Sinusoidal Position Representation

A Sinusoidal Position Representation is a mathematical model that encodes the position of tokens in a sequence using sinusoidal functions to provide the Transformer architecture with the ability to understand and maintain the order of input elements without relying on recurrence mechanisms.

• Context:
  • It can provide a unique encoding for each position in a sequence by utilizing a combination of sine and cosine functions at different frequencies.
  • It can ensure that the encoded positions are easily interpretable by the model, allowing it to infer relative positions and distances between tokens in a sequence.
  • It can be added directly to the embedding vectors of tokens, enabling the model to process positional information alongside the original semantic content of the input.
  • It can enable the model to generalize to sequence lengths beyond those encountered during training, due to the periodic nature of the sinusoidal functions.
  • It can be advantageous over other position encoding methods because it allows for the model to learn to attend by relative positions with minimal computational complexity.
  • It can maintain the values of the positional encoding within a normalized range, due to the bounded nature of sine and cosine functions, ensuring stability in the model's processing.
  • ...
• Example(s):
  • In the Transformer architecture, the sinusoidal position encoding is calculated for each position and added to the token embeddings before they are fed into the encoder or decoder layers.
  • A visualization of sinusoidal position encoding, showing how each dimension of the encoding varies sinusoidally with respect to the position in the sequence.
  • ...
• Counter-Example(s):
  • Learned Position Embeddings: A method where the model learns the position embeddings during training, as opposed to using a predefined mathematical formula.
  • Absolute Position Encoding: Other non-sinusoidal methods of position encoding that do not use the sine and cosine functions.
• See: Transformer (deep learning architecture), Positional Encoding, Sequence Modeling.

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References

2004

• (Andersen & Jensen, 2004) ⇒ T.H. Andersen, and K. Jensen. (2004). "Importance and representation of phase in the sinusoidal model.” In: Journal of the Audio Engineering Society.
  • NOTE: It introduces a novel phase representation, termed "partial period phase," for enhancing the sinusoidal analysis/synthesis framework in audio processing. The authors highlight the significance of precise phase information at specific positions within a partial period for improving the quality of synthesized audio.

2019

• (Kazemnejad, 2019) ⇒ Amirhossein Kazemnejad. (2019). "Transformer Architecture: The Positional Encoding." In: kazemnejad.com
  • NOTE: It elaborates on how sinusoidal position representation is crucial for the Transformer model to understand the order of words or tokens in sequences without recurrence, using sine and cosine functions of different frequencies for each position.

2018

• (Shaw et al., 2018) ⇒ P. Shaw, J. Uszkoreit, and A. Vaswani. (2018). "Self-attention with relative position representations.” In: arXiv preprint arXiv:1803.02155.
  • NOTE: This work extends the Transformer model by introducing relative position representations in the self-attention mechanism. Contrasting with absolute position encodings, the authors propose utilizing sinusoidal position encodings to enhance the model's ability to understand the relative positioning of words in a sequence, which significantly improves performance on various natural language processing tasks.

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