Answer to Question 1-1
a: Word embeddings, such as word2vec, take context into account by considering the neighboring words in a sentence or a document when learning a representation for each word. It does this by predicting a word based on its neighbors (continuous bag of words model) or predicting neighbors based on a word (skip-gram model). The idea is that words that occur in similar contexts tend to have similar meanings. 

On the other hand, TF-IDF takes context into account by considering how important a word is to a document within a collection of documents (corpus). The term frequency (TF) reflects how often a word appears in a specific document. The inverse document frequency (IDF) measures how unique or rare a word is in the entire corpus. Hence, TF-IDF increases with the number of times a word appears in a document but is offset by the number of documents in the corpus that contain the word.

The main difference between the two approaches is that word embeddings capture semantic relationships between words and are based on the surrounding words, while TF-IDF focuses on the importance or rarity of words in documents and is based on word frequency within and across documents. Word embeddings generally capture more nuanced meaning and are better for capturing similarity between words, while TF-IDF is more focused on identifying key words that represent the content of a document.





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Answer to Question 1-2
a. The sentence "I love NLP a lot" segmented into subwords using the given BPE codes would be: "I lo ve N L P a lot".





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Answer to Question 1-3
a: The shape of the output projection would be 10,000 x 300, corresponding to the vocabulary size and the number of dimensions for each word vector.

b: I do not necessarily agree that Bart's training pipeline is broken just because he found no difference in the trained word vectors when varying the context window size between 30, 40, and 50 words. It's possible that the optimal context window size for the news headlines data is lower than 30, so increasing it further may not lead to any change in the embeddings. Additionally, it could also be that the data is not diverse enough or the model has already captured most of the contextual information within the initial 30-word window, so increasing the window size does not add much additional information. Other factors, such as the quality of the news headlines data, the algorithm's parameters, or the number of training epochs, could also affect the outcome. More testing and analysis would be needed to determine the actual cause.





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Answer to Question 1-4
a: True. Subwords capture morpheme-level details which offer flexibility in handling morphological variations in languages.

b: True. A unigram language model estimates the probabilities of the occurrences of individual words, which can be computed from their frequency counts in a corpus.

c: False. One-hot representations only indicate the presence of words and lack the ability to capture or measure semantic difference.

d: False. In latent Dirichlet allocation, a document is modeled as a distribution over topics, not words directly.

e: True. TF-IDF increases the importance of words that are frequent in a document but not across documents, effectively reducing the weight of common words like stopwords.

f: False. In HMMs used for part-of-speech tagging, the hidden states represent the parts of speech, not the words themselves.





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Answer to Question 2-1
a: A suitable model for this prototype could be a shallow neural network consisting of an input layer, one hidden layer, and an output layer. The input layer would accept the 300-dimensional embedding vectors. The hidden layer could have a small number of units, say 16, to keep the model lightweight, followed by a non-linear activation function like ReLU. The output layer would consist of 3 units, each one corresponding to a classification label (happy, neutral, sad), followed by a softmax activation function to produce a probability distribution over the classes. The model's parameter shapes would be as follows: the weights from the input to the hidden layer would have a shape of [300, 16], the biases for the hidden layer would have a shape of [16], the weights from the hidden layer to the output layer would have a shape of [16, 3], and the biases for the output layer would have a shape of [3]. The model would optimize a loss function, such as cross-entropy loss, during training.

b: The model described in subquestion a has two limitations when it comes to audio utterance classification:
1. Input dimension mismatch: The input to the model from subquestion a was a 300-dimensional embedding vector, whereas the input utterances are represented as 80-dimensional spectrograms. The input layer of the model from subquestion a would not be compatible without adjustments.
2. Temporal dependencies: The model from subquestion a does not account for the time-series nature of audio data where temporal dependencies are crucial for understanding context. A simple feed-forward network would likely fail to capture these dependencies, which are important for accurate classification of utterances.

