neural-fields-world-models

name	neural-fields-world-models
description	Neural Fields as World Models methodology — isomorphic world models that preserve sensory topology for physics prediction as geometric propagation rather than abstract state transition. Motor-gated neural fields with local lateral connectivity and action-conditional prediction within spatial maps. Use for: world model architectures, sensory cortex modeling, offline task learning, action-conditional prediction, spatial prediction, embodied AI, neural field implementations. Activation: neural field, world model, isomorphic, spatial topology, motor-gated, action-conditional, offline learning, embodied cognition, sensory preservation.
license	Complete terms in LICENSE.txt
metadata	{"arxiv_id":"2602.18690","published":"2026-06-01","authors":"Joshua Nunley","tags":["neural-fields","world-models","spatial-prediction","embodied-cognition","offline-learning","motor-gated","isomorphic"]}

Neural Fields as World Models

Isomorphic world models that preserve sensory topology, enabling physics prediction as geometric propagation rather than abstract state transition.

Core Concept

Traditional world models compress visual input into latent vectors, discarding spatial structure that characterizes sensory cortex. This paper proposes isomorphic world models — architectures that preserve sensory topology so prediction becomes geometric propagation.

Key insight: Physical prediction, offline task learning, and body-linked representation share a common computational substrate: action-conditional prediction within a spatial map.

Methodology

Motor-Gated Neural Fields

• Architecture: Activity evolves through local lateral connectivity
• Motor modulation: Motor commands multiplicatively modulate specific channels
• Spatial preservation: Sensory topology maintained throughout processing

Three Experiments

1. Ballistic prediction without teleporting

   • Learns motion trajectories without instantaneous jumps
   • Spatial continuity preserved

2. Offline task learning

   • Catching policy improved offline
   • Task error propagated through frozen learned world model

3. Body-selective motor channels

   • Emerges without body labels
   • Self-organized body representation

Key Features

Isomorphic Architecture

• Topological preservation: Spatial structure maintained unlike latent vector compression
• Geometric propagation: Physics prediction as spatial evolution
• Action-conditional: Motor commands gate field evolution

Motor Channel Organization

• Multiplicative modulation: Motor commands scale specific channels
• Body-linked emergence: Selective channels develop without explicit supervision
• Local connectivity: Lateral interactions preserve spatial relationships

Applications

Offline Learning

• Task improvement: Policy refinement without environment interaction
• Error backpropagation: Through frozen world model
• Mental rehearsal: Simulated practice through field dynamics

Embodied AI

• Spatial prediction: Motion trajectories in physical space
• Body representation: Emergent body-selective channels
• Action-conditional: Motor gating for goal-directed behavior

Sensory Cortex Modeling

• Topological structure: Preserves cortical organization principles
• Local interactions: Lateral connectivity mimics cortical circuits
• Prediction substrate: Shared foundation for multiple cognitive functions

Implementation Patterns

Neural Field Architecture

Input → Spatial Field → Local Lateral Connections → Motor-Gated Channels → Output
         ↑                                                      |
         |______________________________________________________|

Key components:

1. Spatial field maintains topological structure
2. Lateral connections enable local propagation
3. Motor gating multiplicatively modulates specific channels
4. Feedback loop for continuous prediction

Motor-Gating Mechanism

• Channel selection: Motor commands activate specific field regions
• Multiplicative scaling: Field values scaled by motor signals
• Selective propagation: Enhanced regions dominate evolution

Advantages Over Latent Vector World Models

Feature	Latent Vectors	Isomorphic Fields
Spatial structure	Discarded	Preserved
Prediction type	Abstract state transition	Geometric propagation
Body representation	Explicit labels	Self-organized
Offline learning	Limited	Effective backpropagation
Teleporting artifacts	Common	Avoided

Experimental Validation

Ballistic Prediction

• Success: Learns smooth trajectories without teleporting
• Baseline comparison: Standard world models show instantaneous jumps

Offline Task Improvement

• Performance: Catching policy enhanced through frozen model propagation
• Learning efficiency: Offline practice effective without environment

Body Channel Emergence

• Discovery: Body-selective channels emerge unsupervised
• Significance: Demonstrates self-organized body representation

Relation to Neuroscience

Cortical Principles

• Sensory topology preservation: Mirrors cortical spatial organization
• Local lateral connectivity: Matches cortical circuit structure
• Motor modulation: Similar to motor cortex gating mechanisms

Behavioral Analogies

• Mental practice: Offline rehearsal for skill improvement
• Dreaming: Action-conditional prediction in sleep
• Motor imagery: Spatial prediction without execution

Pitfalls

Computational Cost

• Spatial resolution: High-dimensional fields require substantial memory
• Lateral connections: Dense connectivity increases computation
• Motor gating: Channel modulation overhead

Training Challenges

• Spatial continuity: Requires careful regularization
• Body emergence: Needs sufficient motor variety
• Offline propagation: Frozen model must be stable

Implementation Issues

• Field initialization: Poor initialization disrupts topology
• Channel balance: Motor gating must avoid channel collapse
• Teleporting avoidance: Spatial propagation needs tuning

Activation Keywords

• neural field world model
• isomorphic architecture
• spatial prediction
• motor-gated neural field
• action-conditional prediction
• offline task learning
• body representation emergence
• sensory topology preservation
• geometric propagation
• embodied world model

Related Skills

• predictive-coding: Hierarchical prediction frameworks
• worldkv-world-memory: World models for memory
• hippocampal-entorhinal-world-model: Brain-inspired world models
• energy-based-neurocomputation: Energy-based prediction
• neuromechanical-locomotion-dynamics: Motor dynamics modeling

References

• arXiv:2602.18690 - Neural Fields as World Models (Nunley, 2026)
• Neural field theory literature
• World model architectures
• Embodied cognition research
• Cortical spatial organization studies