Learned indexes have attracted significant research interest due to their potential to offer better space-time trade-offs compared to B+-tree variants. Among various learned indexes, the PGM-Index based on error-bounded piecewise linear approximation is an elegant data structure that has demonstrated provably superior performance over conventional B+-tree indexes. However, despite numerous efforts to optimize the design of the PGM-Index, few systematically study the root causes of performance mismatches observed in practice. In this paper, we explore two key research questions. Q1 : Why are PGM-Indexes theoretically effective? and Q2 : Why do PGM-Indexes underperform in practice? For Q1 , we show that for a set of N sorted keys, the PGM-Index can achieve a lookup time of O (log log N ) while using O ( N ) space. For Q2 , we identify that querying PGM-Indexes is highly memory-bound, where the internal index search operations often become the bottleneck. To fill the performance gap, we propose PGM++, a simple yet effective extension to the original PGM-Index that employs a mixture of different search strategies, with hyper-parameters automatically tuned through a cost model calibrated by theoretical findings. Extensive experiments show that, at comparable space costs, PGM++ speeds up index lookup queries by up to 2.31X and 1.56X when compared to the original PGM-Index and SOTA baselines.

The rapid advancements of generative artificial intelligence (GenAI) have recently led to renewed attention towards approximate nearest neighbor (ANN) search and vector databases (VectorDB). Among various ANN methodologies, vector quantization techniques like product quantization (PQ) are widely used to generate space-efficient representations for large-scale dense vectors. However, the code-books generated by PQ often reach several gigabytes in size, making them impractical for web-scale, high-dimensional vectors in resource-constrained environments like mobile devices. In this study, we propose SegPQ , a simple yet effective framework for losslessly compressing codebooks generated by any PQ variants, enabling efficient in-memory vector search on devices with limited memory. SegPQ represents the raw PQ codewords as a trained error-bounded piecewise linear approximation model (ϵ-PLA) and pre-computed low-bit residuals. We theoretically demonstrate that, with high probability, the number of bits per compressed codeword is 1.721 + ⌈log 2 ϵ OPT ⌉, where ϵ OPT is the optimal error parameter that can be determined by data characteristics. To accelerate query execution, we further design SIMD-aware query processing algorithms on compressed codebooks to fully exploit the hardware parallelism offered by modern architectures. Extensive experimental studies on real datasets showcase that, for 1 billion vectors, SegPQ reduces PQ codebook memory consumption by up to 4.7 x (approx. 851 MB ) while incurring only 3.3% additional query processing overhead caused by decompression.

Large language models (LLMs) have demonstrated remarkable capabilities and have been extensively deployed across various domains, including recommender systems. Prior research has employed specialized prompts to leverage the in-context learning capabilities of LLMs for recommendation purposes. More recent studies have utilized instruction tuning techniques to align LLMs with human preferences, promising more effective recommendations. However, existing methods suffer from several limitations. The full potential of LLMs is not fully elicited due to low-quality tuning data and the overlooked integration of conventional recommender signals. Furthermore, LLMs may generate inconsistent responses for different ranking tasks in the recommendation, potentially leading to unreliable results. In this article, we introduce Ranker for top- k Recommendations (RecRanker), tailored for instruction tuning LLMs to serve as the Ranker for top- k Recommendations. Specifically, we introduce importance-aware sampling, clustering-based sampling, and penalty for repetitive sampling for sampling high-quality, representative, and diverse training data. To enhance the prompt, we introduce a position shifting strategy to mitigate position bias and augment the prompt with auxiliary information from conventional recommendation models, thereby enriching the contextual understanding of the LLM. Subsequently, we utilize the sampled data to assemble an instruction-tuning dataset with the augmented prompts comprising three distinct ranking tasks: pointwise, pairwise, and listwise rankings. We further propose a hybrid ranking method to enhance the model performance by ensembling these ranking tasks. Our empirical evaluations demonstrate the effectiveness of our proposed RecRanker in both direct and sequential recommendation scenarios. 1

Spatial representation learning (SRL) aims at learning general-purpose neural network representations from various types of spatial data (e.g., points, polylines, polygons, networks, images, etc.) in their native formats. Learning good spatial representations is a fundamental problem for various downstream applications such as species distribution modeling, weather forecasting, trajectory generation, geographic question answering, etc. Even though SRL has become the foundation of almost all geospatial artificial intelligence (GeoAI) research, we have not yet seen significant efforts to develop an extensive deep learning framework and benchmark to support SRL model development and evaluation. To fill this gap, we propose TorchSpatial, a learning framework and benchmark for location (point) encoding,which is one of the most fundamental data types of spatial representation learning. TorchSpatial contains three key components: 1) a unified location encoding framework that consolidates 15 commonly recognized location encoders, ensuring scalability and reproducibility of the implementations; 2) the LocBench benchmark tasks encompassing 7 geo-aware image classification and 10 geo-aware imageregression datasets; 3) a comprehensive suite of evaluation metrics to quantify geo-aware models’ overall performance as well as their geographic bias, with a novel Geo-Bias Score metric. Finally, we provide a detailed analysis and insights into the model performance and geographic bias of different location encoders. We believe TorchSpatial will foster future advancement of spatial representationlearning and spatial fairness in GeoAI research. The TorchSpatial model framework and LocBench benchmark are available at https://github.com/seai-lab/TorchSpatial, and the Geo-Bias Score evaluation framework is available at https://github.com/seai-lab/PyGBS.