Implicit representations encode positional information in word embeddings by generalizing embedding to continuous functions over positions rather than explicitly adding positional embeddings

Carleton College

These are mechanisms that inject positional information into Transformers. Positional encodings are important within the transformer architecture because the ordering of words matters when modeling sequences of text.


Types of Positional Representations:
- absolute positional representations
- relative position representations
- implicit representations
- other representations

Positional Representations of Transformers

Lin, Tianyang & Wang, Yuxin & Liu, Xiangyang & Qiu, Xipeng. (2021). A Survey of Transformers. 

A Survey of Transformers (Lin et. al, 2021)

These representations focus on positional relationships between tokens instead of positions of individual tokens. This works because pairwise positional relationships between input elements (direction and distance) can often be more beneficial than positions of element.

Relative Positional Representations

Implicit Positional Representations

Hybrid approaches have been proposed to make use of both absolute and relative positional encodings

Other representations of positional information in transformers

A straightforward approach for encoding positional context is to treat the positional embedding for each location, $$\mathrm{PE}(i)$$, as a set of learnable parameters or variables. These parameters are optimized and trained alongside the main model parameters. This technique enables the model to develop a unique vector representation for every position, thereby allowing it to differentiate between tokens based on their positions within a sequence.

Learnable Absolute Positional Embeddings

Similar to sinusoidal embeddings, rotary positional embeddings (RoPE) utilize fixed, hard-coded values to represent positions. However, instead of adding positional vectors to token embeddings, RoPE models positional context by rotating the token embeddings in a complex vector space. This results in a multiplicative integration of positional information, distinguishing it from the additive approach common in other methods.

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