# Two Facets of the Same Optimization Coin: Model Degradation and Representation Collapse in Graph Foundation Models

arXiv: https://arxiv.org/abs/2509.08401 · HTML: https://mlsanity.com/paper/2509.08401/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 40 references that are in the map.
- First posted on arXiv 10 Sep 2025.

## Builds on (most cited first, 30 of 36)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [One for All: Towards Training One Graph Model for All Classification Tasks](https://mlsanity.com/paper/2310.00149/) (2023)
- [All in One and One for All: A Simple yet Effective Method towards Cross-domain Graph Pretraining](https://mlsanity.com/paper/2402.09834/) (2024)
- [GFT: Graph Foundation Model with Transferable Tree Vocabulary](https://mlsanity.com/paper/2411.06070/) (2024)
- [What's Behind the Mask: Understanding Masked Graph Modeling for Graph Autoencoders](https://mlsanity.com/paper/2205.10053/) (2022)
- [OpenGraph: Towards Open Graph Foundation Models](https://mlsanity.com/paper/2403.01121/) (2024)
- [UniGraph: Learning a Unified Cross-Domain Foundation Model for Text-Attributed Graphs](https://mlsanity.com/paper/2402.13630/) (2024)
- [Augmenting Low-Resource Text Classification with Graph-Grounded Pre-training and Prompting](https://mlsanity.com/paper/2305.03324/) (2023)
- [SAMGPT: Text-free Graph Foundation Model for Multi-domain Pre-training and Cross-domain Adaptation](https://mlsanity.com/paper/2502.05424/) (2025)
- [GraphCLIP: Enhancing Transferability in Graph Foundation Models for Text-Attributed Graphs](https://mlsanity.com/paper/2410.10329/) (2024)
- [GOFA: A Generative One-For-All Model for Joint Graph Language Modeling](https://mlsanity.com/paper/2407.09709/) (2024)
- [AnyGraph: Graph Foundation Model in the Wild](https://mlsanity.com/paper/2408.10700/) (2024)
- [UniGraph2: Learning a Unified Embedding Space to Bind Multimodal Graphs](https://mlsanity.com/paper/2502.00806/) (2025)
- [Text-Free Multi-domain Graph Pre-training: Toward Graph Foundation Models](https://mlsanity.com/paper/2405.13934/) (2024)
- [Multi-Domain Graph Foundation Models: Robust Knowledge Transfer via Topology Alignment](https://mlsanity.com/paper/2502.02017/) (2025)
- [GFM-RAG: Graph Foundation Model for Retrieval Augmented Generation](https://mlsanity.com/paper/2502.01113/) (2025)
- [VQGraph: Rethinking Graph Representation Space for Bridging GNNs and MLPs](https://mlsanity.com/paper/2308.02117/) (2023)
- [RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry](https://mlsanity.com/paper/2502.03251/) (2025)
- [Towards Graph Foundation Models: Learning Generalities Across Graphs via Task-Trees](https://mlsanity.com/paper/2412.16441/) (2024)
- [LLM as GNN: Graph Vocabulary Learning for Text-Attributed Graph Foundation Models](https://mlsanity.com/paper/2503.03313/) (2025)
- [Learning Graph Quantized Tokenizers](https://mlsanity.com/paper/2410.13798/) (2024)
- [Rethinking Node-wise Propagation for Large-scale Graph Learning](https://mlsanity.com/paper/2402.06128/) (2024)
- [LangGFM: A Large Language Model Alone Can be a Powerful Graph Foundation Model](https://mlsanity.com/paper/2410.14961/) (2024)

## Abstract (arXiv)

Inspired by the success of LLMs, GFMs are designed to learn the optimal embedding functions from multi-domain text-attributed graphs for the downstream cross-task generalization capability. Among the diverse architectures, graph VQ-MAE stands out among the increasingly diverse landscape of GFM. This is attributed to its ability to jointly encode topology and textual attributes from multiple domains into discrete embedding spaces with clear semantic boundaries. Despite its potential, domain generalization conflicts cause imperceptible pitfalls. In this paper, we instantiate two of them, and they are just like two sides of the same GFM optimization coin - Side 1 Model Degradation: The encoder and codebook fail to capture the diversity of inputs; Side 2 Representation Collapse: The hidden embedding and codebook vector fail to preserve semantic separability due to constraints from narrow representation subspaces. These two pitfalls (sides) collectively impair the decoder and generate the low-quality reconstructed supervision, causing the GFM optimization dilemma during pre-training (coin). Through empirical investigation, we attribute the above challenges to Information Bottleneck and Regularization Deficit. To address them, we propose MoT - (1) Information Tinker for Two Pitfalls, which utilizes an edge-wise semantic fusion strategy and a mixture-of-codebooks with domain-aware routing to improve information capacity. (2) Regularization Tinker for Optimization Coin, which utilizes two additional regularizations to further improve gradient supervision in our proposed Information Tinker. Notably, as a flexible architecture, MoT adheres to the scaling laws of GFM, offering a controllable model scale. Compared to SOTA baselines, experiments on 22 datasets across 6 domains demonstrate that MoT achieves significant improvements in supervised, few-shot, and zero-shot scenarios.