Silver Rook Labs · Systems Study 02

Signal Through Structure

Watch a graph decide what a neural network can know.

Message passing carries information farther with every layer. A narrow cut can oversquash distant information; deeper mixing can oversmooth nodes until their distinctions disappear.

Oversquashing
Too much distant information is compressed through too little structure.
Oversmoothing
Repeated mixing makes different nodes increasingly alike.
At the target 0.00% of the source signal has arrived

Experiment

Change the structure. Follow the signal.

Start here Bottleneck Rewired Same propagation. Same layer. A wider information channel.
Graph
Propagation

Information field

Bottleneck · layer 0

Source Target Signal strength
Message-passing graph Nodes are colored and sized by source-signal influence. Select Edit one edge, then choose two nodes to toggle their connection.
Ready 1 of 12 nodes active 23 edges

Competing effects

Reach rises while distinction disappears.

The marker follows the selected layer. Each scale is normalized to its own maximum.

Target influence0.0000

Can information cross the graph?

Node variance0.0000

Do nodes remain distinguishable?

Dirichlet energy0.0000

How much local contrast remains?

Evidence boundary

A small exact model, not a universal claim.

The calculations are deterministic linear message passing on small synthetic graphs. They expose mechanisms described in graph-learning research; they do not establish trained-model performance, a new mitigation method, or state-of-the-art results.

Read the experiment notes and limitations