Tensor parallelism (TP) is a technique used to optimize the performance of transformer models, particularly as they grow in size. It addresses the challenges of running large models on a single GPU by distributing the workload across multiple GPUs. The key idea behind TP is to split the matrices involved in matrix multiplications appropriately, allowing GPUs to work on different parts of the data simultaneously. This can be done through column-parallel or row-parallel matrix multiplication strategies, reducing memory usage and improving efficiency. In the context of Multi-Head Attention (MHA), TP allows for independent computation of attention heads. By splitting the projection matrices for queries, keys, and values among GPUs, each can compute its local attention without needing to communicate with others. The final output is generated through a summation of results from all GPUs. Similarly, TP can be applied to the Feed-Forward Network (FFN) by using column-parallel for the first linear layer and row-parallel for the second. However, there are constraints: the number of GPUs must be less than or equal to the number of attention heads, and both the number of heads and the feed-forward hidden dimension must be divisible by the number of GPUs. Implementing TP in practice is straightforward with the Hugging Face Transformers library. Users can leverage TP through the `tp_plan` argument when loading models. While TP effectively handles large matrix multiplications, it doesn’t solve all issues related to training or serving large models. Scalability is limited by the number of attention heads, and frequent communication between GPUs can hinder performance, particularly across multiple nodes. To fully address these challenges, other forms of parallelism, like Pipeline Parallelism, may be necessary.