"Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity" published by Google Research in 2021. The paper presents an approach to scaling up transformer models to the trillion-parameter scale with a method called "mixture of experts".

The "Switch Transformer" paper presents a new model architecture that uses a routing mechanism to dynamically route tokens to a subset of experts (sub-networks) in each layer of the model. By doing so, it achieves both computational efficiency and model capacity expansion. This approach allows the model to scale up to the trillion-parameter level, which is an order of magnitude larger than previous transformer models.

The core idea behind the Switch Transformer is the "mixture of experts" (MoE) approach. In this approach, the model consists of multiple "expert" sub-networks, each of which specializes in processing a certain type of input.

At each layer, the model decides which expert to route each token to based on the input. This is done using a gating network, which computes a distribution over the experts for each token. The token is then routed to one or more experts based on this distribution.

The MoE approach allows the model to significantly increase its capacity without a corresponding increase in computation. This is because only a small subset of experts needs to be active for each token, allowing the model to scale up the number of experts without increasing the computation cost per token.

The gating network in the MoE layer is formulated as follows:

[ p_k(x) = \frac{\exp(g_k(x))}{\sum_{j=1}^K \exp(g_j(x))} ]

where (g_k(x)) is the gating score for expert (k) computed by a feed-forward network, and (K) is the total number of experts. The model then selects the top (L) experts for each token based on these scores.

The output of the MoE layer is computed as a weighted sum of the outputs of the selected experts:

[ y = \sum_{k=1}^K p_k(x) f_k(x) ]

where (f_k(x)) is the output of expert (k).

To ensure that the computational cost does not grow with the number of experts, the model uses a novel routing algorithm that evenly distributes the tokens among the experts. This ensures that each expert processes approximately the same number of tokens, maximizing the utilization of the experts.

The authors of the paper tested the Switch Transformer on a variety of tasks and found that it outperformed other models in terms of both performance and efficiency. The model achieved state-of-the-art results on the One Billion Word benchmark and was competitive with other models on the WMT'14 English to French translation task. It also demonstrated superior performance on the multilingual translation task, outperforming other models by a large margin.

The Switch Transformer model has significant implications for the field of natural language processing. It demonstrates that it is possible to scale up transformer models to the trillion-parameter level, which opens up new possibilities for tackling more complex tasks and larger datasets.

The model also demonstrates the power of the mixture of experts approach, which allows the model to increase its capacity without a corresponding increase in computation. This approach could be applied to other types of models and tasks, potentially leading to significant advancements in the field.