Demystifying Anthropic's J-Space: A Mathematical Primer

Anthropic's J-space provides a mathematical framework for a "global workspace" within language models, where abstract concepts become concretely represented. This space is geometrically defined as a union of cones built from "J-lens vectors," with each vector capturing a specific vocabulary token's potential influence on the model's output. By projecting a model's internal state onto this space, one can isolate its "verbalizable" component, which reveals the key concepts active in its reasoning at any given moment. This powerful decomposition enables targeted interventions, allowing researchers to efficiently swap conceptual vectors using linear regression to audit and manipulate the model's behavior.