  Direct Preference Optimization (DPO), which derives reward signals directly
from pairwise preference data, has shown its effectiveness on aligning Large
Language Models (LLMs) with human preferences. Despite its widespread use
across various tasks, DPO has been criticized for its sensitivity to the SFT's
effectiveness and its hindrance to the learning capacity towards
human-preferred responses, leading to less satisfactory performance. To
overcome those limitations, the theoretical understanding of DPO are
indispensable but still lacking. To this end, we take a step towards
theoretically analyzing and understanding the limitations of DPO. Specifically,
we provide an analytical framework using the field theory to analyze the
optimization process of DPO. By analyzing the gradient vector field of the DPO
loss function, we find that the DPO loss function decreases the probability of
producing human dispreferred data at a faster rate than it increases the
probability of producing preferred data. This provides theoretical insights for
understanding the limitations of DPO discovered in the related research
experiments, thereby setting the foundation for its improvement.
