Cross-Covariance Attention: A Feature-Based Attention Mechanism
Cross-Covariance Attention, also known as XCA, is an attention mechanism that operates along the feature dimension instead of the token dimension like the conventional transformers. The XCA mechanism is used to improve the performance of transformer models by allowing them to more effectively capture relationships between different features.
What is an Attention Mechanism?
Before delving into what XCA is, it's important to first understand what an attention mechanism is. In essence, attention mechanisms are a way for neural networks to selectively focus on certain parts of an input sequence before making a prediction. This has applications in numerous tasks such as machine translation, speech recognition, and image captioning.
Attention mechanisms work by computing a weighted sum over a set of values, where the weights are determined by the similarity between a query vector and a set of key vectors. The query vector and key vectors are typically obtained from the previous layer of the neural network. The resulting weighted sum is then used as input to the next layer of the neural network.
The Cross-Covariance Attention Mechanism
The XCA mechanism extends this idea by operating along the feature dimension instead of the token dimension. This means that instead of computing a weighted sum over a set of token embeddings, the XCA mechanism computes a weighted sum over a set of feature vectors for each token embedding.
The XCA mechanism works by taking a set of queries, keys, and values, where each query, key, and value has a set of feature vectors associated with it. The XCA mechanism computes the attention weights for each query and key using the cross-covariance matrix:
$$\mathcal{A}_{\mathrm{XC}}(K, Q)=\operatorname{Softmax}\left(\hat{K}^{\top} \hat{Q} / \tau\right)$$
where $\hat{K}$ and $\hat{Q}$ are the normalized cross-covariance matrices of the keys and queries respectively, and $\tau$ is a temperature parameter that controls the distribution of the softmax function. The attention weights are then used to compute a weighted sum over the values to obtain the output token embeddings:
$$\text{XC-Attention}(Q,K,V) = V\mathcal{A}_{\mathrm{XC}}(K, Q)$$
where $V$ is the value set corresponding to the queries and keys.
Why Use Cross-Covariance Attention?
The XCA mechanism provides a way for transformer models to capture relationships between different features in a more effective way. This is important because in many natural language processing tasks, such as machine translation or text classification, the relationships between features can be as important as the features themselves.
The XCA mechanism also provides a way to reduce the computational complexity of attention mechanisms. In conventional transformer models, the attention mechanism operates over the entire sequence of token embeddings, which can be computationally expensive. The XCA mechanism, on the other hand, operates only over the set of feature vectors for each token embedding, which can be much smaller than the full sequence of token embeddings.
Cross-Covariance Attention, or XCA, is an attention mechanism that operates along the feature dimension instead of the token dimension like the conventional transformers. The XCA mechanism is used to improve the performance of transformer models by allowing them to more effectively capture relationships between different features. XCA provides a way to reduce the computational complexity of attention mechanisms and can be used in many natural language processing tasks such as machine translation and text classification.
