Stabilizing LLM Supervised Fine-Tuning via Explicit Distributional Control

Evolution Strategies (ES) has recently emerged as a competitive alternative to reinforcement learning (RL) for large language model (LLM) fine-tuning, offering advantages through simplicity, scalability, and inference-only training. However, recent work suggests that ES fine-tuning on new tasks may induce forgetting of prior tasks. First, this paper shows that prior task forgetting (1) is better characterized as performance drift rather than irreversible forgetting, with prior-task performance often recovering during ES training; and (2) is not a specific failure mode of ES, but can also arise for fine-tuning with RL methods. Second, it analyzes when and why such drift arises, highlighting its dependence on ES training dynamics, particularly random walk behavior in weakly constrained directions of the weight space. Third, based on these insights, it introduces Anchored Weight Decay (AWD) as a parameter-space regularization technique that constrains optimization toward the initial model parameters. AWD effectively stabilizes prior-task performance while preserving target-task performance, achieving benefits comparable to large ES population sizes at much lower computational cost. Thus, contrary to previous beliefs, the paper shows that prior-task forgetting under ES is largely avoidable, positioning ES as a promising approach for continual learning in LLMs.

Low-Rank Adaptation (LoRA) has become one of the most widely used fine-tuning mechanisms for adapting large language models to new domains, tasks, and users. Yet adaptation performance alone can obscure an important failure mode: LoRA updates may improve performance on the target distribution while degrading prior capabilities learned during pretraining and alignment. We show that this forgetting becomes especially severe when the adaptation distribution differs substantially from the models original training or alignment distributions. The challenge is amplified in practical settings, where the original training and alignment data are typically unavailable. Motivated by this constraint, we study how LoRA based adaptation balances new learning against forgetting in a replay-free setting, and introduce a simple output space regularizer that can be added directly to existing training pipelines. Our method removes the ground-truth token from both the base and adapted model distributions, renormalizes the remaining probabilities, and applies KL regularization only over the non-target vocabulary. This preserves the base models relative preferences among alternative tokens without directly opposing the cross-entropy signal required for adaptation. As the regularizer acts only at the loss level, it requires no replay data, architectural changes, adapter redesign, or inference-time overhead, and can be applied directly to existing LoRA variants. Across all LoRA variants tested and across various backbones, our method improves the frontier between new learning and forgetting when the adaptation distribution differs substantially from the base models original training or alignment distributions, suggesting a broadly applicable route toward more reliable LLM updating.

Safety alignment in large language models is remarkably shallow: it is concentrated in the first few output tokens and reversible by fine-tuning on as few as 100 adversarial examples. This fragility becomes critical in real-world deployment, where models undergo sequential adaptation across domains such as medicine, law, and code, causing safety guardrails to erode cumulatively. Yet all existing safety-preserving methods target only single-task fine-tuning, leaving the multi-domain sequential setting entirely unaddressed. We introduce SafeAnchor, a framework that anchors safety in place throughout continual adaptation. SafeAnchor first identifies low-rank safety subspaces in LoRA parameter space via Fisher Information eigendecomposition, then constrains domain-specific gradient updates to the orthogonal complement of these subspaces, and finally monitors for residual safety drift with threshold-triggered corrective replay. Evaluated on Llama-2-7B-Chat and Mistral-7B-Instruct across a three-domain pipeline and eight benchmarks, SafeAnchor retains 93.2% of original safety alignment, outperforming all baselines by 18-42 points, while matching unconstrained fine-tuning to within 1.5 points on domain tasks.