Capability Traps in DPO

Direct Preference Optimization (DPO) is often tuned by selecting checkpoints with high preference margins. We show that this selection rule can fail. Across dense $\beta$ sweeps in three 7B open-weight families under controlled DPO recipes, the DPO preference margin can strongly anticorrelate with capability probes, with the strongest observed case in Llama logic probes (Pearson $r=-0.91$, $n=13$). In Mistral, matched-duration controls show that transient exposure to higher $\beta$ produces persistent arithmetic ($d_z = 3.73$, $p = 0.002$) and format ($d_z = 3.38$, $p = 0.003$) degradation relative to a duration-matched constant-$\beta$ run, while logic and sycophancy show no significant effect. An expanded 14-probe logic suite further shows that aggregate capability scores can hide stable opposition between probe clusters: direct-inference probes are consistently negative while fallacy-detection probes are consistently positive, with 13 of 14 probes sign-stable across 3 seeds and 3 $\beta$ values. Sensitivity profiles differ across architectures: Mistral shows elevated seed variance near $\beta \approx 10^{-2}$, Llama shows capability-specific rigidity, and Qwen trades off smoothly. These findings motivate probe-resolved $\beta$ sweeps rather than margin-based checkpoint selection.