ProtoSeam: Lifting Classifier Training with Latent Gaussian Mixture Models

We propose a lifted reformulation of supervised classification that improves the final accuracy of standard classifiers without changing the architecture at inference time. A network N=N2circ N1 is split at a single semantic interface and one learnable prototype per class is inserted there. Training combines a quadratic consensus penalty that pulls N1(x) toward the prototype of its class with a classification loss of N2 evaluated on samples drawn around the prototypes, whereat no gradient crosses the interface. At inference the prototypes are discarded and the unmodified network N2circ N1 is used. Across CIFAR-10, CIFAR-100, and TinyImageNet with ResNet and vision transformer backbones, lifted training improves test accuracy by up to five percentage points over variants without lifting under a shared tuning protocol. Moreover, we provide theoretical justification of those results.