Hierarchical Geometry of Cognitive States in Transformer Embedding Spaces

Abstract: Recent work has shown that transformer-based LLMs learn rich geometric structure in their embedding spaces, yet the presence of higher-level cognitive organization within these representations remains underexplored. In this work, we investigate whether sentence embeddings encode a graded, hierarchical structure aligned with human-interpretable cognitive or psychological attributes. We construct a dataset of 480 natural-language sentences annotated with continuous ordinal energy scores and discrete tier labels spanning seven ordered cognitive categories. Using fixed sentence embeddings from multiple transformer models, we evaluate the recoverability of these annotations via linear and shallow nonlinear probes. Across models, both continuous scores and tier labels are reliably decodable, with shallow nonlinear probes providing consistent performance gains over linear probes. Lexical TF-IDF baselines perform substantially worse, indicating that the observed structure is not attributable to surface word statistics alone. Nonparametric permutation tests further confirm that probe performance exceeds chance under label-randomization nulls. Qualitative analyses using UMAP visualizations and confusion matrices reveal smooth low-to-high gradients and predominantly adjacent-tier confusions in embedding space. Taken together, these results provide evidence that transformer embedding spaces exhibit a hierarchical geometric organization aligned with human-defined cognitive attributes, while remaining agnostic to claims of internal awareness or phenomenology.