  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.
