Coding in 3D: From Hypervectors to Hyper Innovation (Paper Abstract Included)

Thanks to Vaughn Vernon for his Reactive Domain-Driven Design materials.

In the realm of software development, the integration of cutting-edge technologies has always been a driving force. Imagine a world where code generation is not just a task but an intelligent, context-aware process. Our recent exploration delves into the synergy between Hypervector Embeddings and AI Representations, opening up new possibilities for the domain of Reactive Domain-Driven Design (RDDDS).

?? Revolutionizing Code Generation: RDDDS is known for its complexity, with actors responding dynamically to events and messages. Traditional code generation methods often fall short of capturing this dynamism. That's where our innovation steps in.

?? The Power of Hypervectors: Hypervectors offer a novel approach to represent complex data, reducing dimensionality without sacrificing context. This paves the way for more efficient code generation, particularly in RDDDS.

?? AI Representations: Leveraging AI representations from OpenAI adds an intelligent layer to the process. It's like having an AI collaborator that understands the nuances of your code requirements.

?? Practical Applications: Beyond the theoretical, our work explores real-world applications, enhancing the responsiveness and adaptability of actors in RDDDS systems.

?? Future Endeavors: As we move forward, we're excited about refining the relevance scoring mechanisms and exploring how this innovation can impact large-scale reactive systems.

Join us on this journey of innovation and discover how the fusion of Hypervectors and AI Representations is changing the game in code generation. Stay tuned for more updates and insights as we continue to push the boundaries of what's possible in software development.

#CodeGeneration #AI #Innovation #SoftwareDevelopment #RDDDS #Hypervectors #OpenAI

# vector_search_with_numpy_openai.py
import openai
import numpy as np
from typing import List, Dict

class VectorSearch:
    """
    Vector search using numpy and text embeddings from OpenAI.
    """

    def __init__(self, openai_api_key: str):
        # openai.api_key = openai_api_key
        self.embeddings = {}
        self.documents = []

    def add_documents(self, documents: List[str]):
        """
        Adds documents to the search index and computes their embeddings.

        :param documents: A list of documents (strings) to be added.
        """
        for doc in documents:
            embedding = self._get_embedding(doc)
            self.embeddings[doc] = embedding
            self.documents.append(doc)

    def _get_embedding(self, text: str) -> np.ndarray:
        """
        Generates an embedding for the given text using OpenAI.

        :param text: The text to get an embedding for.
        :return: Numpy array representing the embedding.
        """
        response = openai.embeddings.create(input=text, model="text-embedding-ada-002")
        return np.array(response.data[0].embedding)

    def search(self, query: str, top_k: int = 5) -> List[Dict[str, any]]:
        """
        Performs a vector search for the given query in the added documents.

        :param query: The query string.
        :param top_k: The number of top results to return.
        :return: A list of dictionaries containing the matched documents and their scores.
        """
        query_embedding = self._get_embedding(query)
        scores = {doc: self._cosine_similarity(query_embedding, self.embeddings[doc]) for doc in self.documents}
        sorted_docs = sorted(scores.items(), key=lambda x: x[1], reverse=True)
        return [{"document": doc, "score": score} for doc, score in sorted_docs[:top_k]]

    def _cosine_similarity(self, vec1: np.ndarray, vec2: np.ndarray) -> float:
        """
        Computes the cosine similarity between two vectors.

        :param vec1: First vector.
        :param vec2: Second vector.
        :return: Cosine similarity score.
        """
        return np.dot(vec1, vec2) / (np.linalg.norm(vec1) * np.linalg.norm(vec2))

# Example usage
openai_api_key = 'your-openai-api-key'
vector_search = VectorSearch(openai_api_key)

# Adding Reactive DDD Events 
documents = [
    "InitiateWriting",
    "RequestForEditing",
    "ContentEdited",
    "DraftReadyForReview",
    "RequestForReview",
    "ReviewCompleted",
    "BookReadyForPublishing",
    "PublishBook",
    "BookPublished",
]
vector_search.add_documents(documents)

# Performing a search
query = "I need help with my draft"
results = vector_search.search(query)
print("Search results:", results)
        

Title: Leveraging Hypervector Embeddings and OpenAI Representations for Code Generation in Reactive Domain-Driven Design

Abstract:

In the realm of Reactive Domain-Driven Design (RDDDS), our innovative approach draws upon symbolic notations to convey the fundamental ideas:

1. Introduction:

In RDDDS, we define:

- \(\forall H, C: H \leftrightarrow C\) signifies a bijective mapping between Hypervector Embeddings (\(H\)) and Code Generation (\(C\)).

