论文标题
超越RG：从参数流到度量流量
Beyond RG: from parameter flow to metric flow
论文作者
论文摘要
具有多个自由度的复杂系统通常是棘手的，但是他们的某些行为可能会承认更简单的有效描述。何时进行这种有效描述的问题仍然开放。可以详细理解这种“出现简单性”的范式方法是重新归一化组（RG）。在这里，我们表明，对于通用系统，没有RG构造所需的自相似对称性，模型参数的RG流被模型歧管上的Fisher Information指标的更通用流动所取代。我们证明，传统上使用RG研究的系统包括特殊情况，在这些情况下，可以通过参数流诱导该度量流，从而保持模型模型固定的整体几何形状。但是，通常，几何形状可能会变形，并且不能将度量流降低为参数流 - 尽管正如我们讨论的那样，这可以以增加一个新参数的成本来实现。我们希望我们的框架可以阐明RG的想法如何应用于更广泛的复杂系统。
Complex systems with many degrees of freedom are typically intractable, but some of their behaviors may admit simpler effective descriptions. The question of when such effective descriptions are possible remains open. The paradigmatic approach where such "emergent simplicity" can be understood in detail is the renormalization group (RG). Here, we show that for general systems, without the self-similarity symmetry required by the RG construction, the RG flow of model parameters is replaced by a more general flow of the Fisher Information Metric on the model manifold. We demonstrate that the systems traditionally studied with RG comprise special cases where this metric flow can be induced by a parameter flow, keeping the global geometry of the model-manifold fixed. In general, however, the geometry may deform, and metric flow cannot be reduced to a parameter flow -- though this could be achieved at the cost of augmenting the manifold by one new parameter, as we discuss. We hope that our framework can clarify how ideas from RG may apply in a broader class of complex systems.
