Balanced-KnOTS: Task-Balanced Subspace Selection for Fixed-Rank LoRA Merging

Post-hoc LoRA merging can replace a growing adapter library with one static model, but under a fixed deployment rank, every expert must compete for the same limited shared space. Existing shared-SVD methods optimize aggregate reconstruction, which can preserve substantial total energy while severely underrepresenting individual tasks. We identify this as an aggregate-diagnostic blind spot and show that discarded task components create an irrecoverable projection bottleneck: no subsequent merger restricted to the selected space can reconstruct them. We introduce task-wise projection coverage to quantify per-expert representational availability and propose Balanced-KnOTS, which removes norm-induced task weighting and optimizes a mean–soft-min objective to protect the coverage lower tail before applying the same TIES procedure in the retained coordinates. On 20 independently trained Qwen3-8B security-task LoRA experts consolidated into a single rank-16 adapter, Balanced-KnOTS raises worst-task coverage from 32.84% to 56.98% while leaving mean coverage essentially unchanged. Relative to equal-rank Joint KnOTS-TIES, it improves five of six held-out task metrics, increasing mean expert recovery from 82.80% to 87.55% and worst-task recovery from 54.12% to 63.66%. These results show that fixed-rank consolidation requires controlling how shared capacity is allocated across experts, not only how retained directions are merged.