In this task, you will be presented with a context from an academic paper and a question separated with a
. You have to answer the question based on the context.

Let me give you an example: We evaluate the proposed approach on the Chinese social media text summarization task, based on the sequence-to-sequence model. Large-Scale Chinese Short Text Summarization Dataset (LCSTS) is constructed by BIBREF1 . The dataset consists of more than 2.4 million text-summary pairs in total, constructed from a famous Chinese social media microblogging service Weibo.
Question: Are results reported only for English data?
The answer to this example can be: No
Here is why: Based on the context, the dataset is constructed from a famous Chinese social media microblogging service Weibo.

OK. solve this:
A simple choice of non-sparse gating function BIBREF17 is to multiply the input by a trainable weight matrix INLINEFORM0 and then apply the INLINEFORM1 function. DISPLAYFORM0

We add two components to the Softmax gating network: sparsity and noise. Before taking the softmax function, we add tunable Gaussian noise, then keep only the top k values, setting the rest to INLINEFORM0 (which causes the corresponding gate values to equal 0). The sparsity serves to save computation, as described above. While this form of sparsity creates some theoretically scary discontinuities in the output of gating function, we have not yet observed this to be a problem in practice. The noise term helps with load balancing, as will be discussed in Appendix SECREF51 . The amount of noise per component is controlled by a second trainable weight matrix INLINEFORM1 . DISPLAYFORM0 DISPLAYFORM1 A simple choice of non-sparse gating function BIBREF17 is to multiply the input by a trainable weight matrix INLINEFORM0 and then apply the INLINEFORM1 function. DISPLAYFORM0

We add two components to the Softmax gating network: sparsity and noise. Before taking the softmax function, we add tunable Gaussian noise, then keep only the top k values, setting the rest to INLINEFORM0 (which causes the corresponding gate values to equal 0). The sparsity serves to save computation, as described above. While this form of sparsity creates some theoretically scary discontinuities in the output of gating function, we have not yet observed this to be a problem in practice. The noise term helps with load balancing, as will be discussed in Appendix SECREF51 . The amount of noise per component is controlled by a second trainable weight matrix INLINEFORM1 . DISPLAYFORM0 DISPLAYFORM1
Question: What equations are used for the trainable gating network?
Answer:
DISPLAYFORM0 DISPLAYFORM0 DISPLAYFORM1