Graph Sparsification

My Tremplin Recherche Project: Rethinking GNNs by Fixing Their Geometric Bottlenecks

I'm happy to announce that I have been selected for the Tremplin Recherche 2025/2026 program. This is an incredible opportunity to dedicate a full year to a research topic I find critical: Graph Sparsification for Graph Neural Networks.

This project isn't just about making Graph Neural Networks (GNNs) faster; it's about fundamentally rethinking why they fail and intervening at the source of the problem.

The Stakes: Why GNNs Are Hitting a Wall

GNNs have revolutionized how we learn from structured data, from molecules to social networks. Their power comes from "message passing," where nodes aggregate information from their neighbors over several layers.

But this very mechanism creates fundamental, crippling challenges. The stakes are high, because these issues aren't minor implementation problems—they are deep, structural limitations that prevent GNNs from scaling and learning complex, long-range patterns:

1. Oversmoothing: After a few layers, the repeated averaging of "messages" causes all node features to blur together, becoming indistinguishable. This is a "spectral limitation" that washes out the very information we want to learn.
2. Oversquashing: This is the most critical bottleneck. In real-world graphs, you often have regions where an "exponential" amount of information from distant nodes must be funneled through just a handful of connecting edges. This creates a massive information bottleneck, or "congestion," where signals are hopelessly compressed.

The Real Problem: We're Fixing the Model, Not the Graph

For years, the community has tried to fix these issues with new GNN architectures: adding attention (GAT), using residual connections, etc.

But here is the core issue: These architectural fixes cannot solve the problem.

These bottlenecks are not flaws in the model; they are flaws in the graph's topology. As the research shows, "attention mechanisms cannot create new communication channels" and "residual connections do not change structural boundary growth." We are just pushing more data, more forcefully, through the same broken pipes.

If the geometry of the graph is the problem, the only real solution is to modify the geometry itself.

My Research: Sparsification as Geometric Restructuring

This is the central thesis of my research project. We must stop treating sparsification (removing edges) as a simple compression trick to save memory.

My project reframes sparsification as a topology-level intervention. The goal is not to make the graph smaller, but to make it better.

Instead of just deleting edges randomly, my research will investigate how to "reshape the graph's geometry to improve information flow." We will use principles like discrete Ricci curvature as a diagnostic tool to find the exact "choke points" in the graph—the regions of high negative curvature that cause oversquashing.

By intelligently restructuring the graph—pruning redundant edges and even rewiring bottlenecked areas—we can create a new topology where information can flow efficiently. We are, in effect, performing surgery on the graph to create a "more learnable geometric space" before the GSNN ever begins its message passing.

This is a fundamental shift from a model-driven solution to a geometry-driven one, and I'm incredibly excited to spend the next year exploring it.