Uncertainty calibration for simplex-like invoice embeddings

Develop uncertainty calibration for the simplex-like embedding geometry produced by fine-tuning SBERT on invoice text, so that irregularities pulling points toward the simplex centre can support calibrated predictions.

Background

Fine-tuning SBERT transforms the pre-trained X-shaped embedding manifold into a geometry that qualitatively resembles a simplex, with accounting categories concentrated near vertices. The paper notes that simplex geometry is regarded as advantageous for classification because deviations from the vertices may provide information about prediction uncertainty.

The authors identify the use of this geometry for uncertainty calibration as unresolved and defer it to future work. Such calibration would support the broader goal of an uncertainty-aware invoice-categorisation system that can direct expert attention toward difficult or ambiguous invoices.

References

A simplex geometry is considered to be `optimal' for classification because the classes fall on the vertices and irregularities pull points towards the centre, opening a pathway to uncertainty calibration, which we leave for future work.

— Where A Small Language Model Helps in Invoice Categorisation, Understood Through Embedding Geometry  (2608.18033 - Ceccherini et al., 18 Aug 2026) in Section 3.2, subsection “Fine Tuning”