From Generic Correlation to Input-Specific Credit in On-Policy Self Distillation

• URL: http://arxiv.org/abs/2605.11613v1
• Date: Tue, 12 May 2026 06:43:17 GMT
• Title: From Generic Correlation to Input-Specific Credit in On-Policy Self Distillation
• Abstract summary: On-policy self-distillation has emerged as a promising paradigm for post-training language models.<n>We show that the self-distillation token reward is a Bayesian filtering increment whose trajectory sum is exactly the pointwise mutual information between the response and the feedback given the input.<n>We propose CREDIT, which isolates the input-specific component with a batch-contrastive baseline.
• Score: 22.436966302243565
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: On-policy self-distillation has emerged as a promising paradigm for post-training language models, in which the model conditions on environment feedback to serve as its own teacher, providing dense token-level rewards without external teacher models or step-level annotations. Despite its empirical success, what this reward actually measures and what kind of credit it assigns remain unclear. Under a posterior-compatibility interpretation of feedback conditioning, standard in the implicit-reward literature, we show that the self-distillation token reward is a Bayesian filtering increment whose trajectory sum is exactly the pointwise mutual information between the response and the feedback given the input. This pMI can be raised by input-specific reasoning or by input-generic shortcuts, so we further decompose the teacher log-probability along the input axis. Based on this analysis, we propose CREDIT (Contrastive REward from DIsTillation), which isolates the input-specific component with a batch-contrastive baseline. At the sequence level, CREDIT is a teacher-side surrogate for a contrastive pMI objective that also penalizes responses remaining likely under unrelated inputs. Across coding, scientific reasoning, and tool-use benchmarks on two model families, CREDIT delivers the strongest aggregate performance at negligible additional compute.

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