The Alignment Tax Is Graded: Task-Selective Capability Loss Under Length-Normalized DPO with SFT Retention

Abstract

Setting. This is an empirical characterization study; we propose no new method and run no comparisons against alternative objectives. We fine-tune Qwen3.5-4B with sparse LoRA and length-normalized DPO plus an SFT retention term (the RPO objective) on structured financial-filing tasks, and track downstream capability as the implicit reward margin grows to $\sim 7$ $\beta$-scaled units (nf4 training; $\sim 3$ under fp16 measurement on the unquantized base). Question. Does margin growth degrade capability uniformly across tasks, or selectively? Findings. In a pre-registered study (8 seeds, 6 unseen at freeze) with artifact-aware scoring and TOST equivalence testing, the alignment tax is graded and task-selective: extraction is preserved ($\Delta = -0.55$ pts, equivalent at $\pm5$ pts), json loses little ($\Delta = -3.52$ pts, equivalence fails on a clustered item-level interval), and router degrades severely ($\Delta = -30$ pts). Router's loss concentrates in a margin 1-3 damage window containing a transient format-break spike. The margin is accounted for almost entirely ($\geq 96\%$) by suppression of rejected completions, with chosen reward approximately flat, consistent with the retention term anchoring it; we do not attribute the behavioral damage to any single gradient channel. Gold-logp deflation is task-selective (extraction $-0.15$, json $-1.04$, router $-1.47$ nats/token under fp16), with gold selectively protected relative to incorrect controls on extraction (8/8 seeds). QLoRA reward margins differ up to $3.4\times$ between nf4 training and unquantized fp16 measurement, with an axis-dependent gap. Scope. Length-normalized rewards with SFT retention, sparse LoRA on 8/32 layers, one 4B model, easily-separable synthetic preferences, three structured tasks. A no-retention control and a measured format-alignment metric are left to future work.