Why Go

Go's game structures are graph properties: connectivity between intersections determines outcomes. For research about how network topology shapes learning, a benchmark whose underlying structure is genuinely graph-shaped gives direct access to the foundation. The graph isn't being imposed on Go from outside; it's what Go is.

Why does this project use Go as its testbed?

Not because Go is hard, though it is. The research question is about how the topology of a network shapes what it can learn, and Go is one of the few problems where the thing being learned about is itself a graph.

The board is what makes Go look like a 2D problem. A 19×19 grid printed on a wooden surface; stones placed at intersections; the human reader scans it like an image. But what's on the board isn't a 2D pattern. Stones of the same color connect into groups by orthogonal adjacency. Groups have liberties: the empty intersections that border them. A group lives or dies by its liberty count. The game state is a graph of these connections. The 2D layout is how humans read the state; the graph is the state.

Three properties of the game make the graph structure visible.

The first is groups. Same-colored stones touching orthogonally form a unit. The unit lives or dies together: when its last liberty is taken, all its stones come off the board at once. Group membership isn't an annotation on top of the position; it's the substrate of who can be captured and when. A move that connects two groups creates one larger group with combined liberties; a move that splits a group into two smaller groups exposes each to separate fates.

The second is ladders. A ladder is a sequence of forcing moves where one player chases another diagonally across the board. The chase only works if the chased stones don't have an out. Whether they have an out depends on what's at the far end of the ladder, potentially across the board from where the sequence started. The structural fact: whether a local sequence resolves in your favor depends on what's distant. What determines the outcome is the relationship between the two ends, not where they sit on the board.

The third is life-and-death. A group is unconditionally alive if it can form two distinct enclosed spaces (two eyes). Whether it can do so depends on the topology of the surrounding region: how empty intersections inside and around the group connect, where the boundary lies, what kinds of intrusions the opponent can make. Two-eye formation is what determines whether stones permanently belong to a player or are eventually captured. Life is a connectivity property of the region the group sits in.

All three properties share a structural fact: connectivity between intersections determines what happens on the board. Group capture is a graph property. Ladder resolution is a non-local graph property. Life-and-death is a topological graph property. The 2D coordinates of stones are how humans read positions; what the game is computing about is the connection graph among them.

Most ML benchmarks don't have this property. Image classification has spatial structure; sequence prediction has sequential structure. Neither makes connections between elements determine outcomes. A pixel doesn't have liberties. A token doesn't form a group with adjacent tokens whose collective survival depends on the token's neighbors.

For research about how network topology shapes learning, a benchmark whose structure is genuinely graph-shaped gives direct access to the substrate. The graph isn't being imposed on Go from outside; the graph is what Go is.

That's why this project uses it. Go is one of the few problems where the graph structure isn't a modeling choice. It's what's there.