Does weight pushing in HCLG graphs affect filler model transition weights?

In Kaldi's FST-based decoding architecture, the composition of H, C, L, and G transducers results in a search graph where weight pushing is applied to optimize pruning during the Viterbi beam search. This process is intended to move weights as far forward as possible toward the start of the graph.

There is a specific design consideration regarding how this optimization interacts with filler models and silence transitions during the composition of the L and G transducers. Because filler models introduce specific transition costs to manage non-speech segments, it is unclear if standard weight pushing consistently preserves the intended penalty behavior for these specific paths across different graph scales.

Which mechanisms in the utils/prepare_fst.sh pipeline ensure that filler model weights are not pushed in a way that inadvertently alters the pruning threshold for silence transitions? Does the weight pushing optimization treat filler transitions differently than standard lexical transitions?