We can further reduce computation by decomposing the forward-backward recursions to the co-occurrence features and alignment path features: The potential due to alignment path features (Ψ ap ) does not depend on the subset of blobs, and only depends on the current and previous alignment states h[n] = m and h[n − 1] = m .
on the other hand, the co-occurrence potential Ψ co for a given set of blobs Y depends only on the sentence that it is being aligned to, and does not depend on the video chunk index n. we can decompose the forward recursion as: where δ(m) = Y ∈P Ψ co (X im , Y ).