Patches of Nonlinearity: Instruction Vectors in Large Language Models
Authors: Irina Bigoulaeva, Jonas Rohweder, Subhabrata Dutta, Iryna Gurevych
Organizations: Ubiquitous Knowledge Processing Lab (UKP Lab) · Department of Computer Science, Technical University of Darmstadt · National Research Center for Applied Cybersecurity ATHENE, Germany
Abstract
Despite the recent success of instruction-tuned language models and their ubiquitous usage, very little is known of how models process instructions internally. In this work, we address this gap from a mechanistic point of view by investigating how instruction-specific representations are constructed and utilized in different stages of post-training: Supervised Fine-Tuning (SFT) and Direct Preference Optimization (DPO). Via causal mediation, we identify that instruction representation is fairly localized in models. These representations, which we call Instruction Vectors (IVs), demonstrate a curious juxtaposition of linear separability along with non-linear causal interaction, broadly questioning the scope of the linear representation hypothesis commonplace in mechanistic interpretability. To disentangle the non-linear causal interaction, we propose a novel method to localize information processing in language models that is free from the implicit linear assumptions of patching-based techniques. We find that, conditioned on the task representations formed in the early layers, different information pathways are selected in the later layers to solve that task, i.e., IVs act as circuit selectors.
In language models, the choice between believing the prompt and believing the weights is made by a handful of identifiable attention heads. Instruction tuning changes how models behave under conflict, but whether it rewires the underlying circuit or merely gates/reweights already present components, remains unknown. We provide the first mechanistic base-vs-instruct comparison of conflict-resolution circuits, across three families (Llama-3.2-3B, Qwen-2.5-3B, Gemma-3-4B). Five independent methods, node and edge attribution, superposition role analysis, causal ablation, and path patching, converge on gating, with the same heads, in the same late-layers, are found to be reweighted rather than replaced with a high node overlap (0.60-0.82). Behaviorally, tuning shifts models toward parametric memory, making instruct models reject a terse counterfactual context far more than base ones, the opposite of a naive user-following expectation. Yet this added skepticism is a factor of framing since it disappears when the same false claim is delivered as a coherent, evidential passage. The robustness that instruction tuning buys against terse injection is therefore real but narrow. More broadly, we believe that because the conflict circuit is preserved rather than rebuilt, interpretability and control tools calibrated on base models should transfer directly to their deployed instruct siblings.
Instruction tuning is commonly assumed to endow language models with a domain-general ability to follow instructions, yet the underlying mechanism remains poorly understood. Does instruction-following rely on a universal mechanism or compositional skill deployment? We investigate this through diagnostic probing across nine diverse tasks in three instruction-tuned models. Our analysis provides converging evidence against a universal mechanism. First, general probes trained across all tasks show selective rather than uniform deficits relative to task-specific specialists, indicating that representational sharing is partial and structured rather than global. Second, cross-task transfer is weak and clustered by skill similarity. Third, causal ablation reveals sparse asymmetric dependencies rather than shared representations. Tasks also stratify by complexity across layers, with structural constraints emerging early and semantic tasks emerging late. Finally, temporal analysis shows that the constraint signal becomes decodable only once generation is under way, and remains so throughout the response. These findings indicate that instruction-following is better characterized as skillful coordination of diverse linguistic capabilities rather than deployment of a single abstract constraint-checking process.
Applying steering vectors to large language models (LLMs) is an efficient and effective model alignment technique, but we lack an interpretable explanation for how it works--specifically, what internal mechanisms steering vectors affect and how this results in different model outputs. To investigate the causal mechanisms underlying the effectiveness of steering vectors, we conduct a comprehensive case study on refusal. We propose a multi-token activation patching framework and discover that different steering methodologies leverage functionally interchangeable circuits when applied at the same layer. These circuits reveal that steering vectors primarily interact with the attention mechanism through the OV circuit while largely ignoring the QK circuit. Freezing all attention scores during steering drops performance by only 8.83% across three model families. A mathematical decomposition of the steered OV circuit further reveals semantically interpretable concepts, even in cases where the steering vector itself does not. Leveraging the activation patching results, we show that steering vectors can be sparsified by up to 85-96% while retaining most performance, and that different steering methodologies agree on a subset of important dimensions.