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Topology Matters: A Cautionary Case Study of Graph SSL on Neuro-Inspired Benchmarks

May Kristine Jonson Carlon, Su Myat Noe, Haojiong Wang, Yasuo Kuniyoshi

TL;DR

Topology Matters investigates graph self-supervised learning on connectome-like graphs with a neuro-inspired, multi-scale objective. The authors show that invariance-based SSL is fundamentally misaligned with topological brain properties and is outperformed by simple topology-aware heuristics such as the Jaccard coefficient. They introduce a neuro-inspired synthetic benchmark and a hierarchical SSL framework with explicit edge modeling and SimSiam predictors, evaluated via a rigorous four-stage protocol (hyperparameter search, single-graph probes, transfer learning, and ablations). Across tasks, they observe that learned invariances fail to preserve modular structure and sometimes actively harm topology-driven predictions, motivating the call for topology-preserving objectives that reward modularity and motifs. The work provides a critical caution against applying generic SSL to connectome data and offers a controlled testbed and design principles to guide future topology-aware neuro-inspired AI research.

Abstract

Understanding how local interactions give rise to global brain organization requires models that can represent information across multiple scales. We introduce a hierarchical self-supervised learning (SSL) framework that jointly learns node-, edge-, and graph-level embeddings, inspired by multimodal neuroimaging. We construct a controllable synthetic benchmark mimicking the topological properties of connectomes. Our four-stage evaluation protocol reveals a critical failure: the invariance-based SSL model is fundamentally misaligned with the benchmark's topological properties and is catastrophically outperformed by classical, topology-aware heuristics. Ablations confirm an objective mismatch: SSL objectives designed to be invariant to topological perturbations learn to ignore the very community structure that classical methods exploit. Our results expose a fundamental pitfall in applying generic graph SSL to connectome-like data. We present this framework as a cautionary case study, highlighting the need for new, topology-aware SSL objectives for neuro-AI research that explicitly reward the preservation of structure (e.g., modularity or motifs).

Topology Matters: A Cautionary Case Study of Graph SSL on Neuro-Inspired Benchmarks

TL;DR

Topology Matters investigates graph self-supervised learning on connectome-like graphs with a neuro-inspired, multi-scale objective. The authors show that invariance-based SSL is fundamentally misaligned with topological brain properties and is outperformed by simple topology-aware heuristics such as the Jaccard coefficient. They introduce a neuro-inspired synthetic benchmark and a hierarchical SSL framework with explicit edge modeling and SimSiam predictors, evaluated via a rigorous four-stage protocol (hyperparameter search, single-graph probes, transfer learning, and ablations). Across tasks, they observe that learned invariances fail to preserve modular structure and sometimes actively harm topology-driven predictions, motivating the call for topology-preserving objectives that reward modularity and motifs. The work provides a critical caution against applying generic SSL to connectome data and offers a controlled testbed and design principles to guide future topology-aware neuro-inspired AI research.

Abstract

Understanding how local interactions give rise to global brain organization requires models that can represent information across multiple scales. We introduce a hierarchical self-supervised learning (SSL) framework that jointly learns node-, edge-, and graph-level embeddings, inspired by multimodal neuroimaging. We construct a controllable synthetic benchmark mimicking the topological properties of connectomes. Our four-stage evaluation protocol reveals a critical failure: the invariance-based SSL model is fundamentally misaligned with the benchmark's topological properties and is catastrophically outperformed by classical, topology-aware heuristics. Ablations confirm an objective mismatch: SSL objectives designed to be invariant to topological perturbations learn to ignore the very community structure that classical methods exploit. Our results expose a fundamental pitfall in applying generic graph SSL to connectome-like data. We present this framework as a cautionary case study, highlighting the need for new, topology-aware SSL objectives for neuro-AI research that explicitly reward the preservation of structure (e.g., modularity or motifs).
Paper Structure (52 sections, 12 equations, 5 figures, 1 table)

This paper contains 52 sections, 12 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. From Neuro to AI.
  3. From AI to Neuro.
  4. Contributions
  5. Hierarchical SSL with explicit edge modeling.
  6. Failure analysis of invariance-based SSL.
  7. Rigorous Evaluation.
  8. Neuro-inspired Synthetic Benchmark.
  9. Related Work
  10. Graph Self-Supervised Learning.
  11. Edge and Hierarchical Learning.
  12. Pre-training of Graph Neural Networks.
  13. Method
  14. Problem Setup
  15. Architecture
  16. ...and 37 more sections

Figures (5)

  • Figure 1: Hyperparameter trade-offs. Pareto frontier between node F1 and graph $R^2$ reveals weak trade-off.
  • Figure 2: Training Dynamics. Smoothing for all graphs was done with an exponential moving average (EMA).
  • Figure 3: t-SNE of embeddings. Edges colored by SC weight quartiles show clear clustering. Nodes colored by class show partial separation.
  • Figure 4: Transfer task confusion matrix. Frozen $z_G$ classifies graphs by $K$ (5 classes).
  • Figure 5: Ablation study. Absolute performance for each metric across variants. FULL is highlighted for reference.