c: An improved model for the audio utterance classification task could be a recurrent neural network (RNN) with Long Short-Term Memory (LSTM) or Gated Recurrent Units (GRU) which are equipped to handle time-series data. The input layer would accept the 80-dimensional spectrograms. The intermediate operations would consist of a sequence of LSTM or GRU units which can process the temporal dependencies in the spectrogram data; to keep the model lightweight, we could use a small number of hidden units, such as 32. The output from the final time step of the LSTM/GRU layer would then be fed into a fully connected layer with 3 units (corresponding to the happy, neutral, sad labels), followed by a softmax activation function to generate the probability distribution over the classes. The parameter shapes for an LSTM-based model would be for the LSTM layer: [80, 32] for input weights, [32, 32] for recurrent weights, and [32] for biases, and for the final fully connected layer: [32, 3] for weights and [3] for biases. The model would optimize a loss function, like cross-entropy loss, to train the network.





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Answer to Question 2-2
a: The sequence classification approach, which assigns labels to individual utterances without considering context from the surrounding utterances, is not optimal because dialog often includes utterances whose meaning depends on the previous context. For example, when the Doctor says "For a week, right?" this is labeled as symptom_kneeSwelling, but when the Patient later uses the same phrase "For a week, right?" it is labeled as medication. A model that does not consider context will likely make a mistake here because it would be given the same input (the utterance) but is expected to produce different outputs (the labels) without any additional context.

b: Given that we have a good sentence encoder, I would model the task as a sequence labeling problem. This is because the task at hand involves assigning a label to each utterance in the sequence, which naturally aligns with the sequence labeling paradigm. In contrast, sequence generation would involve generating new sequences, which is not required for dialog act identification. Moreover, sequence labeling allows the use of context from surrounding utterances, which, as noted in the previous subquestion, is crucial for accurate classification in dialog.

c: The model for the dialog act identification task would take the following form:

- Input: A sequence of utterances represented as fixed-size vectors. These vectors are the embeddings produced by the sentence encoder.
- Intermediate Operations: A recurrent neural network (RNN) such as LSTM (Long Short Term Memory) or GRU (Gated Recurrent Unit), to process the sequence of embeddings one by one while keeping track of the context from both past and future utterances through hidden states.
- Output: A sequence of labels, one for each utterance. After processing each utterance, the RNN's output for that time step would be passed through a softmax layer to produce a probability distribution over possible labels, and the label with the highest probability would be assigned to that utterance.





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Answer to Question 3-1
a: In the context of the Transformer decoder, "autoregressive" means that the model predicts each output token one at a time, and the prediction for the current token is dependent on the tokens that have already been predicted. This means during the inference process, for each step, the decoder can only utilize the information from the previous steps to generate the next token in the sequence.

b: The Transformer decoder self-attention needs to be partially masked out during training because the model should not see the future tokens of the sequence it tries to predict. Since the task of the decoder is to predict the next token given the previous ones, it would be problematic if the model had access to the future tokens, as this would be a form of information leakage that could lead to the model learning to simply copy the tokens instead of actually learning to predict them based on the context.

c: To mask the appropriate weights in the decoder self-attention weight matrix, we mark "x" in the positions where the keys correspond to tokens that appear after the query tokens in the sequence. The proper masking for the given scenario would be:

```
,BoS, E, F, G
BoS,,,,,
E,x,,,,
F,x,x,,,
G,x,x,x,
```

The "x" marks indicate that, for example, when the decoder is considering the token "E", it should not be able to attend to "F" or "G" because those are future tokens in the sequence.

d: The attention weights $\bm{\alpha}_{\texttt{Mary}}$ would be the same in both sequences because self-attention operates independently of the absolute position of the tokens in the sequence. The attention mechanism computes the weights based on the similarity (usually measured through a function like the dot product) between the query and the key vectors for a particular token. Since the query and key vectors for "Mary" ($\mathbf{q}_{\texttt{Mary}}$ and $\mathbf{k}_{\texttt{Mary}}$) are the same regardless of whether "Mary" appears at the beginning or the end of the sequence, the attention mechanism will compute the same weights $\bm{\alpha}_{\texttt{Mary}}$. This is also under the assumption that positional encoding is not altering the key or query, and the attention mechanism is solely a function of the current embeddings, not their positions.





