# Shared Parameter Subspaces and Cross-Task Linearity in Emergently Misaligned Behavior

arXiv: https://arxiv.org/abs/2511.02022 · HTML: https://mlsanity.com/paper/2511.02022/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 17 references that are in the map.
- First posted on arXiv 3 Nov 2025.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [Emergent Misalignment: Narrow finetuning can produce broadly misaligned LLMs](https://mlsanity.com/paper/2502.17424/) (2025)
- [Model Organisms for Emergent Misalignment](https://mlsanity.com/paper/2506.11613/) (2025)
- [Convergent Linear Representations of Emergent Misalignment](https://mlsanity.com/paper/2506.11618/) (2025)
- [Mechanistic Mode Connectivity](https://mlsanity.com/paper/2211.08422/) (2022)
- [Where is the Information in a Deep Neural Network?](https://mlsanity.com/paper/1905.12213/) (2019)
- [On the Emergence of Cross-Task Linearity in the Pretraining-Finetuning Paradigm](https://mlsanity.com/paper/2402.03660/) (2024)
- [Fine-tuning Happens in Tiny Subspaces: Exploring Intrinsic Task-specific Subspaces of Pre-trained Language Models](https://mlsanity.com/paper/2305.17446/) (2023)
- [Multi-head Transformers Provably Learn Symbolic Multi-step Reasoning via Gradient Descent](https://mlsanity.com/paper/2508.08222/) (2025)

## Built on by (most cited first, 8 of 8)

- [Position: Anthropomorphic Misalignment Research Needs Stronger Evidence](https://mlsanity.com/paper/2606.07612/) (2026)
- [Character as a Latent Variable in Large Language Models: A Mechanistic Account of Emergent Misalignment and Conditional Safety Failures](https://mlsanity.com/paper/2601.23081/) (2026)
- [Emergent Misalignment Recruits a Pre-existing Persona Subspace](https://mlsanity.com/paper/2607.21356/) (2026)
- [Value Entanglement: Conflation Between Different Kinds of Good In (Some) Large Language Models](https://mlsanity.com/paper/2602.19101/) (2026)
- [Persona-Model Collapse in Emergent Misalignment](https://mlsanity.com/paper/2605.12850/) (2026)
- [Emergent Misalignment Can Be Induced by Sycophancy and Reversed via Alignment Gating](https://mlsanity.com/paper/2606.09068/) (2026)
- [DecodeShare: Tracing the Shared Subspace of LLM Decode-Time Decisions](https://mlsanity.com/paper/2607.20469/) (2026)
- [Emergent Misalignment Is Not Magical](https://mlsanity.com/paper/2608.29118/) (2026)

## Abstract (arXiv)

Recent work has discovered that large language models can develop broadly misaligned behaviors after being fine-tuned on narrowly harmful datasets, a phenomenon known as emergent misalignment (EM). However, the fundamental mechanisms enabling such harmful generalization across disparate domains remain poorly understood. In this work, we adopt a geometric perspective to study EM and demonstrate that it exhibits a fundamental cross-task linear structure in how harmful behavior is encoded across different datasets. Specifically, we find a strong convergence in EM parameters across tasks, with the fine-tuned weight updates showing relatively high cosine similarities, as well as shared lower-dimensional subspaces as measured by their principal angles and projection overlaps. Furthermore, we also show functional equivalence via linear mode connectivity, wherein interpolated models across narrow misalignment tasks maintain coherent, broadly misaligned behavior. Our results indicate that EM arises from different narrow tasks discovering the same set of shared parameter directions, suggesting that harmful behaviors may be organized into specific, predictable regions of the weight landscape. By revealing this fundamental connection between parametric geometry and behavioral outcomes, we hope our work catalyzes further research on parameter space interpretability and weight-based interventions.