PRQ-KMeans, a new method for turning embedding-based representations into semantic IDs, reported higher retrieval scores than RQ-KMeans in an industrial evaluation. The reported gains were 7.4% in Order HitRate, 11.8% in Order MRR, 6.4% in Click HitRate and 8.9% in Click MRR. The industrial measures were recorded at a cutoff of 50 results.
How the comparison was run
PRQ-KMeans is a semantic-ID tokenizer, meaning it builds a hierarchy of codes from embedding-based representations. It removes the global-mean component, refines centroids using Top-k similarity-weighted updates, and uses a projection residual instead of full-codeword subtraction. That residual removes the selected centroid's component rather than the entire codeword, allowing the method to remove commonality progressively as the code hierarchy is built.
Fitting the industrial tokenizer used 7,797,542 items and 9,046,403 training-query records, totaling 16,843,945 representations. Separate Order and Click test sets each contained 30,000 query-item pairs with corresponding observed behavior. The public evaluation used four recommendation benchmarks.
A lead across benchmarks
Across the four public benchmarks, PRQ-KMeans was best or tied-best on all eight reported metrics and exceeded RQ-KMeans in every comparison. Its gains were modest on Sports and Toys, larger on Clothing, and most pronounced on LastFM. On LastFM, item-level Recall@20 was 0.0115 for RQ-KMeans and 0.0179 for PRQ-KMeans, while NDCG@20 rose from 0.0042 to 0.0076.
The paper also compared how the industrial codebook was used. PRQ-KMeans had an independent-code ratio, or ICR, of 58.45%, compared with 55.52% for RQ-KMeans. At levels L2 and L3, prefix utilization was 57.78% and 3.99% for PRQ-KMeans, versus 47.88% and 3.61% for RQ-KMeans. The corresponding used-prefix Gini figures were lower for PRQ-KMeans, at 0.758 and 0.546, than for RQ-KMeans, at 0.774 and 0.569.
The pattern the authors were targeting
The paper's motivation analysis measured carryover in RQ-KMeans residuals from one codebook level to the next. Mean carryover ratios were 9.89% at L1, 10.17% at L2 and 7.44% at L3. L1 and L2 exceeded the study's 7.07% isotropic reference by 2.82 and 3.10 percentage points, respectively, while the terminal L3 level was close to it. In a controlled protocol, L2 prefix utilization increased monotonically from 47.88% when all L1 carryover was retained to 48.46% when none was retained.
Checks beyond the main score
In a five-level hybrid setting, PRQ-OPQ achieved the best Order and Click results on all four downstream metrics among three aligned tokenizers and improved over RQ-OPQ by 0.6% to 1.9%. In component ablations, the complete PRQ-KMeans model was best on every industrial metric and best or tied-best on all eight public metrics. Removing the Projection component was associated with the largest decrease on all four industrial metrics and all six Amazon metrics, while LastFM was most sensitive to Soft.
With the alternative embedding, PRQ-KMeans had the highest HitRate and MRR for both Order and Click. The authors report that it achieved the best overall downstream retrieval performance on the industrial dataset and four public benchmarks.
The manuscript is an arXiv version 2 preprint dated 3 September 2026. All tokenizers used a shared three-stage training, decoding and evaluation pipeline. The authors state that the code will be released upon acceptance.
Paper data and sources
Original title: PRQ-KMeans: Projection Residual Quantization for Semantic ID Tokenization
Authors: Yunxiao Luo, Siyuan Wang, Ben Chen, Chenyi Lei
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text