Questions LOCOST - ufal/NPFL095 GitHub Wiki

  1. What other ways (at least one) can we use to achieve less than asymptotically quadratic time complexity (o(n^2)) as a function of context window size? Some have been shown before but if you have no other ideas or want to see a new one: https://aclanthology.org/2022.findings-naacl.55/

  2. Estimate which sentence sets could be chosen by the GSG as the pseudo summary for k = 1 from the document sentence set:

{"cats playing", "dogs sleeping", "cats dogs in house"}

Check by calculating the explicit average ROUGE-1F1 scores with the rest of the document for each sentence.

ROUGE-1recall​= percentage of unigrams from reference contained in candidate

ROUGE-1precision= percentage of unigrams from candidate contained in reference (used to be percentage of unigrams from reference contained in candidate, solutions using this wrong definition are also valid)

ROUGE-1F1= 2⋅recall⋅precision / (recall+precision)

F1 score is 0 if both precision and recall are 0.

  1. let us have
A = 
1.0 0.0
0.0 2.0

b = (2, 1)^T
c = (1, 3)^T
u = (1, 2)^T
d = 0

Calculate the vector y as in eq. 2 using the definition of circular convolution in eq. 6 (we modulo the indexes as we would with python indexing).

  1. Calculate U and K, the discrete Fourier transforms of u and k. Calculate the inverse DFT of the point-wise product of UK.

bonus: Show that in general multiplying 2d vectors in the spectral domain and then transforming them back is the same as calculating their convolution.

hint: to get the vector z containing the discrete Fourier transform of y we use:

z1 = y1 + y2
z2 = y1 − y2
y1 = (z1 + z2) / 2
y2 = (z1 - z2) / 2