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Home Artificial Intelligence

RAG Defined: Understanding Embeddings, Similarity, and Retrieval

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September 18, 2025
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, I walked by means of constructing a easy RAG pipeline utilizing OpenAI’s API, LangChain, and native information, in addition to successfully chunking massive textual content information. These posts cowl the fundamentals of organising a RAG pipeline in a position to generate responses primarily based on the content material of native information.

Picture by creator

So, up to now, we’ve talked about studying the paperwork from wherever they’re saved, splitting them into textual content chunks, after which creating an embedding for every chunk. After that, we someway magically decide the embeddings which might be acceptable for the consumer question and generate a related response. But it surely’s vital to additional perceive how the retrieval step of RAG truly works.

Thus, on this submit, we’ll take issues a step additional by taking a better take a look at how the retrieval mechanism works and analyzing it in additional element. As in my earlier submit, I will probably be utilizing the Conflict and Peace textual content for instance, licensed as Public Area and simply accessible by means of Mission Gutenberg.

What concerning the embeddings?

With the intention to perceive how the retrieval step of the RAG framework works, it’s essential to first perceive how textual content is reworked and represented in embeddings. For LLMs to deal with any textual content, it should be within the type of a vector, and to carry out this transformation, we have to utilise an embedding mannequin.

An embedding is a vector illustration of information (in our case, textual content) that captures its semantic which means. Every phrase or sentence of the unique textual content is mapped to a high-dimensional vector. Embedding fashions used to carry out this transformation are designed in such a approach that related meanings lead to vectors which might be shut to 1 one other within the vector area. For instance, the vectors for the phrases comfortable and joyful can be shut to 1 one other within the vector area, whereas the vector for the phrase unhappy can be removed from them.

To create high-quality embeddings that work successfully in an RAG pipeline, one must make the most of pretrained embedding fashions, like BERT and GPT. There are numerous varieties of embeddings one can create and corresponding fashions accessible. As an example:

  • Phrase Embeddings: In phrase embeddings, every phrase has a hard and fast vector no matter context. Standard fashions for creating one of these embedding are Word2Vec and GloVe.
  • Contextual Embeddings: Contextual embeddings take note of that the which means of a phrase can change primarily based on context. Take, as an example, the financial institution of a river and opening a checking account. Some fashions that can be utilized for producing contextual embeddings are BERT, RoBERTa, and GPT.
  • Sentence Embeddings: These are embeddings capturing the which means of full sentences. Respective fashions that can be utilized are Sentence-BERT or USE.

In any case, textual content should be reworked into vectors to be usable in computations. These vectors are merely representations of the textual content. In different phrases, the vectors and numbers don’t have any inherent which means on their very own. As a substitute, they’re helpful as a result of they seize similarities and relationships between phrases or phrases in a mathematical type.

As an example, we may think about a tiny vocabulary consisting of the phrases king, queen, lady, and man, and assign every of them an arbitrary vector.

king  = [0.25, 0.75]  
queen = [0.23, 0.77]  
man   = [0.15, 0.80]  
lady = [0.13, 0.82]  

Then, we may attempt to do some vector operations like:

king - man + lady  
= [0.25, 0.75] - [0.15, 0.80] + [0.13, 0.82]  
= [0.23, 0.77]  
≈ queen 👑  

Discover how the semantics of the phrases and the relationships between them are preserved after mapping them into vectors, permitting us to carry out operations.

So, an embedding is simply that — a mapping of phrases to vectors, aiming to protect which means and relationships between phrases, and permitting to carry out computations with them. We will even visualize these dummy vectors in a vector area to see how associated phrases cluster collectively.

Picture by creator

The distinction between these easy vector examples and the true vectors produced by embedding fashions is that precise embedding fashions generate vectors with a whole bunch of dimensions. Two-dimensional vectors are helpful for constructing instinct about how which means might be mapped right into a vector area, however they’re far too low-dimensional to seize the complexity of actual language and vocabulary. That’s why actual embedding fashions work with a lot greater dimensions, typically within the a whole bunch and even 1000’s. For instance, Word2Vec produces 300-dimensional vectors, whereas BERT Base produces 768-dimensional vectors. This greater dimensionality permits embeddings to seize the a number of dimensions of actual language, like which means, utilization, syntax, and the context of phrases and phrases.

