Instructional BiologyWhy a hyperbolic disk, specifically
Most data visualization defaults to a flat, Euclidean layout — nodes and edges scattered across ordinary two-dimensional space. That works fine for data that isn't strongly hierarchical. It works poorly for data that is, because a flat layout has a fixed amount of room near the center and the same fixed amount of room near the edges, while a real hierarchy tends to branch outward exponentially: a handful of broadly influential regulators, exponentially more specific detail — cascades, receptors, peptides, and finally disease and outcome nodes — the further out you go.
A hyperbolic disk solves this by construction. In this geometry, space doesn't grow linearly as you move outward from the center — it grows exponentially, which happens to be exactly the rate at which a real biological hierarchy branches. That's why the six tiers in the graph above — regulator, cascade, receptor, peptide, disease, and outcome, moving from center to boundary — sit naturally at their radius: not because of an arbitrary layout choice, but because that's where a graph of this shape actually wants to sit when it's given a geometry built for hierarchy instead of one built for a flat table.
The research behind the geometry
This isn't a design choice we invented from scratch. Hyperbolic embeddings for hierarchical data were formalized in a widely cited 2017 paper by Nickel and Kiela, Poincaré Embeddings for Learning Hierarchical Representations, which showed that embedding tree-like and hierarchical data directly into a Poincaré ball substantially outperforms standard Euclidean embeddings on the same task.
The core finding, in their own benchmarks: reconstructing the WordNet noun taxonomy — a large, well-studied hierarchical dataset — from a Euclidean embedding required very high dimensionality to get anywhere close to accurate, and still left the mean rank of related concepts in the thousands. A Poincaré embedding, at a fraction of the dimensionality, brought that same reconstruction error down to single digits, and did the same for link-prediction accuracy on multiple network datasets. The reason traces back to geometry, not tuning: a Euclidean space's volume grows only polynomially with radius, while a hyperbolic space's volume grows exponentially — which happens to match how fast a real hierarchy's node count grows as you move away from its root. Forcing exponential branching into a space that can only grow polynomially is what produces the "node crowding" that degrades Euclidean embeddings on this kind of data.
That's the property our Signaling Cascade Knowledge Graph is built to exploit: a biological signaling hierarchy — few master regulators, exponentially more specific downstream detail — is exactly the shape this geometry was shown to represent well, at far lower dimensionality than a comparably accurate Euclidean alternative would require.
Reading the map
Radial position tells you how broadly influential a node is — closer to the center means a wider reach across the downstream network, the way a master regulator affects many cascades at once, while a specific outcome sits far out because it's the endpoint of one particular path, not a hub many paths pass through. Angular position and clustering reflect similarity: nodes that share more context or evidence tend to sit nearer each other around the disk. Edges represent asserted relationships between tiers, each one meant to be traceable back to the evidence that supports it rather than inferred silently.
What you're looking at here is a public, illustrative concept model — a demonstration of the geometry and the interaction pattern, not a rendering of our full internal evidence graph, which is considerably larger and remains internal to ongoing research. We built this public version because we think the geometry itself is worth understanding on its own, independent of any specific dataset behind it.