从头开始构建一个小型矢量存储

随着生成式人工智能的不断发展，矢量数据库在推动生成式人工智能应用方面发挥着至关重要的作用。目前有很多开源的矢量数据库，例如 Chroma、Milvus 以及其他流行的专有矢量数据库，例如 Pinecone、SingleStore。您可以在此网站上阅读不同矢量数据库的详细比较。

但是，您有没有想过这些矢量数据库在幕后是如何工作的？

学习东西的一个好方法是了解事物的底层工作原理。在本文中，我们将使用 Python 从头开始​​构建一个小型内存向量存储“Pixie”，仅使用 NumPy 作为依赖项。

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在深入代码之前，我们先简单讨论一下什么是向量存储。

什么是矢量商店？

向量存储是一个旨在高效存储和检索向量嵌入的数据库。这些嵌入是数据的数字表示（通常是文本，但也可以是图像、音频等），可以捕获高维空间中的语义。矢量存储的关键特征是能够执行有效的相似性搜索，根据矢量表示找到最相关的数据点。矢量存储可用于许多任务，例如：

1. 语义搜索
2. 检索增强生成（RAG）
3. 推荐系统

让我们来编码

在本文中，我们将创建一个名为“Pixie”的小型内存向量存储。虽然它不会具有生产级系统的所有优化，但它将演示核心概念。 Pixie 将有两个主要功能：

1. 存储文档嵌入
2. 执行相似性搜索

设置矢量存储

首先，我们将创建一个名为 Pixie 的类：

import numpy as np
from sentence_transformers import SentenceTransformer
from helpers import cosine_similarity


class Pixie:
    def __init__(self, embedder) -> None:
        self.store: np.ndarray = None
        self.embedder: SentenceTransformer = embedder

1. 首先，我们导入 numpy 来进行高效的数值运算和存储多维数组。
2. 我们还将从sentence_transformers库中导入SentenceTransformer。我们使用 SentenceTransformer 来生成嵌入，但您可以使用任何将文本转换为向量的嵌入模型。在本文中，我们的主要关注点将是向量存储本身，而不是嵌入生成。
3. 接下来，我们将使用嵌入器初始化 Pixie 类。嵌入器可以移到主向量存储之外，但为了简单起见，我们将在向量存储类内初始化它。
4. self.store 会将我们的文档嵌入保存为 NumPy 数组。
5. self.embedder 将保存我们将用来将文档和查询转换为向量的嵌入模型。

摄取文档

为了在我们的向量存储中提取文档/数据，我们将实现 from_docs 方法：

def from_docs(self, docs):
        self.docs = np.array(docs)
        self.store = self.embedder.encode(self.docs)
        return f"Ingested {len(docs)} documents"

这个方法做了一些关键的事情：

1. 它获取文档列表并将它们作为 NumPy 数组存储在 self.docs 中。
2. 它使用嵌入器模型将每个文档转换为向量嵌入。这些嵌入存储在 self.store 中。
3. 它会返回一条消息，确认已摄取了多少文档。 我们嵌入器的编码方法在这里完成繁重的工作，将每个文本文档转换为高维向量表示。

执行相似性搜索

我们矢量存储的核心是相似性搜索功能：

def similarity_search(self, query, top_k=3):
        matches = list()
        q_embedding = self.embedder.encode(query)
        top_k_indices = cosine_similarity(self.store, q_embedding, top_k)
        for i in top_k_indices:
            matches.append(self.docs[i])
        return matches

让我们来分解一下：

1. 我们首先创建一个名为 matches 的空列表来存储我们的匹配项。
2. 我们使用与摄取文档相同的嵌入器模型对用户查询进行编码。这确保了查询向量与我们的文档向量位于同一空间。
3. 我们调用 cosine_similarity 函数（我们将在接下来定义）来查找最相似的文档。
4. 我们使用返回的索引从 self.docs 获取实际文档。
5. 最后，我们返回匹配文档的列表。

