Optimization of Retrieval-Augmented Generation Context with Outlier Detection

In this paper, we focus on methods to reduce the size and improve the quality of the prompt context required for question-answering systems. Attempts to increase the number of retrieved chunked documents and thereby enlarge the context related to the query can significantly complicate the processing and decrease the performance of a Large Language Model (LLM) when generating responses to queries. It is well known that a large set of documents retrieved from a database in response to a query may contain irrelevant information, which often leads to hallucinations in the resulting answers. Our goal is to select the most semantically relevant documents, treating the discarded ones as outliers. We propose and evaluate several methods for identifying outliers by creating features that utilize the distances of embedding vectors, retrieved from the vector database, to both the centroid and the query vectors. The methods were evaluated by comparing the similarities of the retrieved LLM responses to ground-truth answers obtained using the OpenAI GPT-4o model. It was found that the greatest improvements were achieved with increasing complexity of the questions and answers.

Dimensionality Reduction in Sentence Transformer Vector Databases with Fast Fourier Transform

Dimensionality reduction in vector databases is pivotal for streamlining AI data management, enabling efficient storage, faster computation, and improved model performance. This paper explores the benefits of reducing vector database dimensions, with a focus on computational efficiency and overcoming the curse of dimensionality. We introduce a novel application of Fast Fourier Transform (FFT) to dimensionality reduction, a method previously underexploited in this context. By demonstrating its utility across various AI domains, including Retrieval-Augmented Generation (RAG) models and image processing, this FFT-based approach promises to improve data retrieval processes and enhance the efficiency and scalability of AI solutions. The incorporation of FFT may not only optimize operations in real-time processing and recommendation systems but also extend to advanced image processing techniques, where dimensionality reduction can significantly improve performance and analysis efficiency. This paper advocates for the broader adoption of FFT in vector database management, marking a significant stride towards addressing the challenges of data volume and complexity in AI research and applications. Unlike many existing approaches, we directly handle the embedding vectors produced by the model after processing a test input.

Iterative Aggregation Method for Solving Principal Component Analysis Problems

Motivated by the previously developed multilevel aggregation method for solving structural analysis problems a novel two-level aggregation approach for efficient iterative solution of Principal Component Analysis (PCA) problems is proposed. The course aggregation model of the original covariance matrix is used in the iterative solution of the eigenvalue problem by a power iterations method. The method is tested on several data sets consisting of large number of text documents.