  We enhance the biquandle counting invariant using elements of truncated
biquandle-labeled Polyak algebras. These finite type enhancements reduce to the
finite type enhancements defined by Goussarov, Polyak and Viro for the trivial
biquandle of one element and determine (but are not determined by) the
biquandle counting invariant for general biquandles. Unlike the unlabeled case,
biquandle labeled finite type invariants of degree 1 are nontrivial and are
related to biquandle cocycle invariants.