Assessing the similarity of embeddings

After the textual content is reworked into embeddings, inference turns into vector math. That is precisely what permits us to establish and retrieve related paperwork within the retrieval step of the RAG framework. As soon as we flip each the consumer’s question and the information base paperwork into vectors utilizing an embedding mannequin, we will then compute how related they’re utilizing cosine similarity.

Cosine similarity is a measure of how related two vectors (embeddings) are. Given two vectors A and B, cosine similarity is calculated as follows:

Picture by creator

Merely put, cosine similarity is calculated because the cosine of the angle between two vectors, and it ranges from 1 to -1. Extra particularly:

  • 1 signifies that the vectors are semantically similar (e.g., automotive and car).
  • 0 signifies that the vectors haven’t any semantic relationship (e.g., banana and justice).
  • -1 signifies that the vectors are semantically reverse (e.g., sizzling and chilly).

In follow, nevertheless, values close to -1 are extraordinarily uncommon in embedding fashions. It’s because even semantically reverse phrases (like sizzling and chilly) typically happen in related contexts (e.g., it’s getting sizzling and it’s getting chilly). For cosine similarity to succeed in -1, the phrases themselves and their contexts would each must be completely reverse—one thing that doesn’t actually occur in pure language. Consequently, even reverse phrases usually have embeddings which might be nonetheless considerably shut in which means.

Different similarity metrics other than cosine similarity do exist, such because the dot product or Euclidean distance, however these will not be normalized and are magnitude-dependent, making them much less appropriate for evaluating textual content embeddings. On this approach, cosine similarity is the dominant metric used for quantifying the similarity between embeddings.

Again to our RAG pipeline, by calculating the cosine similarity between the consumer’s question embeddings and the information base embeddings, we will establish the chunks of textual content which might be most related—and subsequently contextually related—to the consumer’s query, retrieve them, after which use them to generate the reply.

Discovering the highest ok related chunks

So, after getting the embeddings of the information base and the embedding(s) for the consumer question textual content, that is the place the magic occurs. What we basically do is that we calculate the cosine similarity between the consumer question embedding and the information base embeddings. Thus, for every textual content chunk of the information base, we get a rating between 1 and -1 indicating the chunk’s similarity with the consumer’s question.

As soon as we’ve got the similarity scores, we kind them in descending order and choose the highest ok chunks. These prime ok chunks are then handed into the technology step of the RAG pipeline, permitting it to successfully retrieve related data for the consumer’s question.

To hurry up this course of, the Approximate Nearest Neighbor (ANN) search is commonly used. ANN finds vectors which might be almost probably the most related, delivering outcomes near the true top-N however at a a lot sooner price than actual search strategies. In fact, actual search is extra correct; nonetheless, it’s also extra computationally costly and will not scale effectively in real-world functions, particularly when coping with huge datasets.

On prime of this, a threshold could also be utilized to the similarity scores to filter out chunks that don’t meet a minimal relevance rating. For instance, in some circumstances, a bit would possibly solely be thought of if its similarity rating exceeds a sure threshold (e.g., cosine similarity > 0.3).

So, who’s Anna Pávlovna?

Within the ‘Conflict and Peace‘ instance, as demonstrated in my earlier submit, we cut up the complete textual content into chunks after which create the respective embeddings for every chunk. Then, when the consumer submits a question, like ‘Who’s Anna Pávlovna?’, we additionally create the respective embedding(s) for the consumer’s question textual content.

import os
from langchain.chat_models import ChatOpenAI
from langchain.document_loaders import TextLoader
from langchain.embeddings import OpenAIEmbeddings
from langchain.vectorstores import FAISS
from langchain.text_splitter import RecursiveCharacterTextSplitter
from langchain.docstore.doc import Doc

api_key = 'your_api_key'

