  Auto-regressive neural sequence models have been shown to be effective across
text generation tasks. However, their left-to-right decoding order prevents
generation from being parallelized. Insertion Transformer (Stern et al., 2019)
is an attractive alternative that allows outputting multiple tokens in a single
generation step. Nevertheless, due to the incompatibility between absolute
positional encoding and insertion-based generation schemes, it needs to refresh
the encoding of every token in the generated partial hypothesis at each step,
which could be costly. We design a novel reusable positional encoding scheme
for Insertion Transformers called Fractional Positional Encoding (FPE), which
allows reusing representations calculated in previous steps. Empirical studies
on various text generation tasks demonstrate the effectiveness of FPE, which
leads to floating-point operation reduction and latency improvements on batched
decoding.
