recursion. The autoencoder is trained to reproduce every vector in the full recursion tree, including the initial word embeddings. Given two sentences and of length 4 and 3 respectively, the autoencoders would produce 7 and 5 vector representations including the initial word embeddings. The euclidean distance is then taken between every combination of vectors in and to produce a similarity matrix . is then subject to a dynamic min-pooling layer to produce a fixed size matrix. Since are not uniform in size among all potential sentences, is split into roughly even sections. The output is then normalized to have mean 0 and standard deviation 1 and is fed into a fully connected layer with a softmax output. The dynamic pooling to softmax model is trained using pairs of known paraphrases. Skip-thought vectors Skip-thought vectors are an attempt to create a vector representation of the semantic meaning of a sentence, similarly to the skip gram model. Skip-thought vectors are produced through the use of a skip-thought model which consists of three key components, an encoder and two decoders. Given a corpus of documents, the skip-thought model is trained to take a sentence as input and encode it into a skip-thought vector. The skip-thought vector is used as input for both decoders; one attempts to reproduce the previous sentence and the other the following sentence in its entirety. The encoder and decoder can be implemented through the use of a recursive neural network (RNN) or an LSTM. Since paraphrases carry the same semantic meaning between one another, they should have similar skip-thought vectors. Thus a simple logistic regression can be trained to good performance with the absolute difference and component-wise product of two skip-thought vectors as input. Transformers Similar to how Transformer models influenced paraphrase generation, their application in identifying paraphrases showed great success. Models such as BERT can be adapted with a binary classification layer and trained end-to-end on identification tasks. Transformers achieve strong results when transferring between domains and paraphrasing techniques compared to more traditional machine learning methods such as logistic regression. Other successful methods based on the Transformer architecture include using adversarial learning and meta-learning. Evaluation Multiple methods can be used to evaluate paraphrases. Since paraphrase recognition can be posed as a classification problem, most standard evaluations metrics such as accuracy, f1 score, or an ROC curve do relatively well. However, there is difficulty calculating f1-scores due to trouble