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Answer to Question 3-2
a: Two potential solutions to adapt a summarization model trained on news to the medical domain with many unknown words are:

1. One solution is to fine-tune the summarization model with a medical dataset. This involves retraining the existing model on a corpus of medical texts, allowing the model to learn and adapt to the terminology and language patterns found in medical documents.

2. Another solution is to utilize a technique known as subword tokenization. This method breaks down unknown or rare words into smaller, more manageable subwords or word pieces that the model can understand. This allows the model to handle and generate words that were previously unknown to it by composing them from known subwords.

b: ROUGE-n is based on the principle of n-grams overlap. It compares the n-grams of the system-generated summary with the n-grams of a set of reference summaries to compute the count of overlapping n-grams between them, which evaluates the quality of the machine-generated summary.

c: The model receives high ROUGE-2 scores because ROUGE-2 focuses on the overlap of bi-grams (two-word phrases) between the generated text and reference summaries. The repeated phrases in the generated text match many of the bi-grams from the reference summary, thus artificially inflating the score even though the output contains non-grammatical repetitions.

An alternative metric that can avoid this problem is the BLEU (Bilingual Evaluation Understudy) metric, which incorporates a brevity penalty to punish overly long and repetitive outputs.

To reduce the amount of repetition in the generated output, one can use technique such as:
- Incorporating a penalty term during the decoding phase that discourages the selection of words that have been previously generated.
- Applying a beam search with diversity-promoting heuristics that encourages the generation of varied word choices.
- Introducing a coverage mechanism that keeps track of what content has been covered so far in the summary and minimizes the chance of repetition.





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Answer to Question 3-3
a: An advantage of using BERT with CTC for machine translation is that BERT has been extensively pre-trained on a large corpus, which allows it to create rich and context-aware embeddings for the text inputs. This could potentially capture the nuances of language and lead to more accurate translations.

A disadvantage of this approach is that BERT and CTC are originally designed for different tasks—BERT for natural language understanding and CTC for sequence alignment in tasks like speech recognition. Machine translation is a complex task that may not be well-suited for the direct application of these models without significant modifications.

b: To improve the model while keeping the idea of using BERT as an encoder, one could incorporate an attention mechanism or a transformer-based decoder that is specifically designed for sequence-to-sequence tasks like machine translation. Adding a neural machine translation (NMT) decoder that operates at the word or sub-word level and is trained to consider the context of the entire sentence could lead to significant improvements in the performance of the model.





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Answer to Question 3-4
a: To design a model for the text-to-SQL task, the following steps and components could be included:

1. **Input Representation**: Convert the natural language question into a format that the model can understand, usually using embeddings such as word embeddings.

2. **Table Schema Encoding**: Since the model needs to understand the structure of the tables, encode the schema of the tables, including table names and column names, into a vector space.

3. **Question Understanding**: Use a sequence-to-sequence model, such as an RNN or LSTM, to process the question and understand its intent.

4. **Query Generation**: The model then needs to generate the appropriate SQL query. This can be achieved with a decoder that is trained to output SQL query tokens.

5. **Attention Mechanism**: Incorporate an attention mechanism to focus on relevant parts of the question and the table schema when generating the query.

6. **Execution-Guided Decoding**: Incorporate a component that checks the validity of the intermediate SQL queries against the database to ensure the query is executable and makes sense.

7. **Training**: Use supervised learning with the 30,000 training examples to teach the model how to translate questions into SQL queries. This might include matching the question intent to SQL commands (e.g., "list" corresponds to "SELECT") and conditioning on the database schema.

8. **Evaluation**: Implement a method for evaluating the queries generated by the model, such as comparing the generated SQL query to the ground truth query from the training data, or by executing the query on the database and checking the results.

b: To adapt the model to handle unanswerable questions like "Who is the Chancellor of Germany?" which are unrelated to the database:

1. **Question Relevance Classification**: Before attempting to generate a SQL query, use a binary classifier to determine if the question can be answered by the given database. The classifier can be trained on a labeled dataset where each question is marked as answerable or not by the database schema.

