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 $N=N_2\circ N_1$ is split at a single semantic interface and one learnable prototype per class is inserted there. Training combines a quadratic consensus penalty that pulls $N_1(x)$ toward the prototype of its class with a classification loss of $N_2$ evaluated on samples drawn around the prototypes, whereat no gradient crosses the interface. At inference the prototypes are discarded and the unmodified network $N_2\circ N_1$ 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.