Large language models (LLMs) have demonstrated remarkable proficiency in in-context learning (ICL), where models adapt to new tasks through example-based prompts without requiring parameter updates. However, understanding how tasks are internally encoded and generalized remains a challenge. To address some of the empirical and technical gaps in the literature, we introduce an automated formulation for encoding task information in ICL prompts as a function of attention heads within the transformer architecture. This approach computes a single task vector as a weighted sum of attention heads, with the weights optimized causally via gradient descent. Our findings show that existing methods fail to generalize effectively to modalities beyond text. In response, we also design a benchmark to evaluate whether a task vector can preserve task fidelity in functional regression tasks. The proposed method successfully extracts task-specific information from in-context demonstrations and excels in both text and regression tasks, demonstrating its generalizability across modalities.

Understanding the latent space geometry of large language models (LLMs) is key to interpreting their behavior and improving alignment. Yet it remains unclear to what extent LLMs linearly organize representations related to semantic understanding. To explore this, we conduct a large-scale empirical study of hidden representations in 11 autoregressive models across six scientific topics. We find that high-level semantic information consistently resides in low-dimensional subspaces that form linearly separable representations across domains. This separability becomes more pronounced in deeper layers and under prompts that elicit structured reasoning or alignment behavior—even when surface content remains unchanged. These findings motivate geometry-aware tools that operate directly in latent space to detect and mitigate harmful and adversarial content. As a proof of concept, we train an MLP probe on final-layer hidden states as a lightweight latent-space guardrail. This approach substantially improves refusal rates on malicious queries and prompt injections that bypass both the model’s built-in safety alignment and external token-level filters.