小さなベクター ストアをゼロから構築する

生成 AI の状況が進化する中、ベクター データベースは生成 AI アプリケーションを強化する上で重要な役割を果たしています。現在、Chroma、Milvus などのオープン ソースのベクター データベースや、Pinecone、SingleStore などの一般的な独自のベクター データベースが多数存在します。このサイトでは、さまざまなベクター データベースの詳細な比較を読むことができます。

しかし、これらのベクトル データベースが舞台裏でどのように機能しているか考えたことはありますか?

何かを学ぶための優れた方法は、物事が内部でどのように機能するかを理解することです。この記事では、Python を使用し、NumPy のみを依存関係として使用して、小さなメモリ内ベクター ストア "Pixie" を最初から構築します。

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コードの説明に入る前に、ベクトル ストアとは何かについて簡単に説明します。

ベクターストアとは何ですか?

ベクター ストアは、ベクター エンベディングを効率的に保存および取得するように設計されたデータベースです。これらの埋め込みは、高次元空間で意味論的な意味を捉えるデータ (多くの場合テキストですが、画像、音声などの場合もあります) の数値表現です。ベクトル ストアの主な機能は、効率的な類似性検索を実行し、ベクトル表現に基づいて最も関連性の高いデータ ポイントを見つける機能です。ベクター ストアは、次のような多くのタスクで使用できます。

1. セマンティック検索
2. 検索拡張世代 (RAG)
3. 推薦システム

コードを書いてみましょう

この記事では、「Pixie」という小さなメモリ内ベクトル ストアを作成します。実稼働グレードのシステムのすべての最適化が行われるわけではありませんが、核となる概念は実証されます。 Pixie には 2 つの主な機能があります:

1. ドキュメントの埋め込みを保存する
2. 類似性検索の実行

ベクター ストアのセットアップ

まず、Pixie というクラスを作成します。

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. まず、効率的な数値演算と多次元配列の保存のために numpy をインポートします。
2. また、sentence_transformers ライブラリから SentenceTransformer をインポートします。埋め込みの生成には SentenceTransformer を使用していますが、テキストをベクトルに変換する任意の埋め込みモデルを使用できます。この記事では、エンベディングの生成ではなく、ベクター ストア自体に主に焦点を当てます。
3. 次に、エンベッダーを使用して Pixie クラスを初期化します。エンベッダーはメインのベクター ストアの外に移動できますが、簡単にするためにベクター ストア クラス内で初期化します。
4. self.store は、ドキュメントの埋め込みを NumPy 配列として保持します。
5. self.embedder は、ドキュメントとクエリをベクトルに変換するために使用する埋め込みモデルを保持します。

ドキュメントの取り込み

ベクター ストアにドキュメント/データを取り込むには、from_docs メソッドを実装します。

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

このメソッドはいくつかの重要なことを行います:

1. ドキュメントのリストを取得し、NumPy 配列として self.docs に保存します。
2. エンベッダー モデルを使用して、各ドキュメントをベクトル埋め込みに変換します。これらの埋め込みは self.store.
に保存されます。
3. 取り込まれたドキュメントの数を確認するメッセージを返します。 ここでは、エンベッダーのエンコード メソッドが重労働を行っており、各テキスト ドキュメントを高次元のベクトル表現に変換しています。

類似検索を実行する

ベクトル ストアの中心となるのは類似性検索機能です。

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

これを詳しく見てみましょう:

1. まず、一致を保存するために、match という空のリストを作成します。
2. ドキュメントの取り込みに使用したのと同じエンベッダー モデルを使用してユーザー クエリをエンコードします。これにより、クエリ ベクトルがドキュメント ベクトルと同じ空間に存在することが保証されます。
3. 最も類似したドキュメントを見つけるために、cosine_similarity 関数 (次に定義します) を呼び出します。
4. 返されたインデックスを使用して、self.docs から実際のドキュメントを取得します。
5. 最後に、一致するドキュメントのリストを返します。

コサイン類似度の実装

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

この関数はいくつかの重要なことを行っています:

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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