Truncate Bad, Upweight Good: BoN-Style Distillation via Rank-Based Classification
Organizations: Department of Electrical and Computer Engineering Technion–Israel Institute of Technology · Department of Computer Science Technion–Israel Institute of Technology
Abstract
Inference-time selection methods, such as Best-of-N, improve generation by sampling a pool of candidates and selecting the top-ranked completion according to a reward model. Distillation seeks to amortize this procedure into a single policy by replacing raw rewards with in-pool ranks and learning a policy that upweights higher-ranked completions. However, existing rank-based policies typically use smooth full-support reweighting, so low-ranked completions receive less mass but remain in the target support. Although a sharper reweighting reduces lower-tail mass, it also increases reliance on brittle ranking at the top made by a single reward model. We propose TUP: a Truncate-bad, Upweight-good Policy that removes low-ranked completions from the support and reweights only the retained upper tail with a tunable sharpness. TUP admits a closed-form, prompt-independent normalization and can be trained fully offline via binary cross-entropy, using shifted-truncated win-rates as soft labels and distilled-to-reference log-likelihood ratios as logits. Theoretically, under certain assumptions, we show that for any unknown oracle reward, the best monotone rank-reweighting can be matched by a lower-tail truncation rule, providing formal support for removing the lower tail rather than merely downweighting it. Empirically, we show that TUP is competitive with strong offline alignment baselines.
Figures & tables
| UltraFeedback eval split | Magpie Air eval split | |||||
| Method | ArmoRM | Skywork-Llama | Skywork-Qwen | ArmoRM | Skywork-Llama | Skywork-Qwen |
| Initial | ||||||
| DPO | ||||||
| REBEL | ||||||
| REBEL (random) | ||||||
| QRPO | ||||||
| Reward model | GPT Judge | ||||||
| Train set | Method | ArmoRM | Skywork-Llama | Skywork-Qwen | LC Win | Win | Len |
| UltraFeedback | Initial | 1011 | |||||
| DPO | 1807 | ||||||
| REBEL | 1938 | ||||||
| REBEL (random) | 1959 | ||||||
| QRPO | 3100 | ||||||
| ArmoRM | Skywork-v2-Llama | Skywork-v2-Qwen | GPT Judge | ||||||
| Method | MA | AE | MA | AE | MA | AE | LC Win | Win | Len |
| Initial | |||||||||
| DPO | |||||||||
| REBEL | |||||||||
| REBEL (random) | |||||||||
| QRPO | |||||||||
Appendix figures & tables12 assets
Supplementary material from the paper’s appendix.
Appendix
| ArmoRM | Skywork-v2-Llama | Skywork-v2-Qwen | UF | ||||
|---|---|---|---|---|---|---|---|
| Method | UF | AE | UF | AE | UF | AE | Len |
| Initial | |||||||
| DPO | |||||||
| REBEL | |||||||
| REBEL (rand) | |||||||
| QRPO | |||||||
| ArmoRM | Skywork-v2-Llama | Skywork-v2-Qwen | MA | ||||
|---|---|---|---|---|---|---|---|
| Method | MA | AE | MA | AE | MA | AE | Len |
| Initial | |||||||
| DPO | |||||||
| REBEL | |||||||
| REBEL (random) | |||||||
| QRPO | |||||||
| ArmoRM | Skywork-v2-Llama | Skywork-v2-Qwen | MA | ||||
| Method | MA | AE | MA | AE | MA | AE | Len |
| Initial | |||||||
| DPO | |||||||
| REBEL | |||||||
| REBEL (random) | |||||||
| QRPO | |||||||