- \(\exists Discovery: \forall H, C \rightarrow A\) asserts the existence of a discovery operation such that, for all \(H\) and \(C\), they map to Actor (\(A\)).

- \(\forall A: A\) represents the Universal Language, denoting Actor (\(A\)) as a universal language.

2. Problem Formulation:

We express:

- \(\forall Representation: A \leftrightarrow (H, C)\) entails a bidirectional mapping between Universal Language (\(A\)) and its representation using Hypervector Embeddings (\(H\)) and Code Generation (\(C\)).

- \(\exists Common Purpose: \forall H, C \rightarrow\) Understanding and Collaboration asserts that, for all \(H\) and \(C\), their common purpose is to foster understanding and collaboration.

- \(\forall Role of A: A \leftrightarrow (H, AI)\) signifies the bidirectional association between Universal Language (\(A\)) and its role concerning Hypervector Embeddings (\(H\)) and Artificial Intelligence (\(AI\)).

- \(\exists Operation: \forall H, C \rightarrow\) Creation of A implies that, for all \(H\) and \(C\), the operation leads to the creation of \(A\).

3. Event Relevance Scoring:

To gauge the relevance of an event \(e\) to a specific actor \(a_i\), we invoke a similarity metric, particularly the cosine similarity:

\[

R_{e, a_i} = \frac{{\mathbf{e} \cdot \mathbf{a}_i}}{{\|\mathbf{e}\| \cdot \|\mathbf{a}_i\|}}

\]

This formula computes the relevance score (\(R_{e, a_i}\)), denoting the contextual relevance of the event to the actor.

4. Hypervector Projection:

To mitigate dimensionality issues, we propose a projection scheme that transfers \(\mathbf{e}\) and \(\mathbf{a}_i\) to a lower-dimensional hypervector space:

\[

\mathbf{h}_e = \text{HypervectorProjection}(\mathbf{e}), \quad \mathbf{h}_{a_i} = \text{HypervectorProjection}(\mathbf{a}_i)

\]

5. Relevance Ranking and Selection:

Events are ranked based on their relevance scores, and the top-\(K\) events, selected for actor \(a_i\), are denoted as \(\mathcal{E}_i^{(K)}\).

6. Code Generation:

For each selected event \(e_j \in \mathcal{E}_i^{(K)}\), we map it to a code template or snippet, embodying the desired action of actor \(a_i\) in response to \(e_j\):

\[

\mathcal{C}_{a_i, e_j} = \text{CodeGeneration}(\mathbf{h}_{a_i}, \mathbf{h}_{e_j})

\]

7. Code Composition:

The generated code snippets are amalgamated to form the comprehensive actor implementation:

\[

\mathcal{C}_{a_i} = \text{ComposeCode}(\{\mathcal{C}_{a_i, e_j}\}_{e_j \in \mathcal{E}_i^{(K)}})

\]

8. Validation and Refinement:

The generated code undergoes meticulous validation and refinement processes to ensure accuracy and alignment with system requirements.

9. Integration:

The validated code (\(\mathcal{C}_{a_i}\)) seamlessly integrates with the RDDDS system (\(\mathcal{S}\)), enhancing actor adaptability and system agility.

10. Conclusion and Future Work:

This innovative approach harnesses the collective potential of Hypervector Embeddings (\(H\)) and OpenAI Representations (\(R\)) to expedite code generation in the RDDDS domain. Future research directions may involve the enhancement of relevance scoring mechanisms and exploration of practical applications in large-scale reactive systems.

This comprehensive symbolic notation succinctly encapsulates the core concepts and contributions of the paper, providing a rigorous and formalized representation.