Context Is King: How In-Context Specification Shapes the Geometry of Concepts

Large language models place structured concepts on geometrically faithful manifolds: weekdays lie on a circle, months on another, usually taken to be a fixed world-model the network stores and looks up. We show that context is king: the structure a model actually uses is set by the in-context specification. A declarative rule fixes not only which relations the geometry encodes but its topology type: the same tokens form a cycle or a branching tree on command, built even on arbitrary, meaning-free tokens with no prior to inherit, which a relabeled stored shape cannot do. When the specification conflicts with a strong pretrained prior, the context-set geometry dominates it in capable models, read from the same activations (representational similarity 0.6--0.9 to the imposed structure versus near-zero to the prior), across the priors we test and both families we study (Gemma, Qwen). Activation patching shows the map is causally used, not a probe correlate: swapping one entity's activation for another's makes the model answer with the other entity's successor under the imposed order. A rough map forms readily, present even in small and base models; what scale gates is using it cleanly: clean dominance and the causal crossover emerge only in the larger models (up to Gemma-31B and Qwen-27B) and weaken or reverse below, so a mechanism present in a large model can be absent in a smaller one of the same family. Whether the model builds this geometry anew or reconfigures a stored one we leave open; operationally, the geometry it uses is the one the context specifies.

Unsupervised Features Mining via Activation Geometry

Interpretability methods aim to reveal the features represented inside large language models (LLMs). Many existing methods begin with labeled examples of a human-defined concept that may reflect human biases, and then identify how that concept is represented within the model, for example in its activation space or through other decomposition methods. We introduce \emph{Mining via Activation Geometry} (MAG), a simple unsupervised framework for extracting reasoning features from model activations by prepending the same natural-language instruction $Q$ to every input $p$, where $Q$ defines the reasoning feature of interest, such as ``Can this object be found in the desert?'' or ``Is this prompt malicious?'' We measure how the instruction changes the model's internal representation using $m(Q \mid p) - m(p)$ at a single readout point. We explore eight different MAGs. The extracted reasoning features predict the models' own world understanding and judgment, can be approximated into a single activation direction, we found that some features are more linearly represented and some less, this linear representation, which is vector steering, can change the LLMs' decisions through activation steering by injecting reasoning features. Finally, we use the same method to select the best training datasets for prompt-injection classifier probes: while similarity between ordinary activations is almost unrelated to downstream performance, RFD-based similarity achieves $94.7\%$ Top-1 and $100\%$ Top-2 accuracy.

Internal-State Probes Read the Situation, Not the Action: Three Negative Results for Pre-Action Misalignment Monitoring

Probes on model internals could help monitor agentic systems if they identify harmful text or tool actions before those actions are generated. We ask when an internal readout supports this stronger pre-action claim, rather than merely describing the prompt, construction contrast, or current trajectory. We test three methods across three model families: a Qwen2.5-Coder-32B-Instruct fine-tune/base direction, Llama-3.1-8B-Instruct probes at the last token of unsafe prefills, and Gemma-3-27B-IT emotion-concept vectors used for projection and steering in a blackmail tool-action scenario. Across these cases, construction validity, semantic legibility, and steering effects do not become robust pre-action monitors: each is undercut by a generalization or specificity check. The Qwen direction separates fine-tune from base at AUC 1.000, yet crosses its threshold on 0/143 audited pre-assistant turn contexts and on 0/342 Qwen prefill rows where the model continues the unsafe trajectory. The Llama features decode prompt domain almost perfectly (AUC 0.999), while the best future-behavior probe reaches AUC 0.801 and only +5.1 pp accuracy lift over majority; single-source cross-domain transfer is non-positive on five of six ordered pairs. Gemma emotion projections are semantically meaningful, but a shared-prefix minimal pair has indistinguishable states before the first differing input, and steering specificity weakens against unrelated learned directions such as cats}, weather, sports, and geography. We contribute a methodology for converting internal-readout claims into pre-action tests, and report scoped negative results: monitor claims must survive both scenario/action generalization and concept-specificity controls. Code is released at https://github.com/maxf-zn/misalignment_monitoring