Principled selection of IEM hyperparameters Γ and f

Determine a systematic principle for choosing both the upper signal-to-noise ratio integration limit Γ and the scalar function f used in the generalized Information-Estimation Metric, so that the resulting distance appropriately balances contributions from log-probability ratio values and score differences and adapts to the fine-scale geometry of the data distribution.

Background

The generalized IEM family depends on two key design choices: the maximum SNR Γ that sets the finest geometric resolution captured by the metric, and the scalar functional f that modulates the contribution of the log-probability ratio relative to score differences. Although the authors demonstrate empirical utility for specific choices, they state that a principled, systematic method for determining Γ and f is currently lacking.

References

Moreover, the generalized IEM (\cref{eq:qv_distance_f}) depends on the choice of the function f, which qualitatively controls the relative importance of log-probability ratio values compared to score differences. A systematic principle for determining both \Gamma and f remains an open problem.

— Learning a distance measure from the information-estimation geometry of data  (2510.02514 - Ohayon et al., 2 Oct 2025) in Section 4 (Discussion)