text: Matrix factorization: The second method is based on matrix factorization. The training queries are used to train a bilinear 
  function mapping a model’s embedding and a query’s embedding to a score corresponding to how well the model performs 
  on the query. Routing is done by computing the score of the input query for each model, and choosing the highest-scoring 
  model. We denote this method as RM F . 
  
  BERT classifier: The third method involves fine-tuning a classifier, based on the BERT-base architecture [26], to predict 
  which of the two models produces a better response for the given query or whether they do equally well (a tie). The 
  routing decision is based on the probability of the weak model providing a better response versus the strong model or the 
  tie. We denote this method as RCLS. 
  
  LLM classifier: The last method is based on asking an LLM to provide a score in the range 1–5 of how an AI expert 
  would struggle to respond to a given query based on the query’s complexity. For this, Ong et al. fine-tuned a Llama-3-8B 
  model [4] using their reference set of queries and corresponding scores. We denote this method as RLLM . 