Transformers are a very popular architecture for processing sequential data, notably text and (our interest) proteins. Transformers learn more complex patterns with larger models on more data, as demonstrated by models like GPT-4 and ESM-2. Transformers work by updating tokens according to an attention value computed as a weighted sum of all other tokens. In standard implentations this requires computing the product of a query and key matrix which requires O(N2d) computations and, problematically, O(N2) memory for a sequence of length N and an embedding size of d. To speed up Transformers, and to analyze longer sequences, several variants have been proposed which require only O(N) memory. Broadly, these can be divided into sparse methods, softmax-approximators, and memory-efficient Transformers.
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Understanding positional encoding in Transformers
Transformers are a very popular architecture in machine learning. While they were first introduced in natural language processing, they have been applied to many fields such as protein folding and design.
Transformers were first introduced in the excellent paper Attention is all you need by Vaswani et al. The paper describes the key elements, including multiheaded attention, and how they come together to create a sequence to sequence model for language translation. The key advance in Attention is all you need is the replacement of all recurrent layers with pure attention + fully connected blocks. Attention is very efficeint to compute and allows for fast comparisons over long distances within a sequence.
One issue, however, is that attention does not natively include a notion of position within a sequence. This means that all tokens could be scrambled and would produce the same result. To overcome this, one can explicitely add a positional encoding to each token. Ideally, such a positional encoding should reflect the relative distance between tokens when computing the query/key comparison such that closer tokens are attended to more than futher tokens. In Attention is all you need, Vaswani et al. propose the slightly mysterious sinusoidal positional encodings which are simply added to the token embeddings: