The goal of model selection is to identify the model that generated the data.Goodness of a model is measured using generalizability

which takes two opposite aspects:goodness of fit and model complexity into account.we use generalized KL-divergence defined on the manifold to measure the goodness of fit

and use the conception of curvature from the point of view of differential geometry to explore the intrinsic model complexity that is free of reparametrization;through theoretical analysis

we proved the future residual that is qualified to measure the generalizability can be expressed by using the intrinsic curvature array of model

from which we propose a new model selection criterion KL-divergence and curvature information criterion with very clear and intuitive geometric understanding of model selection.Experimental results reveal its validity.