Determine the further compressibility of weakly concentrated task circuits

Determine how much further the Circuit Condensation endpoints can be compressed for the task–model cells with the narrowest reductions, including docstring completion on Qwen3-0.6B and the Gemma-3 models, where the reported results do not establish the attainable minimum circuit size.

Background

The paper reports that Circuit Condensation substantially reduces circuit size in many task–model combinations, but the reduction is not uniform. The narrowest improvement is 1.3× for docstring completion on Qwen3-0.6B, while Gemma-3-4B and Gemma-3-1B reach the controller’s apparent floor on several tasks. Because these endpoints may be limited by the capability gate or other stopping behavior rather than by true circuit minimality, the paper leaves unresolved how much additional compression is possible in these weakly concentrated cases.

References

Finding a sufficient set efficiently is an open problem. Algorithm~\ref{alg:suf} was built to find small sufficient sets in reasonable time, not provably smallest ones, and it converges on $96$ percent of predictions on some models and $44$ on others. Every size reported here is an upper bound from that search. We presume someone more clever will close this gap to $100$ percent, possibly with minimally sized circuits.

— Through the Looking Glass: Directly Reading and Writing Transformers  (2609.10210 - Oskin, 9 Sep 2026) in Section “Is this as good as it gets?”

Third, the gap is not uniform, and its narrowest cells are genuinely narrow, at $1.3\times$ on docstring/Qwen3-0.6B, while Gemma-3-4B sits at or near the controller's floor on three of four tasks and Gemma-3-1B on two, so we cannot tell how much further those cells would compress.

— Circuit Condensation: Post-Training that Concentrates a Behavior's Causal Circuit  (2608.27254 - Kumar, 27 Aug 2026) in Section 'Where the Result Is Weakest' (Appendix~\ref{app:weakest})