# PRQ-KMeans: Projection Residual Quantization for Semantic ID Tokenization

arXiv: https://arxiv.org/abs/2608.24207 · HTML: https://mlsanity.com/paper/2608.24207/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 31 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Builds on (most cited first, 24 of 24)

- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [Autoregressive Image Generation using Residual Quantization](https://mlsanity.com/paper/2203.01941/) (2022)
- [Ups and Downs: Modeling the Visual Evolution of Fashion Trends with One-Class Collaborative Filtering](https://mlsanity.com/paper/1602.01585/) (2016)
- [Sentence-T5: Scalable Sentence Encoders from Pre-trained Text-to-Text Models](https://mlsanity.com/paper/2108.08877/) (2021)
- [Transformer Memory as a Differentiable Search Index](https://mlsanity.com/paper/2202.06991/) (2022)
- [OneRec: Unifying Retrieve and Rank with Generative Recommender and Iterative Preference Alignment](https://mlsanity.com/paper/2502.18965/) (2025)
- [A Neural Corpus Indexer for Document Retrieval](https://mlsanity.com/paper/2206.02743/) (2022)
- [Learning to Tokenize for Generative Retrieval](https://mlsanity.com/paper/2304.04171/) (2023)
- [Better Generalization with Semantic IDs: A Case Study in Ranking for Recommendations](https://mlsanity.com/paper/2306.08121/) (2023)
- [Generative Recommender with End-to-End Learnable Item Tokenization](https://mlsanity.com/paper/2409.05546/) (2024)
- [QARM: Quantitative Alignment Multi-Modal Recommendation at Kuaishou](https://mlsanity.com/paper/2411.11739/) (2024)
- [CoST: Contrastive Quantization based Semantic Tokenization for Generative Recommendation](https://mlsanity.com/paper/2404.14774/) (2024)
- [OneSearch: A Preliminary Exploration of the Unified End-to-End Generative Framework for E-commerce Search](https://mlsanity.com/paper/2509.03236/) (2025)
- [Differentiable Semantic ID for Generative Recommendation](https://mlsanity.com/paper/2601.19711/) (2026)
- [GLEN: Generative Retrieval via Lexical Index Learning](https://mlsanity.com/paper/2311.03057/) (2023)
- [LLaDA-Rec: Discrete Diffusion for Parallel Semantic ID Generation in Generative Recommendation](https://mlsanity.com/paper/2511.06254/) (2025)
- [Unleash the Potential of Long Semantic IDs for Generative Recommendation](https://mlsanity.com/paper/2602.13573/) (2026)
- [DOS: Dual-Flow Orthogonal Semantic IDs for Recommendation in Meituan](https://mlsanity.com/paper/2602.04460/) (2026)
- [End-to-End Semantic ID Generation for Generative Advertisement Recommendation](https://mlsanity.com/paper/2602.10445/) (2026)
- [Rethinking Generative Recommender Tokenizer: Recsys-Native Encoding and Semantic Quantization Beyond LLMs](https://mlsanity.com/paper/2602.02338/) (2026)
- [QARM V2: Quantitative Alignment Multi-Modal Recommendation for Reasoning User Sequence Modeling](https://mlsanity.com/paper/2602.08559/) (2026)
- [R3-VAE: Reference Vector-Guided Rating Residual Quantization VAE for Generative Recommendation](https://mlsanity.com/paper/2604.11440/) (2026)
- [RQ-GMM: Residual Quantized Gaussian Mixture Model for Multimodal Semantic Discretization in CTR Prediction](https://mlsanity.com/paper/2602.12593/) (2026)
- [Quantizing Intent: Cross-Domain Semantic IDs from Organic Activity for Industrial Ranking](https://mlsanity.com/paper/2606.01396/) (2026)

## Built on by (most cited first, 1 of 1)

- [A Systematic Study of Semantic ID Spaces for Generative Information Retrieval](https://mlsanity.com/paper/2610.08732/) (2026)

## Abstract (arXiv)

Semantic identifiers (SIDs) represent entities as hierarchical token sequences for generative retrieval and recommendation. Residual-quantization tokenizers construct these sequences by selecting a codeword at each level and passing a residual to the next. We view this process as progressive commonality removal: each token captures a component shared within its group, while later tokens should model the remaining differences. This view reveals three limitations: a corpus-wide shared component can consume first-level capacity, hard assignment ignores graded similarities to nearby codewords, and full-codeword subtraction can leave variation along the selected-codeword direction in the next residual. We therefore develop our solution in the post-hoc setting, where residual construction is not constrained by input reconstruction. Specifically, we propose PRQ-KMeans, which removes the global-mean component, refines centroids with Top-k similarity-weighted updates, and replaces full-codeword subtraction with a projection residual that removes each representation's selected-centroid component. Experiments on a large-scale industrial search dataset and four public recommendation benchmarks show that PRQ-KMeans achieves the strongest overall performance among the evaluated tokenizers, including gains of up to 7.4% in HitRate and 11.8% in MRR on the industrial dataset.