# Follow the Geometry, Not the Model: Cold Start Semi-Supervised Learning

arXiv: https://arxiv.org/abs/2609.14451 · HTML: https://mlsanity.com/paper/2609.14451/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 13 Sep 2026.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Unsupervised Data Augmentation for Consistency Training](https://mlsanity.com/paper/1904.12848/) (2019)
- [Temporal Ensembling for Semi-Supervised Learning](https://mlsanity.com/paper/1610.02242/) (2016)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [FlexMatch: Boosting Semi-Supervised Learning with Curriculum Pseudo Labeling](https://mlsanity.com/paper/2110.08263/) (2021)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Label Propagation for Deep Semi-supervised Learning](https://mlsanity.com/paper/1904.04717/) (2019)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [CoMatch: Semi-supervised Learning with Contrastive Graph Regularization](https://mlsanity.com/paper/2011.11183/) (2020)
- [SimMatch: Semi-supervised Learning with Similarity Matching](https://mlsanity.com/paper/2203.06915/) (2022)
- [Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates](https://mlsanity.com/paper/2006.11184/) (2020)
- [In Defense of Core-set: A Density-aware Core-set Selection for Active Learning](https://mlsanity.com/paper/2206.04838/) (2022)
- [Barely-Supervised Learning: Semi-Supervised Learning with very few labeled images](https://mlsanity.com/paper/2112.12004/) (2021)

## Abstract (arXiv)

Modern semi-supervised learning (SSL) couples pseudo-label generation and classifier training, using the classifier's own confidence to select the pseudo-labels that are then used to update the model. In the cold-start regime, where at most a few labels per class are available, this coupling is ill-posed, since the classifier cannot supervise itself before it has learned. To address this problem, we propose VAST (Veracity-Aware Semi-Supervised Training), which decouples these two stages. Probabilistic beliefs over the unlabeled set are first inferred directly from the geometry of a frozen self-supervised embedding and only then distilled into an inductive classifier. The construction rests on the Veracity Matrix, a kernel-based structure that aggregates label evidence across the data manifold and admits an interpretation as a Dirichlet posterior under a per-observation powered-likelihood model. Additionally, we introduce Veracity Propagation, a self-terminating belief-spreading step that extends coverage beyond the kernel neighborhood of the labeled set. Under a controlled protocol in which all methods receive identical frozen embeddings and labeled sets, VAST outperforms the strongest graph-based SSL baselines at every operating point across three datasets, with statistically significant gains in 7 of 9 comparisons, while producing a deployable inductive classifier rather than requiring transductive graph inference. Compared with end-to-end confidence-gated SSL, we further find that these methods underperform in this setting and, in our experiments, do not consistently exceed labeled-only performance.