Explain the impact of varying the number of attention heads on model performance and computational cost.

Varying the number of attention heads in a Transformer model has a significant impact on both model performance and computational cost. Increasing the number of attention heads generally improves model performance up to a point, as it allows the model to capture more diverse relationships and patterns in the data. Each attention head learns a different set of query, key, and value transformations, which allows it to attend to different aspects of the input sequence. With more heads, the model can capture a wider range of relationships, such as syntactic relationships, semantic relationships, and long-range dependencies. However, increasing the number of attention heads also increases the computational cost of the model. The computational cost of the attention mechanism is proportional to the square of the sequence length, so increasing the number of heads multiplies this cost. Each attention head requires its own set of query, key, and value transformations, which increases the number of parameters in the model and the amount of computation required for each forward and backward pass. Therefore, there is a trade-off between model performance and computational cost when choosing the number of attention heads. Typically, the number of attention heads is chosen based on the specific task and the available computational resources. It's also important to consider the dimensionality of the key, query, and value vectors. If the dimensionality is too small, increasing the number of heads will not significantly improve performance. In practice, a common configuration is to use 8 or 12 attention heads, but the optimal number of heads may vary depending on the specific application.