# initialize LLM
llm = ChatOpenAI(openai_api_key=api_key, mannequin="gpt-4o-mini", temperature=0.3)

# initialize embeddings mannequin
embeddings = OpenAIEmbeddings(openai_api_key=api_key)

# loading paperwork for use for RAG 
text_folder =  "RAG information"  

paperwork = []
for filename in os.listdir(text_folder):
    if filename.decrease().endswith(".txt"):
        file_path = os.path.be part of(text_folder, filename)
        loader = TextLoader(file_path)
        paperwork.prolong(loader.load())

splitter = RecursiveCharacterTextSplitter(chunk_size=1000, chunk_overlap=100)
split_docs = []
for doc in paperwork:
    chunks = splitter.split_text(doc.page_content)
    for chunk in chunks:
        split_docs.append(Doc(page_content=chunk))
        
paperwork = split_docs

# create vector database w FAISS 
vector_store = FAISS.from_documents(paperwork, embeddings)
retriever = vector_store.as_retriever()

def major():
    print("Welcome to the RAG Assistant. Sort 'exit' to stop.n")
    
    whereas True:
        user_input = enter("You: ").strip()
        if user_input.decrease() == "exit":
            print("Exiting…")
            break

        # get related paperwork
        relevant_docs = retriever.invoke(user_input)
        retrieved_context = "nn".be part of([doc.page_content for doc in relevant_docs])

        # system immediate
        system_prompt = (
            "You're a useful assistant. "
            "Use ONLY the next information base context to reply the consumer. "
            "If the reply is just not within the context, say you do not know.nn"
            f"Context:n{retrieved_context}"
        )

        # messages for LLM 
        messages = [
            {"role": "system", "content": system_prompt},
            {"role": "user", "content": user_input}
        ]

        # generate response
        response = llm.invoke(messages)
        assistant_message = response.content material.strip()
        print(f"nAssistant: {assistant_message}n")

if __name__ == "__main__":
    major()

On this script, I used LangChain’s retriever object retriever = vector_store.as_retriever(), which by default makes use of the cosine similarity to evaluate the relevance of the doc embeddings with the consumer’s question. It additionally retrieves by default the ok=4 paperwork. Thus, in essence, what we’re doing there’s that we retrieve the prime ok most related to the consumer question chunks primarily based on cosine similarity.

In any case, LangCahin’s .as_retriever() methodology doesn’t permit us to show the cosine similarity values — we simply get the highest ok related chunks. So, so as to check out the cosine similarities, I’m going to regulate our script just a little bit and use .similarity_search_with_score() as an alternative of .as_retriever(). We will simply do that by including the next half to our major() perform:

# REMOVE THIS LINE
retriever = vector_store.as_retriever()

def major():
    print("Welcome to the RAG Assistant. Sort 'exit' to stop.n")

    whereas True:
        user_input = enter("You: ").strip()
        if user_input.decrease() == "exit":
            print("Exiting…")
            break
        
        # ADD THIS SECTION   
        # Similarity search with rating 
        outcomes = vector_store.similarity_search_with_score(user_input, ok=2)

        # Extract paperwork and cosine similarity scores
        print(f"nCosine Similarities for Prime 5 Chunks:n")
        for idx, (doc, sim_score) in enumerate(outcomes):
            print(f"Chunk {idx + 1}:")
            print(f"Cosine Similarity: {sim_score:.4f}")
            print(f"Content material:n{doc.page_content}n")
        
        # CONTINUE WITH REST OF THE CODE...
        # System immediate for LLM technology
        retrieved_context = "nn".be part of([doc.page_content for doc, _ in results])

Discover how we will explicitly outline the variety of retrieved chunks ok, now set as ok=2.

Lastly, we will once more ask and obtain an answear:

Picture by creator

… however now we’re additionally in a position to see the textual content chunks primarily based on which this reply is created, and the respective cosine similarity scores…

Picture by creator

Apparently, completely different parameters can lead to completely different solutions. As an example, we’re going to get barely completely different solutions when retrieving the highest ok=2, ok=4, and ok=10 outcomes. Making an allowance for the extra parameters which might be used within the chunking step, like chunk measurement and chunk overlap, it turns into apparent that parameters play a vital function in getting good outcomes from a RAG pipeline.

• • •

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Tags: EmbeddingsExplainedRAGRetrievalSimilarityUnderstanding

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