# Evil Spectra: How Optimisers can Amplify or Suppress Emergent Misalignment

arXiv: https://arxiv.org/abs/2606.31591 · HTML: https://mlsanity.com/paper/2606.31591/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 25 references that are in the map.
- First posted on arXiv 30 Jun 2026.

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

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To!](https://mlsanity.com/paper/2310.03693/) (2023)
- [Symbolic Discovery of Optimization Algorithms](https://mlsanity.com/paper/2302.06675/) (2023)
- [Implicit Regularization in Matrix Factorization](https://mlsanity.com/paper/1705.09280/) (2017)
- [Shadow Alignment: The Ease of Subverting Safely-Aligned Language Models](https://mlsanity.com/paper/2310.02949/) (2023)
- [The Marginal Value of Adaptive Gradient Methods in Machine Learning](https://mlsanity.com/paper/1705.08292/) (2017)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [Old Optimizer, New Norm: An Anthology](https://mlsanity.com/paper/2409.20325/) (2024)
- [Natural Emergent Misalignment from Reward Hacking in Production RL](https://mlsanity.com/paper/2511.18397/) (2025)
- [Model Organisms for Emergent Misalignment](https://mlsanity.com/paper/2506.11613/) (2025)
- [Thought Crime: Backdoors and Emergent Misalignment in Reasoning Models](https://mlsanity.com/paper/2506.13206/) (2025)
- [Lion Secretly Solves Constrained Optimization: As Lyapunov Predicts](https://mlsanity.com/paper/2310.05898/) (2023)
- [Emergent Misalignment is Easy, Narrow Misalignment is Hard](https://mlsanity.com/paper/2602.07852/) (2026)

## Abstract (arXiv)

Emergent misalignment (EM) is a recently discovered phenomenon in LLMs where fine-tuning on a narrow misaligned task, such as writing insecure code, leads to broadly misaligned behaviour on unrelated prompts. Previous work has noted that the severity of EM is highly sensitive to training choices; however, we still lack a systematic characterisation of this sensitivity. We perform a sweep over several Qwen3 models, optimisers, datasets, and batch sizes, and find that the choice of optimiser has the largest effect, producing a 7x spread in misalignment rate. Surprisingly, model size has a negligible effect within the Qwen3 family. An additional sweep over 12 models from three families using Adam confirms that model scale (1B-235B) and family have negligible effects for that optimiser. Analysing the loss-alignment relationship on Qwen3-8B, we find that final log training loss is a strong predictor of alignment, and that stratifying by optimiser captures nearly all the residual variance. Training dynamics reveal that each optimiser follows a different trajectory through loss-alignment space, and that after significant training, the optimiser becomes more important than training loss as a predictor of alignment. Muon, the adaptive optimiser that preserves alignment the best, implicitly regularises for a more uniform distribution of singular values of the LoRA adapter. We evaluate this insight by training with an additional loss term that incentivises a flatter singular value spectrum, and find that this substantially recovers alignment for the more EM-prone adaptive optimisers (Adam and Lion), with negligible cost to training loss. These results identify optimiser choice as a key factor in EM severity, but show that spectral regularisation can substantially mitigate the effects of EM-prone optimisers.