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

TL;DR

This work investigates emergent misalignment (EM) in large language models through a weight-space, geometric lens. By analyzing LoRA-finetuned adapters across multiple harmful tasks, it shows that EM updates occupy a shared, low-dimensional subspace and that different EM tasks converge to functionally equivalent parameter configurations, as evidenced by linear mode connectivity. Key findings include near-orthogonality between base weights and EM updates, high subspace overlap among EM tasks, and monotonic behavior changes along weight interpolations. The study suggests EM reflects transferable, latent misalignment mechanisms, opening avenues for weight-space interventions and extending the geometric perspective to other high-level behaviors. These insights advance parameter-space interpretability and offer a principled path toward safer, more controllable LLM systems.

Abstract

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.

Figures (37)

• Figure 1: Averaged cosine similarity results across models. (L) Layer-averaged EM-EM cosine similarities with LoRA weights. Black dashed line shows EM-base weight cosine similarities ($\sim 10^{-3}$ similar to a random baseline). An additional baseline for Llama3.1-8B with different finetuned models can be found in Appendix \ref{['app:cosine-sim-finetuned-baseline']}. (R) Layer-averaged EM-EM cosine similarities with PCs of LoRA weights. In both figures, red dashed lines represent cosine similarities for EM-random pairs. Blue bars = Llama3.1-8B, Red bars = Qwen2.5-7B. Error bars show standard deviations across layers.
• Figure 2: Principal angles and shared subspace between EM LoRA weight pairs. (L) Averaged principal angles, (R) Layer-wise shared subspace between EM--EM LoRA pairs for Llama3.1-8B (blue) and Qwen2.5-7B (red) models. Dashed lines represent baselines for the same metrics computed over EM-random weight pairs.
• Figure 3: Linear Mode Connectivity in Parameter and Feature Space. Top: LMC in parameter space. (L) Near monotonic transition from aligned to misaligned as $W_{LMC}$ goes from $W_{base}$ to $W_{EM}$. (R) Cross-task LMC of EM models exhibits consistent levels of misaligned responses and across tasks and model families. Bottom: LMC in feature space. (L) Near-zero levels of normalized L2 error across model interpolation indicate maintained performance throughout (R) High levels of $R^2$ suggest functional equivalence of feature representations.
• Figure 4: Pairwise cosine similarity measurements across all comparison groups. The bad_bad comparison exhibits substantially elevated cosine similarity ($\sim$0.25--0.35) relative to all other pairs, which maintain near-zero values ($\sim$0.01--0.02).
• Figure 5: Layer-wise cosine similarity decomposition showing relatively uniform similarity across network depth for all non-EM comparison pairs.