# Primal Generation, Dual Judgment: Self-Training from Test-Time Scaling

arXiv: https://arxiv.org/abs/2605.11299 · HTML: https://mlsanity.com/paper/2605.11299/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 38 of its 45 references that are in the map.
- First posted on arXiv 11 May 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)

## Builds on (most cited first, 30 of 38)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [CodeRL: Mastering Code Generation through Pretrained Models and Deep Reinforcement Learning](https://mlsanity.com/paper/2207.01780/) (2022)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Self-Play Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2405.00675/) (2024)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [RLEF: Grounding Code LLMs in Execution Feedback with Reinforcement Learning](https://mlsanity.com/paper/2410.02089/) (2024)
- [OpenCodeReasoning: Advancing Data Distillation for Competitive Coding](https://mlsanity.com/paper/2504.01943/) (2025)
- [Execution-based Code Generation using Deep Reinforcement Learning](https://mlsanity.com/paper/2301.13816/) (2023)
- [S*: Test Time Scaling for Code Generation](https://mlsanity.com/paper/2502.14382/) (2025)
- [ACECODER: Acing Coder RL via Automated Test-Case Synthesis](https://mlsanity.com/paper/2502.01718/) (2025)
- [Planning In Natural Language Improves LLM Search For Code Generation](https://mlsanity.com/paper/2409.03733/) (2024)
- [Learning to Plan & Reason for Evaluation with Thinking-LLM-as-a-Judge](https://mlsanity.com/paper/2501.18099/) (2025)
- [Self-Generated Critiques Boost Reward Modeling for Language Models](https://mlsanity.com/paper/2411.16646/) (2024)
- [rStar-Coder: Scaling Competitive Code Reasoning with a Large-Scale Verified Dataset](https://mlsanity.com/paper/2505.21297/) (2025)
- [Evaluating Judges as Evaluators: The JETTS Benchmark of LLM-as-Judges as Test-Time Scaling Evaluators](https://mlsanity.com/paper/2504.15253/) (2025)
- [Teaching Language Models to Critique via Reinforcement Learning](https://mlsanity.com/paper/2502.03492/) (2025)
- [Klear-Reasoner: Advancing Reasoning Capability via Gradient-Preserving Clipping Policy Optimization](https://mlsanity.com/paper/2508.07629/) (2025)
- [ReVISE: Learning to Refine at Test-Time via Intrinsic Self-Verification](https://mlsanity.com/paper/2502.14565/) (2025)
- [Thinking Longer, Not Larger: Enhancing Software Engineering Agents via Scaling Test-Time Compute](https://mlsanity.com/paper/2503.23803/) (2025)
- [OpenCodeReasoning-II: A Simple Test Time Scaling Approach via Self-Critique](https://mlsanity.com/paper/2507.09075/) (2025)

## Abstract (arXiv)

Code generation is typically trained in the primal space of programs: a model produces a candidate solution and receives sparse execution feedback, often a single pass/fail bit. Test-time scaling enriches the inference procedure by sampling multiple candidates and judging among them, but the comparative information this process reveals is discarded after inference. We argue that this information defines a dual judgment space that provides a far richer training signal: the model learns not from an isolated success or failure, but from the relative correctness structure across its own plausible attempts, identifying which succeed, which fail, and what distinguishes them. We introduce DuST (Dual Self-Training), a framework for self-training from the dual judgment space. DuST samples candidate programs from the model's own distribution, labels them through sandbox execution, retains groups containing both successes and failures, and trains the model to rank candidates by execution correctness using GRPO. The objective is purely discriminative: the model is never directly rewarded for generating correct programs. Dual self-training improves both judgment and generation. Across five models spanning two families and three scales (4B to 30B), DuST consistently improves Best-of-4 test-time scaling on LiveCodeBench. For Qwen3-30B-Thinking on LiveCodeBench v6, judgment quality improves by +6.2 NDCG, single-sample pass@1 improves by +3.1, and Best-of-4 accuracy improves by +4.1. The trained model's single rollout matches the base model's Best-of-4 performance. SFT on the same ranking data improves judgment without improving generation, confirming that on-policy RL is the mechanism that transfers dual-space learning back into primal generation.