Using a neural model with convolutional architecture, we are classifying query-document pairs into two classes: relevant (index 0), non-relevant (index 1). Suppose the current query q consists of the terms tq1 and tq2 and the current document of the terms td1,td2 and td3. Using word embeddings, we constructed the following similarity matrix: x Matrix

The convolutional network has two filters (of different sizes), given below:

F1=[0.9−0.20.40.3],F2=⎡⎣⎢0.10.6−0.10.10.30.7⎤⎦⎥.

with the following parameters of the classifier:

W=[0.70.80.10.5],b=[0.2−0.3].

a. Compute the latent semantic vector z that is the result of applying convolutions (and then 1-max pooling) with all filters. z = [Antwort, Antwort]

b. Compute the final prediction vector y^=softmax(zTW+b) for the query-document pair. Hint: In this subtask, only round the end result.

y^ = [Antwort, Antwort]

c. Knowing that the current document is relevant, compute the cross-entropy loss of the model's prediction. Use the natural logarithm and round your answer to two decimals.

cross-entropy loss: Antwort