Interpretation of Multi-Dimensional Value Manifolds

Ascertain whether the multi-dimensional or multi-lobed last-layer value manifolds observed in deeper or larger transformer language models encode multimodal uncertainty, semantic clustering, or training-set heterogeneity, and characterize the specific representational factors responsible for these structures.

Background

The paper identifies low-dimensional value manifolds as a central geometric signature of Bayesian-style uncertainty representation in transformers. While smaller models and domain-restricted prompts often yield near one-dimensional manifolds, deeper or larger models can exhibit multi-dimensional or multi-lobed manifolds under mixed-domain prompting. The authors note that this phenomenon is not fully theoretically understood.

They propose possible explanations, including multimodal uncertainty, semantic clustering, and training-set heterogeneity, but explicitly state that determining which of these factors (if any) the manifolds encode remains an open question. This problem is crucial for interpreting how uncertainty and task structure are represented in larger models and for linking geometric diagnostics to semantics or data properties.