Prompting steers large language models (LLMs) and vision-language models (VLMs) without weight updates, but it remains unclear how instruction changes reshape internal representations to produce behavior. We introduce a nested geometric decomposition framework that treats prompting as a transformation of the representational geometry of the content following the prompt. For each prompt pair, we align representations of the same stimuli under two prompts using increasingly expressive stimulus-invariant maps: translation, rigid transformation with uniform scaling, sequential axis scaling, affine transformation, and nonlinear transformation. We then causally test each map by replacing a single layer's prompt-A hidden state for held-out stimuli with its mapped counterpart and measuring recovery of prompt-B representational geometry and behavior. Across three LLMs, three VLMs, and six text or image datasets spanning style, emotion, scene content, and number, prompts consistently reshape representations toward the instructed task structure. Cross-validated variance decomposition shows that much prompt-induced activation change is captured by shape-preserving maps, especially translation and rigid transformation with uniform scaling, while tier profiles reveal model- and task-specific routing strategies across layers. Crucially, although translation and rigid tiers already improve behavioral agreement, affine transformation is the first tier to nearly recover target-prompt task geometry and yields corresponding behavioral gains. This suggests that cross-dimensional linear mixing is a key mechanism by which prompts reorganize representations toward instructed task structure. Our framework decomposes prompt-induced representational change into interpretable geometric components and reveals how models route task-relevant structure to produce prompt-driven behavior.
Large language models can be steered at inference time through prompting or activation interventions, but activation steering methods often underperform compared to prompt-based approaches. We propose a framework that formulates prompt steering as a form of activation steering and investigates whether distilling successful prompt steering behavior into simpler, interpretable models can close this gap. Our analysis reveals that popular activation steering methods are not faithful to the mechanics of prompt steering, which applies strong interventions on some tokens while barely affecting others. Based on these insights, we introduce Prompt Steering Replacement (PSR) models that estimate token-specific steering coefficients from the activations themselves and are trained to imitate prompt-based interventions. Experiments on three steering benchmarks across multiple language models show that PSR models outperform existing activation steering methods, especially when controlling for high-coherence completions, and also compare favorably to prompting on AxBench and persona steering.
One of the most common complaints about large language models (LLMs) is their prompt sensitivity -- that is, the fact that their ability to perform a task or provide a correct answer to a question can depend unpredictably on the way the question is posed. We investigate this variation by comparing two very different but commonly-used styles of prompting: instruction-based prompts, which describe the task in natural language, and example-based prompts, which provide in-context few-shot demonstration pairs to illustrate the task. We find that, despite large variation in performance as a function of the prompt, the model engages some common underlying mechanisms across different prompts of a task. Specifically, we identify task-specific attention heads whose outputs literally describe the task -- which we dub lexical task heads -- and show that these heads are shared across prompting styles and trigger subsequent answer production. We further find that behavioral variation between prompts can be explained by the degree to which these heads are activated, and that failures are at least sometimes due to competing task representations that dilute the signal of the target task. Our results together present an increasingly clear picture of how LLMs' internal representations can explain behavior that otherwise seems idiosyncratic to users and developers.
Zhuonan Yang, Jacob Xiaochen Li, Francisco Piedrahita Velez +5
Large language models process prompts by propagating activations through dozens of layers before generating a response. We ask whether the task-relevant information contained in an instruction prompt can be compressed into a single activation vector and re-injected into the model, replacing the original token sequence? We show this is achievable using a learned weighted sum of activations extracted at an intermediate layer and injected at an early layer of the target LLM. The compressed vector preserves task-relevant information, incurring an accuracy drop of under 2% relative to full prompt processing. Beyond its practical implications, including reducing per-query computation for fixed instruction prompts without reprocessing the original token sequence, our analysis reveals structure in the activation space of LLMs: (i) mid-layer representations transfer meaningfully to early layers, suggesting a degree of cross-layer compatibility in how information is encoded; (ii) a single activation vector encodes a quantifiable and recoverable amount of semantic information; (iii) a weighted sum of activations is a robust representation compressor.