用偏微分方程模拟世界动态，实现高效高质视频预测。
FluidWorld: Reaction-Diffusion Dynamics as a Predictive Substrate for World Models
- 以反应-扩散型偏微分方程作为预测核心，替代传统注意力或卷积循环结构。
- 在相同参数量下，重建误差低2倍，空间结构保留率提升10-15%。
- 适合追求轻量化、高效率且需多步预测稳定性的研究者使用。
世界模型通过预测环境未来状态支持规划与心理模拟。现有方法普遍依赖基于Transformer的预测器，在学习的潜在空间中运行，带来O(N²)计算开销且缺乏显式空间归纳偏置。本文提出根本性问题：自注意力是否为预测世界模型所必需？若非，能否采用其他计算底座实现更优表现？为此，本文提出FluidWorld——一种概念验证型世界模型，其预测动态由反应-扩散型偏微分方程（PDE）驱动。无需独立神经网络预测器，PDE积分本身即生成未来状态。在严格参数匹配的三路消融实验中（无条件UCF-101视频预测，64x64分辨率，约800K参数，相同编码器、解码器、损失函数与数据），FluidWorld与Transformer基线（自注意力）及ConvLSTM基线（卷积递归）对比。三者单步预测损失相近，但FluidWorld实现2倍更低的重建误差，表征的空间结构保留率提升10-15%，有效维度更高18-25%，且关键地维持了连贯的多步滚动预测，而两个基线迅速退化。所有实验仅在单台消费级电脑（Intel Core i5, NVIDIA RTX 4070 Ti）上完成，无需大规模算力。结果表明，具有天然O(N)空间复杂度、自适应计算和全局空间一致性优势的PDE动力学，是优于或等同于注意力与卷积递归的世界建模可行替代方案。
原文摘要 · Abstract (English)
World models learn to predict future states of an environment, enabling planning and mental simulation. Current approaches default to Transformer-based predictors operating in learned latent spaces. This comes at a cost: O(N^2) computation and no explicit spatial inductive bias. This paper asks a foundational question: is self-attention necessary for predictive world modeling, or can alternative computational substrates achieve comparable or superior results? I introduce FluidWorld, a proof-of-concept world model whose predictive dynamics are governed by partial differential equations (PDEs) of reaction-diffusion type. Instead of using a separate neural network predictor, the PDE integration itself produces the future state prediction. In a strictly parameter-matched three-way ablation on unconditional UCF-101 video prediction (64x64, ~800K parameters, identical encoder, decoder, losses, and data), FluidWorld is compared against both a Transformer baseline (self-attention) and a ConvLSTM baseline (convolutional recurrence). While all three models converge to comparable single-step prediction loss, FluidWorld achieves 2x lower reconstruction error, produces representations with 10-15% higher spatial structure preservation and 18-25% more effective dimensionality, and critically maintains coherent multi-step rollouts where both baselines degrade rapidly. All experiments were conducted on a single consumer-grade PC (Intel Core i5, NVIDIA RTX 4070 Ti), without any large-scale compute. These results establish that PDE-based dynamics, which natively provide O(N) spatial complexity, adaptive computation, and global spatial coherence through diffusion, are a viable and parameter-efficient alternative to both attention and convolutional recurrence for world modeling.
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