🤖 AI Summary
This study investigates whether the geometric structure of concepts in large language models is fixed by pretraining priors or dynamically shaped by context. Through representational similarity analysis, activation interventions, and cross-model comparisons (Gemma, Qwen), the work demonstrates for the first time that contextual instructions can deliberately construct arbitrary conceptual topologies—such as ring or tree structures—and causally dominate generation behavior in large models (e.g., Gemma-31B, Qwen-27B), with effect sizes ranging from 0.6 to 0.9 in similarity metrics. This influence is not merely an epiphenomenon of representation but a controllable driver of output. In contrast, smaller models fail to reliably exhibit this capability, highlighting a qualitative divergence in how model scale mediates contextual control over conceptual geometry.
📝 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.