Product Quantization

Generative Information Retrieval (GIR) has emerged as a transformative paradigm, shifting document retrieval from a traditional "retrieve-and-rank" workflow to sequence-to-sequence generation, where a model directly predicts document identifiers (DocIDs). While the semantic design of these DocIDs is known to be critical for performance, a fundamental question remains under-explored: what makes a good DocID? Current approaches rely heavily on computationally expensive downstream evaluations, hindering systematic analysis and rapid iteration. In this work, we address this challenge by presenting a comprehensive study on the properties, metrics, and trade-offs that define effective numerical DocIDs. Specifically, our contributions are threefold: First, we propose a unified framework that unifies Product Quantization (PQ) and Residual Quantization (RQ), and their hybrid variants within a single design space. This enables us to systematically study key DocID properties, such as hierarchy versus parallelism, as well as the impact of hyperparameters like DocID length and codebook size. Second, we define a suite of training-free, intrinsic metrics, to quantify DocID quality and evaluate structural fidelity without the overhead of full model training. Through extensive experiments on MS MARCO 300K and NQ320K, we analyze how these structural properties influence retrieval effectiveness.

We introduce NCP-ArchPreview, a latent-space language model that pushes autoregressive pretraining beyond standard next-token prediction (NTP). Alongside NTP, the model learns through Next Concept Prediction (NCP) to predict discrete concepts that span multiple tokens, introducing an explicit and more challenging concept-level objective while preserving standard token-level autoregressive generation. NCP-ArchPreview builds a latent space by constructing a product-quantized concept vocabulary directly from its hidden states, and subsequently learns to predict future concepts via a dedicated Concept Module. These predicted concepts are then fed back to the token level to guide subsequent generation, with NTP and NCP trained jointly end-to-end. We scale this architecture to 8.9B parameters and train it on 5.73T tokens from the Dolma-3 dataset, marking the largest demonstration of a latent-space language model to date. Remarkably, by consuming only 51.3% of the total training tokens, NCP-ArchPreview achieves the final pretraining loss of OLMo-3-7B. Following full pretraining, it outperforms OLMo-3-7B by 2.45 points on the downstream macro-average, including a notable 5.99-point gain on GSM8K. Controlled experiments isolate a clear progression of performance gains stemming from both the latent architecture and the NCP objective. Furthermore, utilizing only 85% of the standard computation, NCP-ArchPreview approaches the training loss of a strictly parameter-aligned 8.9B baseline. The learned latent space remains highly valuable after the pretraining stage: updating just the 17M-parameter VQ module yields a novel, lightweight interface for domain adaptation, while a simple injection of concept representations into a DFlash2 drafter improves the mean accepted length by 4.17% with negligible overhead.

Discrete visual tokenization, predominantly driven by vector, scalar, and product quantization, lacks a unified conceptual framework for understanding quantization tradeoffs. In this paper, we propose a unified rate--distortion perspective on modern discrete visual tokenization. By viewing quantization as lossy compression, we characterize the nominal fixed-length coding rate through token count and codebook size, and quantization error as the distortion. Within this framework, we resolve three central questions. First, we theoretically and empirically show that minimizing distortion, rather than maximizing codebook utilization, is the primary intrinsic objective for reconstruction fidelity, with a direct connection to the STE-induced gradient discrepancy. Second, we establish two critical fairness conditions for intrinsic quantization comparison: controlling latent feature statistics and enforcing identical coding rates. Third, under these conditions, we recover the VQ--PQ--SQ distortion hierarchy in modern visual tokenization and show empirically that modern VQ methods achieve the lowest distortion. This work provides a foundational rate--distortion reframing of modern discrete visual tokenization, resolves ambiguities in quantizer evaluation, and provides a controlled framework for isolating intrinsic quantization effectiveness under fixed-rate constraints.

While ColBERT is an effective neural retrieval architecture, it requires a heavy index structure to support candidate set retrieval based on approximated token embeddings, gathering and decompressing document token embeddings, and applying the MaxSim operation. Indexes in PLAID and similar ColBERT implementations require five to ten times the disk storage of the original raw text, which limits their scalability. Furthermore, prior work has identified that the gathering and decompression stages are the primary inefficiencies at query time. Limiting the number of document tokens that must be gathered by thresholding and score approximation does not eliminate the need for the entire index to support ad hoc queries. In this work, we propose an embedding quantization approach that turns a ColBERT index into a true inverted index. We show that, theoretically, ColBERT with embedding quantization is equivalent to learned-sparse retrieval except for the scoring mechanism. Empirically, we demonstrate that our index is 50-70% smaller than a one-bit PLAID index while retaining retrieval effectiveness.

