self .four_d_embedding = FourDFeatureEmbedding(hidden_dim=hidden_dim)
self .language_model = AutoModel.from_pretrained(language_model_name)
self .fusion_attention = torch.nn.MultiheadAttention(
hidden_dim, num_heads=8 , batch_first=True
)
self .action_head = SpatiotemporalActionHead(hidden_dim=hidden_dim)
def forward (self, video_frames, language_input_ids, spatial_coords=None , temporal_coords=None ):
"""
Predict 4D robot action from video and language instruction.
Args:
video_frames: (batch, num_frames, 3, height, width)
language_input_ids: (batch, lang_seq_len) tokenized instruction
spatial_coords: (batch, num_frames, height, width, 3) optional 3D coordinates
temporal_coords: (batch, num_frames, height, width) optional time values
Returns:
actions: Dict with 4D action components
"""
video_features = self .video_encoder(video_frames)
if spatial_coords is not None and temporal_coords is not None :
spatial_mean = spatial_coords.mean(dim=1 )
temporal_mean = temporal_coords.mean(dim=1 )
video_features_mean = video_features.mean(dim=1 )
video_features = self .four_d_embedding(
video_features_mean, spatial_mean, temporal_mean
).unsqueeze(1 ) + video_features
lang_output = self .language_model(language_input_ids)
lang_features = lang_output.last_hidden_state
video_summary = video_features.reshape(
video_features.shape[0 ], -1 , video_features.shape[-1 ]
).mean(dim=1 , keepdim=True )
fused, _ = self .fusion_attention(lang_features, video_summary, video_summary)
action_context = fused.mean(dim=1 )
actions = self .action_head(action_context)
return actions
5. Training Loss with Temporal Coherence
Define loss encouraging temporally smooth action sequences.
def vla_4d_loss (
predicted_actions,
target_actions,
prev_actions=None ,
lambda_temporal=0.1 ,
lambda_spatial=1.0
):
"""
Loss combining spatial accuracy and temporal coherence.
Args:
predicted_actions: Dict with 4D action predictions
target_actions: Ground truth actions
prev_actions: Previous action (for temporal continuity)
lambda_temporal, lambda_spatial: Loss weights
Returns:
total_loss: Combined loss
"""
losses = {}
position_loss = torch.nn.functional.mse_loss(
predicted_actions['position_delta' ],
target_actions['position_delta' ]
)
rotation_loss = torch.nn.functional.mse_loss(
predicted_actions['rotation_delta' ],
target_actions['rotation_delta' ]
)
gripper_loss = torch.nn.functional.binary_cross_entropy(
predicted_actions['gripper' ],
target_actions['gripper' ]
)
spatial_loss = position_loss + rotation_loss + gripper_loss
losses['spatial' ] = lambda_spatial * spatial_loss
duration_loss = torch.nn.functional.mse_loss(
predicted_actions['duration' ],
target_actions['duration' ]
)
if prev_actions is not None :
position_change = torch.norm(
predicted_actions['position_delta' ] - prev_actions['position_delta' ],
dim=-1
)
coherence_penalty = position_change.mean()
temporal_loss = duration_loss + coherence_penalty
else :
temporal_loss = duration_loss
losses['temporal' ] = lambda_temporal * temporal_loss
total_loss = sum (losses.values())
return total_loss, losses
Practical Guidance
Robotic tasks requiring smooth, temporally coherent manipulation
Fine-grained control with strict timing requirements
Tasks with multiple sequential sub-steps
Scenarios where action duration impacts success
Simple point-to-point movement tasks
Real-time systems where temporal prediction adds unacceptable overhead
Scenarios without sufficient temporal annotation data
max_time: Maximum action duration in seconds (10-30 typical)position_scale: Spatial movement magnitude (0.05-0.2m typical)lambda_temporal: Weight of temporal coherence loss (0.05-0.2)num_frames: Video frames for temporal understanding (4-16) Performance Optimization:
Pre-encode videos once to avoid redundant feature extraction
Use causal temporal masking to prevent information leakage
Batch actions during inference for parallelism
Integration with Robotics:
VLA-4D outputs directly map to robot command APIs. Temporal parameter (Δt) determines action duration in robot hardware; execute spatial component at smooth pace over predicted duration for natural motion.
Reference 