The concept of “Retriever + Generator End-to-end Training” (referred to as “RAG”) by Lewis et al. (2020) integrates retrieval and generation into a single, cohesive framework. This method enhances the accuracy of generating relevant and accurate responses by training both components together, ensuring that the retriever provides relevant documents and the generator produces high-quality responses. Let’s break down the details step by step:

Components of RAG

  1. Retriever:

    • The retriever is responsible for searching a large corpus to find documents relevant to the input query.
    • It maximizes the overall likelihood by optimizing mixture weights over the retrieved documents.

  2. Generator:

    • The generator takes the documents retrieved by the retriever and generates the final output, such as an answer to a question or a piece of text based on the given input.
    • It maximizes the generation likelihood given the single retrieved document.

Training Process

The training process in RAG involves simultaneous optimization of both the retriever and the generator, which are interconnected through the end-to-end backpropagation mechanism.

  1. Query Encoding ($q(x)$):

    • The input query is encoded into a query embedding vector $q(z)$.
    • This vector is used to search for relevant documents in the document index.

  2. Document Encoding (enc, $d(z)$):

    • Each document in the corpus is encoded into an embedding vector $d(z)$.

  3. Document Retrieval ($d(z)$):

    • The retriever component uses the query embedding $q(z)$ to identify a set of top-$k$ relevant documents $z$ from a large corpus.
    • This process involves measuring the similarity between the query embedding and the document embeddings $d(z)$, often using techniques like Maximum Inner Product Search (MIPS).

  4. Generation (p, G):

    • The generator takes each retrieved document $z$ and the query embedding $q(z)$ to generate the output text $y$.
    • The generation is modeled as a mixture model: for each query, a document is selected, and then the response is generated based on that document.

End-to-End Backpropagation

The key innovation in RAG is the end-to-end backpropagation through both the retriever and the generator, allowing the model to be trained jointly.

Likelihood Maximization

  • The retriever and generator are trained to maximize the joint likelihood of the retrieved document and the generated response.
  • The overall probability $P_{\text{RAG}}(y|x)$ is approximated by summing over the top-$k$ retrieved documents $z$:

$$ P_{\text{RAG}}(y|x) \approx \sum_{z \in \text{top-}k(p_R(x))} p_R(z|x) \prod_{i} p_G(y_i|x, z, y_{1:i-1}) $$

Here, $p_R$ is the probability distribution of the retriever, and $p_G$ is the probability distribution of the generator.

Components of RAG

  1. Retriever:

    • The retriever is responsible for searching a large corpus to find documents relevant to the input query.
    • It maximizes the overall likelihood by optimizing mixture weights over the retrieved documents.

  2. Generator:

    • The generator takes the documents retrieved by the retriever and generates the final output, such as an answer to a question or a piece of text based on the given input.
    • It maximizes the generation likelihood given the single retrieved document.

Training Process

The training process in RAG involves simultaneous optimization of both the retriever and the generator, which are interconnected through the end-to-end backpropagation mechanism.

  1. Query Encoding ($q(x)$):

    • The input query is encoded into a query embedding vector $q(x)$.
    • This vector is used to search for relevant documents in the document index.

  2. Document Retrieval ($d(z)$):

    • The retriever component uses the query embedding $q(x)$ to identify a set of top-$k$ relevant documents $z$ from a large corpus.
    • This process involves measuring the similarity between the query embedding and the document embeddings $d(z)$, often using techniques like Maximum Inner Product Search (MIPS).

  3. Document Encoding (enc, $d(z)$):

    • Each document in the corpus is encoded into an embedding vector $d(z)$.

  4. Generation ($p_G$):

    • The generator takes each retrieved document $z$ and the query embedding $q(x)$ to generate the output text $y$.
    • The generation is modeled as a mixture model: for each query, a document is selected, and then the response is generated based on that document.

End-to-End Backpropagation

The key innovation in RAG is the end-to-end backpropagation through both the retriever and the generator, allowing the model to be trained jointly.

Detailed Breakdown

  1. Likelihood Maximization:

    • The retriever and generator are trained to maximize the joint likelihood of the retrieved document and the generated response.
    • The overall probability $P_{\text{RAG}}(y|x)$ is approximated by summing over the top-$k$ retrieved documents $z$:

    $$ P_{\text{RAG}}(y|x) \approx \sum_{z \in \text{top-}k(p_R(x))} p_R(z|x) \prod_{i} p_G(y_i|x, z, y_{1:i-1}) $$

    • RAG-Sequence Model:

    • Uses the same retrieved document to generate the complete sequence.

    • Treats the retrieved document as a single latent variable that is marginalized to get the seq2seq probability $p(y|x)$ via a top-$k$ approximation.

    • Concretely, the top $k$ documents are retrieved using the retriever, and the generator produces the output sequence probability for each document, which are then marginalized:

      $$ P_{\text{RAG-Sequence}}(y|x) \approx \sum_{z \in \text{top-}k(p_R(x))} p_R(z|x) \prod_{i} p_G(y_i|x, z, y_{1:i-1}) $$

    • RAG-Token Model:

    • Can draw a different latent document for each target token and marginalize accordingly.

    • Allows the generator to choose content from several documents when producing an answer.

    • The top $k$ documents are retrieved using the retriever, and then the generator produces a distribution for the next output token for each document, before marginalizing and repeating the process with the following output token:

      $$ P_{\text{RAG-Token}}(y|x) = \sum_{z \in \text{top-}k(p_R(x))} p_R(z|x) \prod_{i} p_G(y_i|x, z, y_{1:i-1}) $$

  2. Retriever Training:

    • The retriever is trained to give higher similarities to helpful documents by adjusting the embeddings.
    • The probability of the retriever $p_R(z|x)$ is computed based on the inner product of the document embedding $d(z)$ and the query embedding $q(x)$:

    $$ p_R(z|x) \propto \exp(d(z)^T q(x)) $$

    Where $d(z) = \text{enc}_d(z)$ and $q(x) = \text{enc}_q(x)$.

  3. Generator Training:

    • The generator is trained to maximize the likelihood of generating the correct response given the retrieved document.
    • The generator’s probability $p_G(y|x, z, y_{1:i-1})$ depends on both the query and the retrieved document.

Challenges and Considerations

  1. Stale Search Index:

    • One issue with the end-to-end training is that the search index can become stale because the document embeddings $d(z)$ might change during training.
    • This necessitates regular re-indexing or adopting techniques to handle dynamic embeddings.

  2. Efficiency:

    • The training process can be computationally intensive as it involves computing embeddings for a large corpus and performing retrieval during training.
    • Efficient indexing and retrieval methods are crucial to making this feasible.

Summary

RAG represents a sophisticated approach to combining retrieval and generation, enabling the system to dynamically and jointly optimize both components. By leveraging end-to-end backpropagation, RAG can significantly improve the relevance and quality of generated responses, making it a powerful method for tasks that require integrating large-scale information retrieval with natural language generation.