Effect of DPO Temperature on Adapter-Absorbed Heterogeneity

Determine whether increasing the DPO inverse-temperature parameter lowers the numerical rank of client heterogeneity gradient blocks and increases the fraction of gradient heterogeneity absorbed by private LoRA adapters.

Background

The appendix analyzes how the DPO inverse-temperature parameter affects the weighting of preference pairs in client gradients. The authors hypothesize that larger values concentrate the gradient weights on misordered pairs, potentially lowering the numerical rank of the heterogeneity blocks and enabling private adapters to absorb a larger fraction of client-specific heterogeneity. The hypothesis is explicitly untested because all reported experiments use the same inverse temperature.

References

We conjecture that this lowers the numerical rank of $Z_{i,\ell}$ and increases the absorbed fraction $\kappa2_\parallel/\kappa2$. All our experiments use $\beta=0.2$, so this is untested.

— Personalized Federated Direct Preference Optimization via LoRA Adapters  (2610.12885 - Jiang et al., 9 Oct 2026) in Appendix, Section “DPO-Specific Structure”