| Method | ArmoRM | Skywork-Llama | Skywork-Qwen | Prompts retained (of 2415) |
|---|---|---|---|---|
| DPO | 53.1% | 55.3% | 49.1% | 276 |
| REBEL | 50.9% | 50.2% | 45.8% | 463 |
| REBEL (random) | 64.9% | 63.2% | 61.8% | 238 |
| QRPO | 51.4% | 56.6% | 56.6% | 415 |
| QRPO (random) | 54.2% | 53.1% | 46.7% | 240 |
| BoNBoN | 71.0% | 60.7% | 56.5% | 169 |
| Model | Role in this work | Model type | Global Rank | Type Rank |
|---|---|---|---|---|
| ArmoRM-Llama3-8B-v0.1 | Training proxy reward model | Classifier | #34 | #26 |
| Skywork-Reward-V2-Llama-3.1-8B | Evaluation reward model | Classifier | #1 | #1 |
| Skywork-Reward-V2-Qwen3-8B | Evaluation reward model | Classifier | #6 | #3 |
| GPT judge | Generative | #36 | #10 |
| Method | Dataset variant | Num ref | Checkpoint | |||
| DPO | offpolicy2best | 0.01 | 3e-07 | 6 | - | 300 |
| REBEL | offpolicy2best | 1e-06 | 3e-07 | 6 | - | 200 |
| REBEL (rand.) | offpolicy2random | 1e-06 | 1e-06 | 6 | - | 100 |
| QRPO | offpolicy2best | 3e-04 | 3e-07 | 3 | - | 100 |
| QRPO (rand.) | offpolicy2random | 3e-04 | 3e-07 | 3 | - | 100 |
| BoNBoN | offpolicy2best | 1e-03 | 1e-06 | 6 | - | 476 |
| Method | Dataset variant | Num ref | Checkpoint | |||
| DPO | offpolicy2random | 0.01 | 1e-06 | 6 | - | 480 |
| REBEL | offpolicy2best | 1e-06 | 1e-07 | 6 | - | 640 |
| REBEL (rand.) | offpolicy2random | 1e-04 | 1e-06 | 6 | - | 320 |
| QRPO | offpolicy2best | 1e-03 | 1e-07 | 1 | - | 320 |
| QRPO (rand.) | offpolicy2random | 1e-03 | 1e-07 | 1 | - | 320 |
| BoNBoN | offpolicy2best | 1e-03 | 1e-06 | 6 | - | 764 |
| Method | Dataset variant | Num ref | Checkpoint | |||
| DPO | offpolicy2random | 0.03 | 3e-07 | 6 | - | 480 |
| REBEL | offpolicy2best | 1e-04 | 1e-07 | 6 | - | 480 |
| REBEL (rand.) | offpolicy2random | 1e-04 | 3e-07 | 6 | - | 320 |
| QRPO | offpolicy2best | 3e-03 | 1e-07 | 1 | - | 764 |
| QRPO (rand.) | offpolicy2random | 3e-03 | 1e-06 | 1 | - | 764 |
| BoNBoN | offpolicy2best | 1e-03 | 1e-07 | 6 | - | 480 |
| Asset | Role in this work | Reported license or terms |
|---|---|---|
| QRPO reference codebase | Experimental framework and baseline implementation. | MIT license. |
| QRPO UltraFeedback reference datasets offpolicy2best , offpolicy2random | Preprocessed UltraFeedback reference-completion pools and ArmoRM scores used for training and evaluation. | MIT license. |
| QRPO Magpie Air reference datasets offpolicy2best , offpolicy2random | Preprocessed Magpie Air reference-completion pools and ArmoRM scores used for training and evaluation. | MIT license for the QRPO preprocessed releases; the upstream Magpie Air dataset card does not declare a separate license field. |
| openbmb/UltraFeedback | Source instruction-tuning dataset underlying the UltraFeedback QRPO setting. | MIT license. |
| tatsu-lab/alpaca_eval | AlpacaEval prompt set used for GPT-judge evaluation. | CC-BY-NC-4.0 license. |
| allenai/reward-bench | RewardBench leaderboard context for the reward and judge models in Table 8 . | ODC-BY-1.0 license. |
Language Model Distillation
Language model distillation transfers a larger model’s capabilities to smaller or specialized models using outputs, probabilities, or internal representations.
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