Attention mechanisms
Source: transformers

# Attention mechanismsMost transformer models use full attention in the sense that the attention matrix is square. It can be a bigcomputational bottleneck when you have long texts. Longformer and reformer are models that try to be more efficient anduse a sparse version of the attention matrix to speed up training.## LSH attention[Reformer](model_doc/reformer) uses LSH attention. In the softmax(QK^t), only the biggest elements (in the softmaxdimension) of the matrix QK^t are going to give useful contributions. So for each query q in Q, we can consider onlythe keys k in K that are close to q. A hash function is used to determine if q and k are close. The attention mask ismodified to mask the current token (except at the first position), because it will give a query and a key equal (sovery similar to each other). Since the hash can be a bit random, several hash functions are used in practice(determined by a n_rounds parameter) and then are averaged together.## Local attention[Longformer](model_doc/longformer) uses local attention: often, the local context (e.g., what are the two tokens to theleft and right?) is enough to take action for a given token. Also, by stacking attention layers that have a smallwindow, the last layer will have a receptive field of more than just the tokens in the window, allowing them to build arepresentation of the whole sentence.Some preselected input tokens are also given global attention: for those few tokens, the attention matrix can accessall tokens and this process is symmetric: all other tokens have access to those specific tokens (on top of the ones intheir local window). This is shown in Figure 2d of the paper, see below for a sample attention mask:<div class="flex justify-center">    <img scale="50 %" align="center" src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/local_attention_mask.png"/></div>Using those attention matrices with less parameters then allows the model to have inputs having a bigger sequencelength.## Other tricks### Axial positional encodings[Reformer](model_doc/reformer) uses axial positional encodings: in traditional transformer models, the positional encodingE is a matrix of size \\(l\\) by \\(d\\), \\(l\\) being the sequence length and \\(d\\) the dimension of thehidden state. If you have very long texts, this matrix can be huge and take way too much space on the GPU. To alleviatethat, axial positional encodings consist of factorizing that big matrix E in two smaller matrices E1 and E2, withdimensions \\(l_{1} \times d_{1}\\) and \\(l_{2} \times d_{2}\\), such that \\(l_{1} \times l_{2} = l\\) and\\(d_{1} + d_{2} = d\\) (with the product for the lengths, this ends up being way smaller). The embedding for timestep \\(j\\) in E is obtained by concatenating the embeddings for timestep \\(j \% l1\\) in E1 and \\(j // l1\\)in E2.