实现余弦相似度

import numpy as np


def cosine_similarity(store_embeddings, query_embedding, top_k):
    dot_product = np.dot(store_embeddings, query_embedding)
    magnitude_a = np.linalg.norm(store_embeddings, axis=1)
    magnitude_b = np.linalg.norm(query_embedding)

    similarity = dot_product / (magnitude_a * magnitude_b)

    sim = np.argsort(similarity)
    top_k_indices = sim[::-1][:top_k]

    return top_k_indices

这个函数正在做几件重要的事情：

1. It calculates the cosine similarity using the formula: cos(θ) = (A · B) / (||A|| * ||B||)
2. First, we calculate the dot product between the query embeddings and all document embeddings in the store.
3. Then, we compute the magnitudes (Euclidean norms) of all vectors.
4. Lastly, we sort the found similarities and return the indices of the top-k most similar documents. We are using cosine similarity because it measures the angle between vectors, ignoring their magnitudes. This means it can find semantically similar documents regardless of their length.
5. There are other similarity metrics that you can explore such as:
   1. Euclidean distance
   2. Dot product similarity

You can read more about cosine similarity here.

Piecing everything together

Now that we have built all the pieces, let's understand how they work together:

1. When we create a Pixie instance, we provide it with an embedding model.
2. When we ingest documents, we create vector embeddings for each document and store them in self.store.
3. For a similarity search:
   1. We create an embedding for the query.
   2. We calculate cosine similarity between the query embeddings and all document embeddings.
   3. We return the most similar documents. All the magic happens inside the cosine similarity calculation. By comparing the angle between vectors rather than their magnitude, we can find semantically similar documents even if they use different words or phrasing.

Seeing it in action

Now let's implement a simple RAG system using our Pixie vector store. We'll ingest a story document of a "space battle & alien invasion" and then ask questions about it to see how it generates an answer.

import os
import sys
import warnings

warnings.filterwarnings("ignore")

import ollama
import numpy as np
from sentence_transformers import SentenceTransformer

current_dir = os.path.dirname(os.path.abspath(__file__))
root_dir = os.path.abspath(os.path.join(current_dir, ".."))
sys.path.append(root_dir)

from pixie import Pixie


# creating an instance of a pre-trained embedder model
embedder = SentenceTransformer("all-MiniLM-L6-v2")

# creating an instance of Pixie vector store
pixie = Pixie(embedder)


# generate an answer using llama3 and context docs
def generate_answer(prompt):
    response = ollama.chat(
        model="llama3",
        options={"temperature": 0.7},
        messages=[
            {
                "role": "user",
                "content": prompt,
            },
        ],
    )
    return response["message"]["content"]


with open("example/spacebattle.txt") as f:
    content = f.read()
    # ingesting the data into vector store
    ingested = pixie.from_docs(docs=content.split("\n\n"))
    print(ingested)

# system prompt
PROMPT = """
    User has asked you following question and you need to answer it based on the below provided context. 
If you don't find any answer in the given context then just say 'I don't have answer for that'. 
In the final answer, do not add "according to the context or as per the context". 
You can be creative while using the context to generate the final answer. DO NOT just share the context as it is.

    CONTEXT: {0}
    QUESTION: {1}

    ANSWER HERE:
"""

while True:
    query = input("\nAsk anything: ")
    if len(query) == 0:
        print("Ask a question to continue...")
        quit()

    if query == "/bye":
        quit()

    # search similar matches for query in the embedding store
    similarities = pixie.similarity_search(query, top_k=5)
    print(f"query: {query}, top {len(similarities)} matched results:\n")

    print("-" * 5, "Matched Documents Start", "-" * 5)
    for match in similarities:
        print(f"{match}\n")
    print("-" * 5, "Matched Documents End", "-" * 5)

    context = ",".join(similarities)
    answer = generate_answer(prompt=PROMPT.format(context, query))
    print("\n\nQuestion: {0}\nAnswer: {1}".format(query, answer))

    continue

Here is the output:

Ingested 8 documents

Ask anything: What was the invasion about?
query: What was the invasion about?, top 5 matched results:

----- Matched Documents Start -----
Epilogue: A New Dawn
Years passed, and the alliance between humans and Zorani flourished. Together, they rebuilt what had been lost, creating a new era of exploration and cooperation. The memory of the Krell invasion served as a stark reminder of the dangers that lurked in the cosmos, but also of the strength that came from unity. Admiral Selene Cortez retired, her name etched in the annals of history. Her legacy lived on in the new generation of leaders who continued to protect and explore the stars. And so, under the twin banners of Earth and Zorani, the galaxy knew peace—a fragile peace, hard-won and deeply cherished.