2. **Confidence Scoring**: Implement a confidence measurement system within the model that assesses how likely a question is to be answerable based on its understanding of the database schema and the question itself.

3. **Fallback Responses**: For questions classified as unanswerable or with low-confidence scores, design the system to provide a default response indicating that the question cannot be answered with the available data instead of generating an invalid SQL query.

4. **Incorporate External Knowledge**: If applicable, integrate an external knowledge base that the model can refer to for questions that don't pertain directly to the database but are within its general domain.

5. **Continual Learning**: Allow the model to learn from its mistakes by incorporating feedback loops where wrong predictions on unanswerable questions improve the classification model over time.





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Answer to Question 4-1
a: The advantage of adding adapters to a frozen BERT model is that it allows for task-specific fine-tuning without the need to retrain the entire model. This can save significant computational resources and time, especially when dealing with a small dataset. Additionally, by keeping the pre-trained BERT parameters fixed, we avoid overfitting on the small dataset as the only parameters being updated are those in the adapters.

b: The adapters should be inserted somewhere within the BertLayer where they can transform the features before they are passed on to subsequent layers. Since the adapters consist of two linear projections, they should be placed after the self-attention operation outputs from BertSelfAttention, and before the data is passed to the BertOutput. Specifically, they could be placed after the (attention): BertSelfOutput and before the (output): BertOutput within each BertLayer.

c: To calculate the number of parameters added by inserting the adapters, follow these steps:
1. First projection in adapter: It projects from the original BERT layer size (768) down to 256 dimensions. Therefore the number of parameters here is: 768 * 256.
2. Second projection in adapter: It projects from 256 dimensions back up to the original layer size (768). The number of parameters here is: 256 * 768.
3. The adapter is added to each of the original BERT layers (12 in total), so multiply the sum of parameters from steps 1 and 2 by 12 to get the total number of additional parameters. 

The total number of parameters added would be calculated as:
Total params = (768 * 256 + 256 * 768) * 12





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Answer to Question 4-2
a: The approach of using the BERT CLS token for sentence representation differs from pooling methods like mean pooling or max pooling in several ways. The BERT CLS token is a special token added at the beginning of each input sequence, and the final hidden state corresponding to this token (as shown in the figure) is intended to represent the aggregate sequence representation for classification tasks. During training, BERT learns to embed information relevant to downstream tasks into this CLS token vector.

Pooling methods like mean pooling or max pooling involve aggregating the word vectors across the entire input sequence by either taking the average (mean pooling) or the maximum (max pooling) value for each dimension of the word vectors.

Advantages of using the BERT CLS token for sentence representation include:
1. Contextual Representation: The CLS token vector captures the contextual relationship between words in the sequence, as BERT is trained on a large corpus and learns context-dependent representations.
2. Task Optimization: In BERT, the CLS token is fine-tuned for specific tasks during the fine-tuning phase, making it task-specific and potentially more effective for the target application (such as retrieval in DPR).
3. Simplicity: It simplifies the pipeline by directly providing a fixed-size vector after processing the input with BERT, without additional pooling operations.

Comparatively, pooling methods provide non-contextual sentence-level representations that may not capture complex relationships between tokens and could be less task-specific. However, mean or max pooling could still be effective in some scenarios and are computationally less demanding.

b: In DPR, the training objective that pushes relevant question-passage pairs closer and irrelevant pairs away is essential for effective retrieval. Including irrelevant/negative pairs in the training has several purposes:
1. Contrastive Learning: The model learns to differentiate between relevant and irrelevant content, which improves its ability to select the most appropriate passages during inference.
2. Prevent Overfitting: Training with only positive examples could lead to a model that overfits to the specific pairs it has seen and fails to generalize well to new questions or passages.
3. Robust Retrieval: By understanding what makes a passage irrelevant, the model becomes more robust and accurate in its retrieval process.

If we leave out the irrelevant/negative pairs in the training objective, the model would not learn how to discriminate between relevant and irrelevant information. This could result in a retrieval system that is less accurate, as it would not have a basis to distinguish between a good match and a poor match for a given question, potentially returning non-informative or unrelated passages during inference.





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