用物理场动态计算，实现多任务神经架构统一设计
Metriplector: From Field Theory to Neural Architecture
- 输入定义物理场系统，场演化过程即计算
- 图像识别准确率达81.03%，语言建模仅需3.6倍少训练数据
- 适合需要统一框架的跨模态任务研究者
我们提出Metriplector，一种神经架构原语：输入定义抽象物理系统（场、源、算子），其动力学过程即为计算。多个场通过耦合的度量-泊松动力学演化，由诺特定理导出的应力-能量张量T^{μν}作为输出读取。该公式支持自然的实例化谱系：仅用耗散分支即可精确求解屏蔽泊松方程；启用完整结构（含反对称泊松括号）后，可实现图像识别、语言建模和机器人控制。我们在五个领域评估：在CIFAR-100上达到81.03%准确率（226万参数）；在Reacher机器人控制中取得88%成功率（参数<100万）；零结构注入下97.2%正确解数独；语言建模达1.182 bits/byte，训练样本仅为GPT基线的3.6倍；迷宫路径规划F1=1.0，从15×15泛化至未见的39×39网格。
原文摘要 · Abstract (English)
We present Metriplector, a neural architecture primitive in which the input configures an abstract physical system -- fields, sources, and operators -- and the dynamics of that system is the computation. Multiple fields evolve via coupled metriplectic dynamics, and the stress-energy tensor T^{μν}, derived from Noether's theorem, provides the readout. The metriplectic formulation admits a natural spectrum of instantiations: the dissipative branch alone yields a screened Poisson equation solved exactly via conjugate gradient; activating the full structure -- including the antisymmetric Poisson bracket -- gives field dynamics for image recognition, language modeling, and robotic control. We evaluate Metriplector across five domains, each using a task-specific architecture built from this shared primitive with progressively richer physics: 81.03% on CIFAR-100 with 2.26M parameters; 88% CEM success on Reacher robotic control with under 1M parameters; 97.2% exact Sudoku solve rate with zero structural injection; 1.182 bits/byte on language modeling with 3.6x fewer training tokens than a GPT baseline; and F1=1.0 on maze pathfinding, generalizing from 15x15 training grids to unseen 39x39 grids.
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