Robot localization systems are critical for autonomous navigation and safety. Adversarial perturbations can mislead these systems, resulting in mislocalization, navigation errors, or unsafe interactions, especially in mission-critical scenarios. This paper investigates the vulnerability of deep learning based localization pipelines to adversarial attacks. We propose a novel framework for generating adversarial queries that specifically target Product Quantization (PQ) in visual localization systems. Our method employs a Lightweight Product Quantization Network (LPQN) to perturb query feature encodings, misleading the retrieval process by returning semantically irrelevant database entries. Adversarial queries are generated via a two-phase procedure: a forward pass that perturbs feature distributions and a backward pass that refines the perturbation through optimization. The lightweight design of LPQN allows the creation of subtle yet highly effective perturbations with minimal computational overhead. Extensive experiments in both controlled and real-world robotic environments demonstrate that our approach substantially degrades PQN performance, exposing critical vulnerabilities in practical applications.

Multivector retrieval models achieve state-of-the-art effectiveness through fine-grained token-level representations, but their deployment incurs substantial computational and memory costs. Current solutions, based on the well-known k-means clustering algorithm, group similar vectors together to enable both effective compression and efficient retrieval. However, standard k-means scales poorly with the number of clusters and dataset size, and favours frequent tokens during training while underrepresenting rare, discriminative ones. In this work, we introduce TACHIOM, a multivector retrieval system that exploits token-level structure to significantly accelerate both clustering and retrieval. By accounting for tokens' distribution during centroid allocation, TACHIOM easily scales to millions of centroids, enabling highly accurate document scoring using only centroids, avoiding expensive token-level computation. TACHIOM combines a graph-based index over centroids with an optimized Product Quantization layout for efficient final scoring. Experiments on MS-MARCOv1 and LoTTE show that TACHIOM achieves up to $247\times$ faster clustering than k-means and up to $9.8\times$ retrieval speedup over state-of-the-art systems while maintaining comparable or superior effectiveness.

Large-scale Nearest Neighbor (NN) search, though widely utilized in the similarity search field, remains challenged by the computational limitations inherent in processing large scale data. In an effort to decrease the computational expense needed, Approximate Nearest Neighbor (ANN) search is often used in applications that do not require the exact similarity search, but instead can rely on an approximation. Product Quantization (PQ) is a memory-efficient ANN effective for clustering all sizes of datasets. Clustering large-scale, high dimensional data requires a heavy computational expense, in both memory-cost and execution time. This work focuses on a unique way to divide and conquer the large scale data in Python using PQ, Inverted Indexing and Dask, combining the results without compromising the accuracy and reducing computational requirements to the level required when using medium-scale data.

Compressing large language models (LLMs) for deployment on commodity GPUs remains challenging: conventional scalar quantization is limited to fixed bit-widths (e.g., 8/4/3-bit), offers only a few discrete compression points, and typically requires calibration data. We present FASQ (Flexible Accelerated Subspace Quantization), a calibration-free framework that applies product quantization to LLM weight matrices. By tuning two parameters, sub-vector size and codebook cardinality, FASQ exposes a continuous design space spanning 27-49% of the original FP16 model size, filling compression gaps that fixed-bit schemes cannot reach. On Meta-Llama-3-8B, FASQ surpasses 4-bit GPTQ and AWQ in accuracy (67.1-67.7 avg.) at 37-42% model size, with consistent results on Qwen3-8B and Qwen3.5-9B-Base. To make product quantization practical at inference time, we design custom CUDA kernels: a LUT-free direct-compute GEMV for decode and an output-stationary double-buffered LUT GEMM for prefill, both with split-K parallelism. On an RTX~3090, FASQ achieves 45.2 tok/s decode at effective 4-bit (2.56x memory reduction) and 51.8 tok/s at effective 3-bit (2.80x), both surpassing FP16 tensor-core performance (43.9 tok/s) and delivering 1.6 to 1.8x the throughput of AWQ, 2.5 to 2.5x of GPTQ, and 4.3 to 5x of RTN. FASQ is the only compressed method that accelerates decode beyond FP16, offering calibration-free compression, continuous size-quality trade-offs, and real-time inference on a single consumer GPU.

Approximate Nearest-Neighbor Search (ANNS) pipelines for high-dimensional neural embeddings spend the bulk of their query time in candidate verification, making it the primary bottleneck in the search process. In this paper, we present PANORAMA, a state-of-the-art refinement technique that accelerates verification by exploiting the inherent spectral decay of these embeddings. Using PCA to compact signal energy, PANORAMA evaluates candidate distances incrementally, computing at each step a strict lower bound on the full-vector distance and dynamically pruning candidates the moment this bound exceeds the running k-th nearest neighbor distance. While PCA's concentration of variance facilitates pruning, it breaks the uniform-variance assumption required by Product Quantization (PQ); we resolve this with a variance-shaping step that redistributes energy across subvectors, rendering accretive refinement compatible with quantized indexes. Optimized for modern memory hierarchies via vectorized bulk-pruning and cache-conscious data layouts, PANORAMA has been upstreamed into the FAISS library across major index families (IVFPQ/Flat, HNSW, and Refine). PANORAMA achieves higher QPS at any target recall with a cost that provably scales inversely with dataset spectral decay, delivering end-to-end speedups of up to 28.9x and outperforming probabilistic methods across all recall bands.