EnRep: Energy-Induced Representations for Classification without Backpropagation

Modern classification relies heavily on learned representations, raising the question of whether discriminative features must always emerge through data-driven learning. We introduce EnRep, a framework that constructs energy-induced representations from prescribed energy functionals and extracts spectral features. Unlike learned feature extractors, it does not use backpropagation or iterative learning for feature construction, and the resulting features are coupled with a simple closed-form classifier. Using a single prescribed energy functional, we evaluate EnRep on synthetic spatial pattern data and two image benchmarks spanning handwritten digits and colorectal histology, with comparisons against a raw-input and a trained neural baseline. Across the tested tasks, EnRep outperforms raw-input classification and, on the synthetic benchmarks, markedly exceeds the accuracy of the trained neural baseline, while its closed-form readout avoids iterative optimization once the representation is constructed. These results demonstrate that energy structure can provide informative and computationally efficient representations without learning the feature extractor from data. More broadly, these findings suggest that energy can serve not only as an objective to be optimized, but also as a source of representations for classification.