# GAC: Noise-Aware Adaptive Mixing for Hybrid SFT-RL Post-Training

arXiv: https://arxiv.org/abs/2605.26184 · HTML: https://mlsanity.com/paper/2605.26184/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 35 references that are in the map.
- First posted on arXiv 25 May 2026.

## Builds on (most cited first, 27 of 27)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [On-Policy RL Meets Off-Policy Experts: Harmonizing Supervised Fine-Tuning and Reinforcement Learning via Dynamic Weighting](https://mlsanity.com/paper/2508.11408/) (2025)
- [SRFT: A Single-Stage Method with Supervised and Reinforcement Fine-Tuning for Reasoning](https://mlsanity.com/paper/2506.19767/) (2025)
- [Towards a Unified View of Large Language Model Post-Training](https://mlsanity.com/paper/2509.04419/) (2025)
- [Direction-oriented Multi-objective Learning: Simple and Provable Stochastic Algorithms](https://mlsanity.com/paper/2305.18409/) (2023)
- [On the Non-decoupling of Supervised Fine-tuning and Reinforcement Learning in Post-training](https://mlsanity.com/paper/2601.07389/) (2026)

## Built on by (most cited first, 1 of 1)

- [Outcome-Routed Distillation and Reinforcement Learning for Diffusion Language Models](https://mlsanity.com/paper/2610.19271/) (2026)

## Abstract (arXiv)

Hybrid post-training combining supervised fine-tuning (SFT) and reinforcement learning (RL) is the standard paradigm for aligning large language models, yet fixed mixing schedules cannot adapt when the relative noise of the two signals evolves. We derive a noise-aware mixing weight mu* by minimizing an MSE upper bound on the mixed stochastic gradient, yielding a closed-form that balances gradient noise variance and SFT-RL disagreement. Building on the token-wise reweighting of CHORD, the practical Guided Adaptive Controller (GAC) adds EMA smoothing, a schedule prior, and capped updates around this estimator, with all statistics estimated online from existing training tensors. The noise-aware controller alone outperforms the best rule-based controller by +3.0 percentage points on AMC; the full system reaches +3.8 points over HPT across math, code, science, and logic benchmarks, while reducing KL-drift area by 28% and large absolute mixing-weight changes by more than 70%, at less than 1% overhead. Gains grow with model size from 1.5B to 14B. Resources: Qwen3.5-4B compact-backbone release: https://huggingface.co/YueLinHu/GAC-Qwen3.5-4B; reference implementation: https://github.com/deepnovacore/GAC; GAC project page: https://deepnovacore.github.io/GAC/