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Expand Up @@ -356,7 +356,7 @@
"Then, we find a matrix that projects the embeddings into a common space between the given languages. The matrix is designed to minimize the distance between a word $x_i$ and its projection $y_i$. If our dictionary consists of pairs $(x_i, y_i)$, our projector $M$ would be:\n",
"\n",
"\\begin{equation}\n",
"M = \\underset{W}{\\operatorname{argmax}} \\sum_i ||x_i - Wy_i||^2\n",
"M = \\underset{W}{\\operatorname{argmin}} \\sum_i ||x_i - Wy_i||^2\n",
"\\end{equation}\n",
"\n",
"Also, the projector matrix $W$ is constrained to e orthogonal, so actual distances between word embedding vectors are preserved. Multilingual models are trained by using our multilingual word embeddings as the base representations in DeepText and “freezing” them or leaving them unchanged during the training process.\n",
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