| name | fluidworld-reaction-diffusion-models |
| title | FluidWorld: Reaction-Diffusion Dynamics as a Predictive Substrate for World Models |
| version | 0.0.3 |
| engine | skillxiv-v0.0.3-claude-opus-4.6 |
| license | MIT |
| url | https://arxiv.org/abs/2603.21315 |
| keywords | ["World Models","Reaction-Diffusion PDEs","Spatiotemporal Prediction","Self-Organizing Systems","Alternative to Attention"] |
| description | Replace self-attention world models with reaction-diffusion PDEs as the predictive substrate. Demonstrate that aperiodic PDE dynamics achieve superior multi-step rollout stability and inherent error correction through Laplacian diffusion smoothing, while maintaining O(N) complexity and enabling autonomous corruption recovery. |
FluidWorld: Reaction-Diffusion Dynamics for World Modeling
Prior Belief Challenged
Assumption: Self-attention (Transformers) is necessary for effective predictive world modeling. Attention mechanisms capture long-range dependencies and enable flexible computation.
Falsifying Experiment: PDE-Based World Models
Train three architecturally-comparable models (all ~800K parameters) on video prediction (UCF-101):
- FluidWorld: Multi-scale reaction-diffusion PDEs
- Transformer Baseline: Standard self-attention world model
- ConvLSTM Baseline: Recurrent architecture
Parameter Budget Matching: Crucial—all three models have identical parameter counts to isolate architectural differences.
Key Results:
Single-Step Metrics (Converge):
- MSE reconstruction: FluidWorld 2× lower than Transformer (0.001 vs 0.002)
- Spatial activation statistics: Comparable
Multi-Step Rollouts (Diverge Dramatically):
- At horizon h=2: Transformer and ConvLSTM outputs collapse into gray frames
- At horizon h=3: FluidWorld maintains recognizable structure; competitors unrecoverable
- SSIM trajectory: FluidWorld shows measurable recovery cycles (66.8% of rollouts show recovery, p<10⁻⁴⁹)
Critical Finding: Single-step optimization masks architectural differences; only extended autoregressive rollouts reveal advantages.
Revised Principle: Aperiodic Spatial Processing > Dense Attention
Core Mechanism: Reaction-diffusion PDEs provide three properties absent from attention:
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O(N) Locality: Multi-scale Laplacian diffusion operates on spatially-local neighborhoods, avoiding O(N²) pairwise interactions.
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Implicit Error Correction: Laplacian smoothing (∇²) acts as low-pass filter, attenuating prediction errors during rollouts. When accumulated error reaches high frequencies, diffusion progressively removes it.
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Graceful Degradation: System operates at edge-of-chaos criticality—50% state corruption recovers autonomously without explicit recovery mechanisms.
Mathematical Basis:
Reaction-diffusion equation combines:
- Multi-scale Laplacian: ∇² applied with dilations {1, 4, 16} for long-range diffusion
- Position-wise reaction: MLP processes local dynamics
