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Mar 11

Functional Bayesian Tucker Decomposition for Continuous-indexed Tensor Data

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there are finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, real-world data is often not naturally posed in this setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions. Then, we convert each GP into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications. We release the code of FunBaT at https://github.com/xuangu-fang/Functional-Bayesian-Tucker-Decomposition.

Empowering Large Language Models to Set up a Knowledge Retrieval Indexer via Self-Learning

Retrieval-Augmented Generation (RAG) offers a cost-effective approach to injecting real-time knowledge into large language models (LLMs). Nevertheless, constructing and validating high-quality knowledge repositories require considerable effort. We propose a pre-retrieval framework named Pseudo-Graph Retrieval-Augmented Generation (PG-RAG), which conceptualizes LLMs as students by providing them with abundant raw reading materials and encouraging them to engage in autonomous reading to record factual information in their own words. The resulting concise, well-organized mental indices are interconnected through common topics or complementary facts to form a pseudo-graph database. During the retrieval phase, PG-RAG mimics the human behavior in flipping through notes, identifying fact paths and subsequently exploring the related contexts. Adhering to the principle of the path taken by many is the best, it integrates highly corroborated fact paths to provide a structured and refined sub-graph assisting LLMs. We validated PG-RAG on three specialized question-answering datasets. In single-document tasks, PG-RAG significantly outperformed the current best baseline, KGP-LLaMA, across all key evaluation metrics, with an average overall performance improvement of 11.6%. Specifically, its BLEU score increased by approximately 14.3%, and the QE-F1 metric improved by 23.7%. In multi-document scenarios, the average metrics of PG-RAG were at least 2.35% higher than the best baseline. Notably, the BLEU score and QE-F1 metric showed stable improvements of around 7.55% and 12.75%, respectively. Our code: https://github.com/IAAR-Shanghai/PGRAG.

Curator: Efficient Indexing for Multi-Tenant Vector Databases

Vector databases have emerged as key enablers for bridging intelligent applications with unstructured data, providing generic search and management support for embedding vectors extracted from the raw unstructured data. As multiple data users can share the same database infrastructure, multi-tenancy support for vector databases is increasingly desirable. This hinges on an efficient filtered search operation, i.e., only querying the vectors accessible to a particular tenant. Multi-tenancy in vector databases is currently achieved by building either a single, shared index among all tenants, or a per-tenant index. The former optimizes for memory efficiency at the expense of search performance, while the latter does the opposite. Instead, this paper presents Curator, an in-memory vector index design tailored for multi-tenant queries that simultaneously achieves the two conflicting goals, low memory overhead and high performance for queries, vector insertion, and deletion. Curator indexes each tenant's vectors with a tenant-specific clustering tree and encodes these trees compactly as sub-trees of a shared clustering tree. Each tenant's clustering tree adapts dynamically to its unique vector distribution, while maintaining a low per-tenant memory footprint. Our evaluation, based on two widely used data sets, confirms that Curator delivers search performance on par with per-tenant indexing, while maintaining memory consumption at the same level as metadata filtering on a single, shared index.