Artificial Unintelligence? Operation Mismatch Limits Circuits’ Use of Shared Representational Structure

Language models often encode ordered concepts such as weekdays and months in low-dimensional circular subspaces. The causal role of this geometry is less clear: circuits for different tasks may organize their representations with analogous circular geometry without being able to use one another's computations. We test this possibility by discovering sparse task circuits and transplanting their activations across nine cyclic task families. We found that Qwen produced held-out circular geometry and selection-sufficient circuits for seven families; the resulting masks had little neuron overlap (median Jaccard $0.122$). Across 42 directed task pairs, a donor performing the target's signed shift increased normalized restoration by $0.651$ over a different-shift donor (95\% bootstrap CI $[0.474,0.838]$; sign-flip $p<10^{-6}$). The discrete operation match predicted repair, whereas continuous similarity between fitted operators was nearly uncorrelated with control-adjusted transfer strength ($\rho=0.031$). Activations from low-overlap task circuits can therefore support cross-task repair across circularly structured representations when their signed operations agree. A clean latent shape leaves that compatibility unresolved, so geometric claims about computation require operation-specific interventions.