Long-horizon benchmarks often show that agents fail more as tasks become longer. This observation is useful for deployment, but it does not by itself explain why failure occurs. More stages create more opportunities for ordinary errors to compound; longer tasks may also contain harder individual decisions or become harder as conversation history, tool outputs, and environment changes accumulate. We use trajectory-induced degradation to mean this last possibility: earlier execution makes later work harder. When the harmful accumulation is specifically the text visible to the model, it is often called context rot. In this position paper, we argue that to claim a"long-horizon failure", benchmarks must compare actual full-task success against a baseline prediction built from short, individual stages. We call the log-ratio between this prediction and actual success the horizon residual. The comparison must use the same agent configuration and specify in advance how stages, checkpoints, information, and budgets will be chosen. The residual shows that the full rollout differs from the chosen baseline; targeted experiments are still needed to explain why.
On-policy self-distillation (OPSD) improves the reasoning abilities of LLMs by internalizing privileged context into model parameters through self-distillation. Two recent research lines promote vanilla OPSD by choosing which tokens to learn from and by controlling how much privileged information the teacher receives, respectively. However, we show that each line optimizes one variable while holding the other fixed, which leads to a suboptimal solution. We argue that the two variables are coupled through the student's learning capacity: the privileged information sets the per-token divergence the teacher prescribes, while token weighting selects which of these the student must absorb. We formalize the two lines of work into a unified optimization framework, which maximizes the aggregate teacher--student divergence, subject to a budget on the aggregate learning difficulty the student can absorb. Under this modelling, we propose Unified On-Policy Self-Distillation (USD), a lightweight online algorithm to solve the Lagrangian. USD reveals that a single dual variable governs both decisions: at one price for learning difficulty, it simultaneously sets the token-selection threshold and the direction of privileged-information adjustment, keeping supervision matched to the student's evolving capacity. Through extensive experiments, USD consistently demonstrates superior performance over OPSD and token- and PI-side baselines across various model scales on various reasoning benchmarks. Code is available at https://github.com/lauvlalala/USD.
Yongkang Yang, Zhezheng Hao, Hong Zhang et al.· 1 citation
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