Generality of the L-curve heuristic for selecting matched mass in partial soft-matching

Ascertain the generality of applying the L-curve heuristic to select the matched mass parameter s in the partial soft-matching distance for neural representational comparison, where s ∈ [0,1] specifies the fraction of mass transported in the partial optimal transport formulation.

Background

The partial soft-matching distance extends optimal transport-based representational comparisons by allowing a fraction of units to remain unmatched, controlled by a hyperparameter s that sets the total transported mass. Choosing s is nontrivial because the abundance of outliers and the magnitude of noise are often unknown in neural data.

The authors adopt an L-curve heuristic—selecting s at the elbow of the transport cost versus regularization curve—to balance alignment quality and regularization strength. While this approach works well empirically across their experiments, they explicitly note that its generality is uncertain, motivating a need to determine when and how reliably the heuristic applies.