Chapter 3: The Invasion
Kael's warning proved true. The Krell arrived in a wave of bio-mechanical ships, each one bristling with organic weaponry and shields that regenerated like living tissue. Their tactics were brutal and efficient. The Titan Fleet, caught off guard, scrambled to mount a defense. Admiral Cortez's voice echoed through the corridors of the Prometheus. "All hands to battle stations! Prepare to engage!" The first clash was catastrophic. The Krell ships, with their organic hulls and adaptive technology, sliced through human defenses like a knife through butter. The outer rim colonies fell one by one, each defeat sending a shockwave of despair through the fleet. Onboard the Prometheus, Kael offered to assist, sharing Zorani technology and knowledge. Reluctantly, Cortez agreed, integrating Kael’s insights into their strategy. New energy weapons were developed, capable of piercing Krell defenses, and adaptive shields were installed to withstand their relentless attacks.

Chapter 5: The Final Battle
Victory on Helios IV was a much-needed morale boost, but the war was far from over. The Krell regrouped, launching a counter-offensive aimed directly at Earth. Every available ship was called back to defend humanity’s homeworld. As the Krell armada approached, Earth’s skies filled with the largest fleet ever assembled. The Prometheus led the charge, flanked by newly built warships and the remaining Zorani vessels that had joined the fight. "This is it," Cortez addressed her crew. "The fate of our species depends on this battle. We hold the line here, or we perish." The space above Earth turned into a maelstrom of fire and metal. Ships collided, energy beams sliced through the void, and explosions lit up the darkness. The Krell, relentless and numerous, seemed unbeatable. In the midst of chaos, Kael revealed a hidden aspect of Zorani technology—a weapon capable of creating a singularity, a black hole that could consume the Krell fleet. It was a desperate measure, one that could destroy both fleets. Admiral Cortez faced an impossible choice. To use the weapon would mean sacrificing the Titan Fleet and potentially Earth itself. But to do nothing would mean certain destruction at the hands of the Krell. "Activate the weapon," she ordered, her voice heavy with resolve. The Prometheus moved into position, its hull battered and scorched. As the singularity weapon charged, the Krell ships converged, sensing the threat. In a blinding burst of light, the weapon fired, tearing the fabric of space and creating a black hole that began to devour everything in its path.

Chapter 1: The Warning
It began with a whisper—a distant signal intercepted by the outermost listening posts of the Titan Fleet. The signal was alien, unlike anything the human race had ever encountered. For centuries, humanity had expanded its reach into the cosmos, colonizing distant planets and establishing trade routes across the galaxy. The Titan Fleet, the pride of Earth's military might, stood as the guardian of these far-flung colonies.Admiral Selene Cortez, a seasoned commander with a reputation for her sharp tactical mind, was the first to analyze the signal. As she sat in her command center aboard the flagship Prometheus, the eerie transmission played on a loop. It was a distress call, but its origin was unknown. The message, when decoded, revealed coordinates on the edge of the Andromeda Sector. "Set a course," Cortez ordered. The fleet moved with precision, a testament to years of training and discipline.

Chapter 4: Turning the Tide
The next battle, over the resource-rich planet of Helios IV, was a turning point. Utilizing the new technology, the Titan Fleet managed to hold their ground. The energy weapons seared through Krell ships, and the adaptive shields absorbed their retaliatory strikes. "Focus fire on the lead ship," Cortez commanded. "We break their formation, we break their spirit." The flagship of the Krell fleet, a massive dreadnought known as Voreth, was targeted. As the Prometheus and its escorts unleashed a barrage, the Krell ship's organic armor struggled to regenerate. In a final, desperate maneuver, Cortez ordered a concentrated strike on Voreth's core. With a blinding flash, the dreadnought exploded, sending a ripple of confusion through the Krell ranks. The humans pressed their advantage, driving the Krell back.
----- Matched Documents End -----


Question: What was the invasion about?
Answer: The Krell invasion was about the Krell arriving in bio-mechanical ships with organic weaponry and shields that regenerated like living tissue, seeking to conquer and destroy humanity.

We have successfully built a tiny in-memory vector store from scratch by using Python and NumPy. While it is very basic, it demonstrates the core concepts such as vector storage, and similarity search. Production grade vector stores are much more optimized and feature-rich.

Github repo: Pixie

Happy coding, and may your vectors always point in the right direction!

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