Topology as Governance
Paper reference: Section 1, "Topology as a governance object"; Table 2
The pipeline DAG is not just a wiring diagram — it determines where governance has leverage, how errors propagate, and what kind of intervention is structurally worthwhile.
Four canonical motifs
| Motif | Structure | Failure surface | Governance action |
|---|---|---|---|
| Chain | A → B → C | Quality and masking accumulate with depth | Improve upstream first |
| Fan-out | A → | One failure contaminates all branches | Prioritize the fan-out node |
| Diamond | A → {B, C} → D | Correlated errors at D when A fails | Fix A, not D |
| Merge | {B, C} → D | Throughput limited by bottleneck path | Invest where \(\partial C_\text{op}/\partial c(v)\) is largest |
from minimal_oversight.topology import detect_motifs
motifs = detect_motifs(pipeline)
for m in motifs:
print(f"[{m.motif.value}] {m.risk_description}")
Delegation centrality
DC(v) measures how many downstream nodes are affected by a correction at \(v\). A node with high fan-out and deep descendants has high centrality — improving it has outsized impact.
The SOTA priority score combines centrality with masking and task complexity:
where \(\kappa(v) = 1 - \sigma_\text{skill}(v)\) is the task complexity. The node with the highest \(S(v)\) benefits most from an expensive model upgrade.
from minimal_oversight.topology import rank_nodes_by_risk
risks = rank_nodes_by_risk(pipeline)
for r in risks:
print(f"{r.name}: DC={r.delegation_centrality:.1f}, SOTA={r.sota_score}")
Fan-out amplification
When a fan-out node's corrector is removed, errors propagate to all children simultaneously. In the SDLC pipeline, removing the reviewer's corrector creates three simultaneous cascades at test, requirements, and security.
This is why the SOTA model should go to the corrector at the fan-out node, not the executor at the generator. The corrector's improvement propagates to all branches; the executor's improvement is local.
The paper's Demonstration 1 formalizes this as the SOTA priority score. In the SDLC pipeline (Notebook 1), placing the expensive model as corrector at the reviewer yields ~10× more system improvement than placing it as executor at the generator (\(\Delta C_\text{op}\): +0.008 vs +0.0008), because the corrector's improvement propagates through all three downstream branches.
Conditional fragility (diamond pattern)
In a diamond (A → {B, C} → D), B and C share a common upstream source. When A fails, both B and C receive degraded input — their errors are correlated, not independent.
Average quality comparisons miss this: the difference between correlated and independent error sources is less than 1%. But conditioning on A's failure reveals a 1.4x fragility ratio:
The prescription: fix A upstream rather than adding redundancy at D. Redundant voters at D fail on the same cases when the errors are correlated.
from minimal_oversight.topology import conditional_fragility
ratio = conditional_fragility(pipeline, "merge_node", parent_corrs, shared_catch_rate)
print(f"Fragility ratio: {ratio:.1f}x")
Optimal DAG shape
Should a pipeline be deep and narrow or wide and shallow?
- Depth costs capacity: each layer adds masking, and beyond \(D_\text{max}\) quality saturates
- Width costs resilience: each fan-out branch amplifies cascade risk
The optimal shape is a pyramid: wide at the top (cheap agents with voting), narrow in the middle (capable specialists), and redundant at the merge gate (multiple evaluators with independent error sources).