# MABLE: Masked Autoencoding with Bi-Lipschitz Decoding for Embeddings and Graph Metric Learning

arXiv: https://arxiv.org/abs/2607.02990 · HTML: https://mlsanity.com/paper/2607.02990/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 32 references that are in the map.
- First posted on arXiv 3 Jul 2026.

## Builds on (most cited first, 27 of 27)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [GraphMAE: Self-Supervised Masked Graph Autoencoders](https://mlsanity.com/paper/2205.10803/) (2022)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [Contrastive learning, multi-view redundancy, and linear models](https://mlsanity.com/paper/2008.10150/) (2020)
- [GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learner](https://mlsanity.com/paper/2304.04779/) (2023)
- [Accurate Learning of Graph Representations with Graph Multiset Pooling](https://mlsanity.com/paper/2102.11533/) (2021)
- [How Mask Matters: Towards Theoretical Understandings of Masked Autoencoders](https://mlsanity.com/paper/2210.08344/) (2022)
- [What's Behind the Mask: Understanding Masked Graph Modeling for Graph Autoencoders](https://mlsanity.com/paper/2205.10053/) (2022)
- [Posterior Collapse and Latent Variable Non-identifiability](https://mlsanity.com/paper/2301.00537/) (2023)
- [TorchSpatial: A Location Encoding Framework and Benchmark for Spatial Representation Learning](https://mlsanity.com/paper/2406.15658/) (2024)
- [MIM-Refiner: A Contrastive Learning Boost from Intermediate Pre-Trained Representations](https://mlsanity.com/paper/2402.10093/) (2024)
- [GFM4MPM: Towards Geospatial Foundation Models for Mineral Prospectivity Mapping](https://mlsanity.com/paper/2406.12756/) (2024)

## Abstract (arXiv)

We propose MABLE (Masked Autoencoding with Bi-Lipschitz Decoding for Embeddings and Graph Metric Learning), a self-supervised framework for learning node and graph embeddings from large, heterogeneous graphs, demonstrated here on geospatial mineral-exploration data. MABLE combines masked reconstruction with fixed cosine-similarity losses that align matched augmented views while keeping unpaired embeddings well spread. A bi-Lipschitz feature decoder ties a low-dimensional reconstruction component of each node embedding to feature similarity, while matched-node consistency shapes the remaining context used by graph pooling. Lipschitz-controlled pooling helps stabilize graph-level representations under perturbations of retained node embeddings, while augmentation alignment trains robustness to masking, node dropping, and sampling variation. Across local copper and regional Arabian Shield studies, MABLE embeddings provide complementary downstream signal and produce coherent embedding-derived layers for hypothesis generation without learned discriminators or hard-negative selection.