Since deep learning models are usually deployed in non-stationary environments, it is imperative to improve their robustness to out-of-distribution (OOD) data. A common approach to mitigate distribution shift is to regularize internal representations or predictors learned from in-distribution (ID) data to be domain invariant. Past studies have primarily learned pairwise invariances, ignoring the intrinsic structure and high-order dependencies of the data. Unlike machines, human recognizes objects by first dividing them into major components and then identifying the topological relation of these components. Motivated by this, we propose Reconstruct and Match (REMA), a general learning framework for object recognition tasks to endow deep models with the capability of capturing the topological homogeneity of objects without human prior knowledge or fine-grained annotations. To identify major components from objects, REMA introduces a selective slot-based reconstruction module to dynamically map dense pixels into a sparse and discrete set of slot vectors in an unsupervised manner. Then, to model high-order dependencies among these components, we propose a hypergraph-based relational reasoning module that models the intricate relations of nodes (slots) with structural constraints. Experiments on standard benchmarks show that REMA outperforms state-of-the-art methods in OOD generalization and test-time adaptation settings.