  Semantic channel equalization has emerged as a solution to address language
mismatch in multi-user semantic communications. This approach aims to align the
latent spaces of an encoder and a decoder which were not jointly trained and it
relies on a partition of the semantic (latent) space into atoms based on the
the semantic meaning. In this work we explore the role of the semantic space
partition in scenarios where the task structure involves a one-to-many mapping
between the semantic space and the action space. In such scenarios,
partitioning based on hard inference results results in loss of information
which degrades the equalization performance. We propose a soft criterion to
derive the atoms of the partition which leverages the soft decoder's output and
offers a more comprehensive understanding of the semantic space's structure.
Through empirical validation, we demonstrate that soft partitioning yields a
more descriptive and regular partition of the space, consequently enhancing the
performance of the equalization algorithm.
