# Drift-Constrained Optimization: Only Direction Matters in Fine-Tuning Instruct Models

arXiv: https://arxiv.org/abs/2609.13680 · HTML: https://mlsanity.com/paper/2609.13680/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 54 references that are in the map.
- First posted on arXiv 12 Sep 2026.

## Builds on (most cited first, 30 of 34)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [The FLORES-101 Evaluation Benchmark for Low-Resource and Multilingual Machine Translation](https://mlsanity.com/paper/2106.03193/) (2021)
- [Kimi K2.5: Visual Agentic Intelligence](https://mlsanity.com/paper/2602.02276/) (2026)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Do Llamas Work in English? On the Latent Language of Multilingual Transformers](https://mlsanity.com/paper/2402.10588/) (2024)
- [xCOMET: Transparent Machine Translation Evaluation through Fine-grained Error Detection](https://mlsanity.com/paper/2310.10482/) (2023)
- [Training Neural Networks with Fixed Sparse Masks](https://mlsanity.com/paper/2111.09839/) (2021)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [Understanding Catastrophic Forgetting in Language Models via Implicit Inference](https://mlsanity.com/paper/2309.10105/) (2023)
- [Safety Layers in Aligned Large Language Models: The Key to LLM Security](https://mlsanity.com/paper/2408.17003/) (2024)
- [LlaSMol: Advancing Large Language Models for Chemistry with a Large-Scale, Comprehensive, High-Quality Instruction Tuning Dataset](https://mlsanity.com/paper/2402.09391/) (2024)
- [BIG-Bench Extra Hard](https://mlsanity.com/paper/2502.19187/) (2025)
- [What Would Elsa Do? Freezing Layers During Transformer Fine-Tuning](https://mlsanity.com/paper/1911.03090/) (2019)
- [MegaScience: Pushing the Frontiers of Post-Training Datasets for Science Reasoning](https://mlsanity.com/paper/2507.16812/) (2025)
- [FreezeOut: Accelerate Training by Progressively Freezing Layers](https://mlsanity.com/paper/1706.04983/) (2017)
- [Tower+: Bridging Generality and Translation Specialization in Multilingual LLMs](https://mlsanity.com/paper/2506.17080/) (2025)
- [Lego-MT: Learning Detachable Models for Massively Multilingual Machine Translation](https://mlsanity.com/paper/2212.10551/) (2022)
- [Seed-X: Building Strong Multilingual Translation LLM with 7B Parameters](https://mlsanity.com/paper/2507.13618/) (2025)
- [CURLoRA: Stable LLM Continual Fine-Tuning and Catastrophic Forgetting Mitigation](https://mlsanity.com/paper/2408.14572/) (2024)

## Abstract (arXiv)

Fine-tuning instruct models often improves target performance while inducing behavioral drift from the reference model, which can degrade existing capabilities. Rather than treating this drift as an uncontrolled consequence of optimization, we specify a behavioral drift budget before optimization and ask how to boost the target-task performance within it. Locally, behavioral drift induces a shared geometry anchored at the reference model, with the drift budget defining a boundary within this space. In this space, drift determines distance from the reference, leaving update direction as the remaining degree of freedom. Fine-tuning updates can therefore be compared through their directional efficiency, naturally reformulating fine-tuning as a direction-selection problem. This reformulation makes a concrete prediction: changing the accessible directions can qualitatively alter the outcome of fine-tuning. We test this prediction in a stringent QA-only setting, where strong instruct models are fine-tuned only on final answers but must still generate multi-step reasoning at inference. Despite this mismatch, a coarse layer-selective probe reverses the failure of QA-only fine-tuning and reveals the existence of effective directions, with multiple neighboring configurations improving target performance while preserving reasoning and general capabilities. Across Qwen3-8B and Qwen3-14B, these directions substantially improve scientific reasoning and multilingual translation. Over more than 100 languages, the resulting models match or outperform dedicated translation systems and provide a stronger initialization for subsequent reinforcement learning. Our results suggest that fine-tuning is not just about how much a model changes, but how that change is spent. https://github.com/CONE-MT/DCO and https://huggingface.co/collections/LLaMAX/dco