An adaptive pattern recognition system optimizes an invariance objective and an input fidelity objective to accurately recognize input patterns in the presence of arbitrary input transformations. A fixed state or value of a feature output can nonlinearly reconstruct or generate multiple spatially distant input patterns and respond similarly to multiple spatially distant input patterns, while preserving the ability to efficiently evaluate the input fidelity objective. Exemplary networks, including a novel factorization of a third-order Boltzmann machine, exhibit multilayered, unsupervised learning of arbitrary transformations, and learn rich, complex features even in the absence of labeled data. These features are then used to classify unknown input patterns, to perform dimensionality reduction or compression.