SVDoRA: Spectral Verification-Aware Direction-Oriented Rank Adaptation via Outcome-Guided Spectral Annealing

SVD-based parameter-efficient fine-tuning selects spectral directions by correctness-agnostic scoring criteria and treats every selected direction as a generation update. We propose SVDoRA, a verification-aware adapter that uses gold-outcome labels to allocate capacity across a residual subspace and two spectral roles: task-specific generation directions (TSGD) and task-specific verification directions (TSVD). After a short residual-adapter warmup, a one-time calibration pass regenerates answers, labels them against gold outcomes, and selects the two roles by outcome-guided spectral annealing; the chosen directions then stay fixed for the rest of training. Compared with standard rank-$r$ LoRA, SVDoRA trains $r$ residual singular values and $k_g+k_v$ direction coefficients in addition to the two residual factors—24 extra scalars per target matrix at the canonical $r=16$, $k_g=k_v=4$ setting. SVDoRA reaches 88.1% average accuracy on Qwen2.5-7B commonsense reasoning at rank 16 (+1.4 pp over LoRA-DASH) and 79.0% at 1.5B rank 16; it leads the Llama-3 GSM8K$+$MATH average (48.4%), with competitive transfer to factual QA and code generation.