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Sine and cosine — a.k.a., sin(θ) and cos(θ) — are functions revealing the shape of a right triangle. Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse .
What is cos sin equal to?
Sine, Cosine and Tangent
| Sine Function: | sin(θ) = Opposite / Hypotenuse |
|---|---|
| Cosine Function: | cos(θ) = Adjacent / Hypotenuse |
| Tangent Function: | tan(θ) = Opposite / Adjacent |
What is a position embedding?
The position embedding encodes the absolute positions from 1 to maximum sequence length (usually 512). That is, each position has a learnable embedding vector. The absolute position embedding is used to model how a token at one position attends to another token at a different position.
Why is positional encoding important in a Transformers?
Positional Encoding Unlike sequential algorithms like `RNN`s and `LSTM`, transformers don’t have a mechanism built in to capture the relative positions of words in a sentence. This is important because the distance between words provides crucial contextual information. This is where positional encoding steps in.
What does the tensor mean in positional encoding?
This means that that our positional encoding tensor should be a representative of the position at each index, and our network will take care of whatever operations need to be done to that. This encoding is going to have the same dimension as the sequence length, which could be very long.
How does the Transformer architecture affect the RNNs?
This will integrate the words’ order in the backbone of RNNs. But the Transformer architecture ditched the recurrence mechanism in favor of multi-head self-attention mechanism. Avoiding the RNNs’ method of recurrence will result in massive speed-up in the training time. And theoretically, it can capture longer dependencies in a sentence.
How is positional encoding represented in a matrix?
At this point we’ve done everything we need to do, so let’s summarize: 1 Positional encoding is represented by a matrix. 2 The “positions” are just the indices in the sequence. 3 Each row of the PE matrix is a vector that represents the interpolated position of the discrete value associated with the row index