This work shows that context is king: the structure a model actually uses is set by the in-context specification, and whether the model builds this geometry anew or reconfigures a stored one the authors leave open is the one the context specifies.
Abstract
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.
Geometric Lens, a training-free, hyperparameter-free method for reading out the exact concept a hidden vector encodes at any layer, and Laguerre Autoencoder, a 2D visualizer that renders both the decision geometry and a model's full reasoning trajectory in one view are developed.
VisualPatchWorld is introduced, which represents world dynamics as code and first selects a qualitative dynamical form with short active probes, then fits that form's free parameters from recorded state-action traces by minimizing multi-step prediction error.
Zero symbol collapse in all 32 seeds is demonstrated, with the blackboard achieving 79-100% semantic binding across three encoder architectures (CNN, V-JEPA 300M, CLIP ViT-L), two environments, and three texture conditions.
B\"urger et al.\ (2024) demonstrated that truth representations in large language models are universal across statement polarity but reside within a multidimensional subspace. The truth value of a statement is linearly readable from a residual stream of language model, but it is not clear how much of that representation fits on a single direction, which component builds it, or what it is made of. We conducted a study based on these questions, with one instrument: a training-free axis, the dominant direction of the singular value decomposition (SVD) of hidden-state differences over true/false minimal pairs, identified without labels up to one global sign. Extensive evaluation across 14 models from 6 diverse architectural families (including MoE), read and extract at cost $O(d)$ per token. We close with a pre-registered prediction on whether the arrangement extends to categories whose truth is computed rather than retrieved.
Large language models (LLMs) increasingly handle in-context learning (ICL) tasks where a long, novel context defines the rules, knowledge, and output schema for a series of questions. On benchmarks that grade against every detail of the context, even strong open-weights models pass only 12-16% of tasks: a single overlooked rule fails the whole response. We argue this brittleness is structural: the dominant"read-and-reason"paradigm asks the model to extract, plan, generate, and self-verify in one forward pass. We therefore ask whether explicit context compilation can fix it, how it compares to existing long-context strategies (gist retrieval, multi-agent self-play), and where the resulting harness benefit holds across task structure and model scale. We propose the Context Compilation Architecture (CCA), whose central novelty is a typed intermediate representation (IR) with fixed slots (rules.{must_do, must_not, conditional}, output_spec, available_tools, data_profile) into which any prose context is compiled once; executable verifiers and a violation-gated correction loop follow as downstream consequences. On CL-bench (1,899 tasks across 4 open base models), CCA outperforms vanilla prompting and two long-context baselines (ReadAgent-P, Ctx2Skill) on every base model, lifting Kimi K2.5 from 15.4% to 21.4% with gains concentrated on rule-dense sub-categories. Code and cached completions are available at https://github.com/TonyQJH/cca-emnlp2026.
Jin-Hu Qi, Minda Hu, Wen-Tao Zhang et al.· 0 citations
The results empirically show that relation geometry is not equally well-represented for all relations in semantic space, suggesting that there is a difference in how well semantic relations might be learned from distributional information alone.
