Module 02: Minimum-Cycle Prediction
Goal: for each node, predict the length of the shortest cycle passing through that node.
Why This Module Is Important
Shortest-cycle-through-node is substantially harder than degree and better reflects whether a model can capture nontrivial graph structure. This module is a stress test for representational expressivity: it checks if the network can go beyond local counting and reason about cycle context.
It is also practically useful for identifying nodes in dense feedback-like regions of a graph. That makes it a good bridge task between pure benchmarking and meaningful structural analysis.
How It Was Trained
- Same training regime as degree: random generated graphs.
- 4 node features, hidden size 64, 4 layers, dropout 0.2.
- 5000 epochs, learning rate 0.001, 50 graphs per epoch.
- Accuracy is exact match after rounding predicted cycle length to integer.
uv run python -m ai.min_cycle.train --model gcn --name v1 --epochs 5000
uv run python -m ai.min_cycle.train --model sage --name v1 --epochs 5000
uv run python -m ai.min_cycle.train --model gin --name v1 --epochs 5000
uv run python -m ai.min_cycle.train --model loopy --name r3_v1 --r 3 --epochs 5000Saved Results
Source: ai/trained/min_cycle/*/info.json.
| Model | Accuracy (%) | MAE | MSE | Best Epoch |
|---|---|---|---|---|
| loopy_r3_v1 | 85.14 | 0.2258 | 0.0510 | 1750 |
| gcn_v1 | 43.35 | 1.0887 | 1.1852 | 100 |
| gin_v1 | 38.10 | 1.4728 | 2.1691 | 3100 |
| sage_v1 | 23.67 | 2.8893 | 8.3479 | 50 |
Why Models Behave Differently Here
Cycle tasks reward models that preserve richer structural signals.
Your results show loopy_r3_v1 clearly ahead (85.14%
accuracy, low MAE), while the baseline families trail behind. This is
consistent with cycle-aware inductive bias providing a direct advantage
for shortest-cycle estimation.
Another important signal is best epoch spread: some models peak early, others much later. That indicates architecture-specific optimization dynamics and suggests per-model early-stopping rules may outperform a single shared training schedule.