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.
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Question: Training and testing are done in alternating steps: In each epoch, for training, we first present to an LSTM network 1000 samples in a given language, which are generated according to a certain discrete probability distribution supported on a closed finite interval. We then freeze all the weights in our model, exhaustively enumerate all the sequences in the language by their lengths, and determine the first $k$ shortest sequences whose outputs the model produces inaccurately.  experimented with 1, 2, 3, and 36 hidden units for $a^n b^n$ ; 2, 3, 4, and 36 hidden units for $a^n b^n c^n$ ; and 3, 4, 5, and 36 hidden units for $a^n b^n c^n d^n$ .  Following the traditional approach adopted by BIBREF7 , BIBREF12 , BIBREF9 and many other studies, we train our neural network as follows. At each time step, we present one input character to our model and then ask it to predict the set of next possible characters, based on the current character and the prior hidden states. Given a vocabulary $\mathcal {V}^{(i)}$ of size $d$ , we use a one-hot representation to encode the input values; therefore, all the input vectors are $d$ -dimensional binary vectors. The output values are $(d+1)$ -dimensional though, since they may further contain the termination symbol $\dashv $ , in addition to the symbols in $\mathcal {V}^{(i)}$ . The output values are not always one-hot encoded, because there can be multiple possibilities for the next character in the sequence, therefore we instead use a $k$ -hot representation to encode the output values. Our objective is to minimize the mean-squared error (MSE) of the sequence predictions. 
 Question: What training settings did they try?

Answer: Training and testing are done in alternating steps: In each epoch, for training, we first present to an LSTM network 1000 samples in a given language, which are generated according to a certain discrete probability distribution supported on a closed finite interval. We then freeze all the weights in our model, exhaustively enumerate all the sequences in the language by their lengths, and determine the first $k$ shortest sequences whose outputs the model produces inaccurately.  experimented with 1, 2, 3, and 36 hidden units for $a^n b^n$ ; 2, 3, 4, and 36 hidden units for $a^n b^n c^n$ ; and 3, 4, 5, and 36 hidden units for $a^n b^n c^n d^n$ .  Following the traditional approach adopted by BIBREF7 , BIBREF12 , BIBREF9 and many other studies, we train our neural network as follows. At each time step, we present one input character to our model and then ask it to predict the set of next possible characters, based on the current character and the prior hidden states. Given a vocabulary $\mathcal {V}^{(i)}$ of size $d$ , we use a one-hot representation to encode the input values; therefore, all the input vectors are $d$ -dimensional binary vectors. The output values are $(d+1)$ -dimensional though, since they may further contain the termination symbol $\dashv $ , in addition to the symbols in $\mathcal {V}^{(i)}$ . The output values are not always one-hot encoded, because there can be multiple possibilities for the next character in the sequence, therefore we instead use a $k$ -hot representation to encode the output values. Our objective is to minimize the mean-squared error (MSE) of the sequence predictions.


Question: The split methods (beyond random split) are the following:

Output length: Variation of the setup described by BIBREF2 where the train set consists of examples with output (sparql query or action sequence) length $\le \hspace{-2.5pt} N$, while the test set consists of examples with output length $> \hspace{-2.5pt} N$. For CFQ, we use $N = 7$ constraints. For scan, we use $N = 22$ actions.

Input length: Variation of the above setup, in which the train set consists of examples with input (question or command) length $\le N$, while test set consists of examples with input length $> N$. For CFQ, we use $N=19$ grammar leaves. For SCAN, we use $N=8$ tokens.

Output pattern: Variation of setup described by BIBREF8, in which the split is based on randomly assigning clusters of examples sharing the same output (query or action sequence) pattern. Query patterns are determined by anonymizing entities and properties; action sequence patterns collapse primitive actions and directions.

Input pattern: Variation of the previous setup in which the split is based on randomly assigning clusters of examples sharing the same input (question or command) pattern. Question patterns are determined by anonymizing entity and property names ; command patterns collapse verbs and the interchangeable pairs left/right, around/opposite, twice/thrice. 
 Question: What are other approaches into creating compositional generalization benchmarks?

Answer: random  Output length Input length Output pattern Input pattern


Question: We optimized our single-task baseline to get a strong baseline in order to exclude better results in multi-task learning in comparison to single-task learning only because of these two following points: network parameters suit the multi-task learning approach better and a better randomness while training in the multi-task learning. To exclude the first point, we tested different hyperparameters for the single-task baseline. We tested all the combinations of the following hyperparameter values: 256, 512, or 1024 as the sizes for the hidden states of the LSTMs, 256, 512, or 1024 as word embedding sizes, and a dropout of 30 %, 40 %, or 50 %. We used subword units generated by byte-pair encoding (BPE) BIBREF16 as inputs for our model. To avoid bad subword generation for the synthetic datasets, in addition to the training dataset, we considered the validation and test dataset for the generating of the BPE merge operations list. We trained the configurations for 14 epochs and trained every configuration three times. We chose the training with the best quality with regard to the validation F1-score to exclude disadvantages of a bad randomness. We got the best quality with regard to the F1-score with 256 as the size of the hidden states of the LSTMs, 1024 as word embedding size, and a dropout of 30 %. For the batch size, we used 64. 
 Question: What are the strong baselines you have?

Answer:
optimize single task with no synthetic data