Criterion C4 — Minimality
Section titled “Criterion C4 — Minimality”| Validity type | Construct |
| Pass condition | The circuit is the smallest set of components satisfying sufficiency; removing any member degrades performance |
| Evidence family | Causal (per-component ablation) |
| Minimum reporting | Per-component ablation result for each member; confirmation no member can be removed without behavioral degradation |
| Common failure mode | Circuit grown by correlation or attribution score without a per-component pruning pass |
What this criterion requires
Section titled “What this criterion requires”Minimality requires no redundant members. Every component must be individually necessary given the other components. If removing c_i while leaving all other members intact has no effect on performance, c_i is redundant and should be removed.
Formally: for circuit C = {c_1, …, c_n}, minimality requires that for every c_i in C, ablating c_i while leaving all others intact produces a performance decrease.
Minimality and the “than” factors
Section titled “Minimality and the “than” factors”The than_factor_specialization.py script tests this directly for the 5 “than” factors (f121, f219, f421, f546, f608): if all 5 activate similarly across comparative, rather-than, and quantity contexts, they are a non-minimal set — one factor would be sufficient. If they specialize by context (the script’s SPECIALIZED verdict), each factor is individually necessary for its context type — the set is minimal and each member has a distinct functional role.
The per-component pruning pass
Section titled “The per-component pruning pass”- Take proposed circuit C.
- Ablate only c_i (zero or resample).
- Measure performance on target task.
- If not degraded relative to full-circuit ablation: remove c_i from C.
- Repeat until no member can be removed.
Report the set of members pruned and ablation results for each.
Minimality and redundancy
Section titled “Minimality and redundancy”Multiple minimal circuits can exist (backup name-mover heads in IOI). This is a finding about architectural redundancy, not a failure of minimality. Report both minimal circuits and describe their relationship.
Minimum reporting rule
Section titled “Minimum reporting rule”- List every component in the final circuit.
- Per-component ablation result (method, metric, delta) for each member.
- Set of components pruned during minimality pass, if any.
- If no minimality pass was run, flag as open criterion.
Common failure
Section titled “Common failure”Discovery methods (ACDC, EAP, weight classifier) return components ranked by attribution score. Taking top-k without per-component ablation check risks including redundant members.