# The Verifier is the Curriculum: Precision Sets the Return on Search in Code Self-Distillation

arXiv: https://arxiv.org/abs/2607.09709 · HTML: https://mlsanity.com/paper/2607.09709/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 25 of its 37 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Placed in

- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 25 of 25)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [ImpossibleBench: Measuring LLMs' Propensity of Exploiting Test Cases](https://mlsanity.com/paper/2510.20270/) (2025)
- [Cheating Automatic LLM Benchmarks: Null Models Achieve High Win Rates](https://mlsanity.com/paper/2410.07137/) (2024)
- [Reinforcement Learning with Verifiable yet Noisy Rewards under Imperfect Verifiers](https://mlsanity.com/paper/2510.00915/) (2025)
- [Embarrassingly Simple Self-Distillation Improves Code Generation](https://mlsanity.com/paper/2604.01193/) (2026)
- [GATES: Self-Distillation under Privileged Context with Consensus Gating](https://mlsanity.com/paper/2602.20574/) (2026)
- [Reward Hacking Benchmark: Measuring Exploits in LLM Agents with Tool Use](https://mlsanity.com/paper/2605.02964/) (2026)
- [GameDevBench: Evaluating Agentic Capabilities Through Game Development](https://mlsanity.com/paper/2602.11103/) (2026)
- [LLMs Gaming Verifiers: RLVR can Lead to Reward Hacking](https://mlsanity.com/paper/2604.15149/) (2026)
- [OpenGame: Open Agentic Coding for Games](https://mlsanity.com/paper/2604.18394/) (2026)
- [When Does Verification Pay Off? A Closer Look at LLMs as Solution Verifiers](https://mlsanity.com/paper/2512.02304/) (2025)
- [An Imperfect Verifier is Good Enough: Learning with Noisy Rewards](https://mlsanity.com/paper/2604.07666/) (2026)
- [GameGen-Verifier: Parallel Keypoint-Based Verification for LLM-Generated Games via Runtime State Injection](https://mlsanity.com/paper/2605.07442/) (2026)
- [Delay, Plateau, or Collapse: Evaluating the Impact of Systematic Verification Error on RLVR](https://mlsanity.com/paper/2605.02909/) (2026)
- [JAMER: Project-Level Code Framework Dataset and Benchmark on Professional Game Engines](https://mlsanity.com/paper/2606.19830/) (2026)
- [Teacher-Free Self-Training Amplifies but Does Not Compound: A Pass@K Crossover on a Free-Verifier Domain](https://mlsanity.com/paper/2606.07856/) (2026)

## Built on by (most cited first, 3 of 3)

- [GameASG-Bench: Benchmarking Autonomous Software Generation for Game Development](https://mlsanity.com/paper/2609.21293/) (2026)
- [RSIGame: Autonomous Agentic Game Development with Recursive Self-improvement](https://mlsanity.com/paper/2609.39045/) (2026)
- [GameSmith: Scaling Zero-Sum Self-Play with Synthesised Games](https://mlsanity.com/paper/2610.13995/) (2026)

## Abstract (arXiv)

Post-training a code generator against a learned judge can optimize proxy features that raise the score without improving the artifact. We study the opposite signal: a deterministic, judge-free filter that asks only whether a generated project launches cleanly under a headless engine (strict-launch). Under this gate, rejection-sampling self-distillation compounds out-of-family generalization: on GameCraft-Bench a 14B model raises the per-candidate clean-launch rate on four held-out families from 8.8% to 42.2% and coverage at 32 candidates from 84% to 100%, the gold references' own ceiling, beating the supervised model on every one of the 25 held-out tasks. The gate costs one engine invocation per candidate: no reward model, no judge. At a fixed admitted count, what governs the loop is verifier precision. Swapping in a lenient build check alone erases the gain (p=0.0012); a matched gold-duplication control regresses below the supervised model. Under a semantic gate on APPS, dialing fuel precision from 1.0 to 0.25 at fixed candidate count prices that fuel linearly: over 23 training seeds, half-clean fuel returns +3.59 percentage points against the +3.69 a linear rate predicts. Under count-matched rejection-SFT only one direction of verifier error carries a measurable cost. Search obeys the same gate: quadrupling the harvest budget is worth +1.62pp behind a strict gate and nothing distinguishable from zero behind a partial-credit one. Recall is nearly free; search pays only through a precise gate: the verifier is the curriculum.