On-policy distillation (OPD) trains a student on its own responses using token-level feedback from a teacher. As responses grow longer, the student's prefix can depart from the teacher's own reasoning, weakening its feedback on later tokens. Updates based on this feedback can reinforce the same deviations in later responses and destabilize training. Prior approaches such as length control and loss reweighting limit learning from problematic responses but leave their prefixes unchanged. Fixed cutoffs can also discard later reasoning. We propose \textbf{Adaptive Teacher Intervention for On-Policy Distillation (ATI-OPD)} to improve subsequent teacher guidance by revising the student's reasoning prefix. ATI-OPD replaces the earliest high-disagreement segment with a short teacher segment, then lets the student resume its own reasoning from the revised text. To handle renewed disagreement, it excludes persistently divergent suffixes from the distillation loss while retaining useful student continuation. Training diagnostics show less teacher-student disagreement, fewer gradient spikes, and fewer extremely long responses. Across five mathematical reasoning benchmarks and two teacher-student pairs, ATI-OPD improves average student-only accuracy over standard OPD.
Mingzhe Lu, Jian Qin, Ruize Qin, Jinhao Liu, Yunpeng Li, Hang Su
Narrative-driven recommendation allows users to express multifaceted needs through free-form text where stated preferences naturally qualify and condition one another. Existing methods typically treat narratives as flat keyword combinations or unconstrained generative queries, failing to capture how complex preferences hierarchically refine and contextualize each other. We propose the Preference Dependency Graph Framework (PDG-F), a narrative-driven recommendation framework centered on explicit preference dependencies. Specifically, PDG-A (PDG-Agent) first parses unstructured requests to organize user preferences and their mutual qualifications into a directed acyclic Preference Dependency Graph (PDG). Through this graph, candidate evidence from the open Web is acquired via directed path retrieval, and final recommendations are determined by topological path ranking. Comprehensive experiments across three diverse domains spanning English and Chinese contexts confirm that PDG-F consistently achieves superior recommendation performance over competitive baselines, open-domain retrieval agents, and frontier language models. Further diagnostic analyses show that our dependency-guided retrieval markedly raises the attainable candidate-pool ceiling, demonstrating the fundamental value of modeling preference dependencies in narrative-driven recommendation.