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Shared Residual Distillation learns from peer solutions without labelling one correct

Key Takeaways

  • The method keeps conservative prediction changes shared across unverified trajectories, with no peer ensemble required at inference.
  • ## Useful reasoning can appear in an incorrect answer
  • Shared Residual Distillation asks whether a language model can learn from several of its own solutions without first deciding which complete solution is correct.
  • The authors note that a trajectory ending with a wrong answer can still contain useful intermediate reasoning, making final-answer correctness an incomplete description of its training value.
  • The method is an on-policy form of self-distillation.

Useful reasoning can appear in an incorrect answer

Shared Residual Distillation asks whether a language model can learn from several of its own solutions without first deciding which complete solution is correct. The authors note that a trajectory ending with a wrong answer can still contain useful intermediate reasoning, making final-answer correctness an incomplete description of its training value.
The method is an on-policy form of self-distillation. It uses the model's own unverified peer trajectories rather than reference answers, an external teacher or a verifier that labels every solution before training.

Keep shared changes conservatively

SRD compares how the peers change a prediction distribution relative to a control. It retains adjustments that agree in direction and are conservative in magnitude. The resulting supervision does not require treating any entire trajectory as authoritative.
The trained model needs no peers at inference time. That distinction separates the training process from the cost of using the resulting model: the reported approach is not simply a voting ensemble that must generate several complete solutions for each deployed request.

What the reported gains measure

Starting from corresponding base models, the authors report mean AIME24–26 avg@12 rising from 11.02 to 16.20 for Qwen3-1.7B, from 19.07 to 45.46 for Qwen3-4B and from 21.39 to 54.44 for Qwen3-8B. These are the paper's stated benchmark measures, not single-attempt accuracy or proof of general reasoning reliability.
The researchers also report controlled ablations and no degradation on two general-capability benchmarks. Franklin's reading is to inspect whether the shared-residual construction explains the gain and whether the evaluation covers the intended use beyond competition-style mathematics.
Agreement between generated solutions is not an independent source of truth. The contribution here is a specific way to extract a training signal from their distributional changes, with reported outcomes that still depend on the model, training setup and benchmark.
Read the SRD paper.

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