# ProtoSeam: Lifting Classifier Training with Latent Gaussian Mixture Models

arXiv: https://arxiv.org/abs/2609.35174 · HTML: https://mlsanity.com/paper/2609.35174/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 41 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Deep Metric Learning via Lifted Structured Feature Embedding](https://mlsanity.com/paper/1511.06452/) (2015)
- [Large-Margin Softmax Loss for Convolutional Neural Networks](https://mlsanity.com/paper/1612.02295/) (2016)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [Decoupled Neural Interfaces using Synthetic Gradients](https://mlsanity.com/paper/1608.05343/) (2016)
- [Training Neural Networks with Local Error Signals](https://mlsanity.com/paper/1901.06656/) (2019)
- [Greedy Layerwise Learning Can Scale to ImageNet](https://mlsanity.com/paper/1812.11446/) (2018)
- [Inducing Neural Collapse in Imbalanced Learning: Do We Really Need a Learnable Classifier at the End of Deep Neural Network?](https://mlsanity.com/paper/2203.09081/) (2022)
- [Semi-Supervised Learning with Normalizing Flows](https://mlsanity.com/paper/1912.13025/) (2019)
- [Training Neural Networks Without Gradients: A Scalable ADMM Approach](https://mlsanity.com/paper/1605.02026/) (2016)
- [Rethinking Feature Distribution for Loss Functions in Image Classification](https://mlsanity.com/paper/1803.02988/) (2018)
- [Layer-Parallel Training of Deep Residual Neural Networks](https://mlsanity.com/paper/1812.04352/) (2018)
- [Lifted Neural Networks](https://mlsanity.com/paper/1805.01532/) (2018)
- [Fenchel Lifted Networks: A Lagrange Relaxation of Neural Network Training](https://mlsanity.com/paper/1811.08039/) (2018)

## Abstract (arXiv)

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.