# PROOF-Gen: From Optimized Data to Better Distillation

arXiv: https://arxiv.org/abs/2608.23911 · HTML: https://mlsanity.com/paper/2608.23911/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Tool learning and function calling, one of 16 directions in LLM agents and tool use.
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Placed in

- LLM agents and tool use / [Tool learning and function calling](https://mlsanity.com/agents/tool-learning-and-function-calling/)

## Builds on (most cited first, 17 of 17)

- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Automatic Prompt Optimization with "Gradient Descent" and Beam Search](https://mlsanity.com/paper/2305.03495/) (2023)
- [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)
- [Optimizing Instructions and Demonstrations for Multi-Stage Language Model Programs](https://mlsanity.com/paper/2406.11695/) (2024)
- [FireAct: Toward Language Agent Fine-tuning](https://mlsanity.com/paper/2310.05915/) (2023)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [APIGen: Automated Pipeline for Generating Verifiable and Diverse Function-Calling Datasets](https://mlsanity.com/paper/2406.18518/) (2024)
- [Agent-R: Training Language Model Agents to Reflect via Iterative Self-Training](https://mlsanity.com/paper/2501.11425/) (2025)
- [Magnet: Multi-turn Tool-use Data Synthesis and Distillation via Graph Translation](https://mlsanity.com/paper/2503.07826/) (2025)
- [RL for Reasoning by Adaptively Revealing Rationales](https://mlsanity.com/paper/2506.18110/) (2025)
- [AgentArk: Distilling Multi-Agent Intelligence into a Single LLM Agent](https://mlsanity.com/paper/2602.03955/) (2026)
- [Does RL Expand the Capability Boundary of LLM Agents? A PASS@(k,T) Analysis](https://mlsanity.com/paper/2604.14877/) (2026)

## Abstract (arXiv)

Supervised fine-tuning on teacher-generated trajectories is the standard first stage for distilling tool-calling capabilities into deployable models. Post-training pipelines that drive shipped tool-calling agents re-run this stage on a daily or weekly cadence, paying the frontier-teacher cost each cycle, yet the mechanism is generate-and-filter (keep the teacher's passing trajectories, discard the rest) and each cycle leaves behind the same hard scenarios because failures supply no signal. On τ2-bench, 57% of teacher trials fail, two-thirds of them near-misses (most tool calls correct, undone by one decisive error). We introduce PROOF-Gen (Per-scenario Reflective Optimization to Overcome FailedGeneration), which recovers golden trajectories from these failures via per-scenario prompt optimization. For each failed task, a reflector analyzes the execution trace and evaluation feedback, then writes corrective guidance that steers the teacher to a passing trajectory. The guidance is stripped before training, so the student learns from clean demonstrations with no task-specific scaffold. On τ2-bench, per-scenario optimization recovers 93% of failed scenarios. Fine-tuned on the combined data, Qwen3-4B-Instruct-2507 improves from Pass1=0.132 to 0.529 and Gemma 4 E4B-it gains +7.2pp on BFCL v4 multi-turn. In a deployed pipeline, the method lifts trajectory quality by +6.3pp goal completion and transfers to a deployed on-device model (+1.5pp goal completion; +1.7 to +5.0pp across response-quality metrics), with positive transfer in every locale (non-English average +1.48pp).