HypRQ-VAE: Hyperbolic Item Indexing for Long-Tail-Aware Generative Recommender Systems
Longfeng Wu, Tong Zeng, Giovanni Seni, Zhimin Peng, Bhanu Pratap Singh Rawat, Si Zhang, Yao Zhou, Lecheng Zheng, Bo Ji, Yujun Yan, Dawei Zhou
cs.IR
2026-09-03
HypRQ-VAE moves residual quantization into the Poincare ball, where exponential volume growth fits power-law catalogs. Tail Hit@10 rises 52.7% over TIGER on MovieLens while head items gain 14.1%.
Generative recommendation asks an LLM to generate the semantic ID of the next item, a short tuple of discrete tokens produced by quantizing item content. The standard RQ-VAE pipeline does this in Euclidean space. Real catalogs are long-tailed: a few head items absorb most interactions while a long tail of niche items stays sparse. Euclidean volume grows polynomially with radius, so sparse tail items get treated as outliers during quantization and the codebook allocation skews toward the head.
HypRQ-VAE is the first framework to build item indices in hyperbolic space. An item embedding is encoded, projected onto the Poincare ball with the exponential map, and used as the initial residual. Each quantization level finds the nearest codeword in hyperbolic space, recurses the residual with Mobius subtraction, and aggregates selected codewords with Mobius addition before mapping back for reconstruction. Collisions, where distinct items land on the same code tuple, are resolved by a cascading reassignment driven by codebook proximity, from the last level upward until every item is unique.
The geometric argument is that hyperbolic volume grows exponentially, which is tree-like and fits power-law data: head items sit near the origin, tail items spread into the branches. A second stage fine-tunes LLaMA-2-7B with LoRA over semantic ID sequences, with trie-constrained decoding.
Against TIGER, the Euclidean counterpart, with items split into head 20% and tail 80%:
| Split | MovieLens H@10 | Instruments H@5 | Arts N@5 |
| Head gain | +14.1% | +11.9% | +2.3% |
| Tail gain | +52.7% | +32.0% | +16.1% |
Overall results lead all baselines on every metric, but by much smaller margins (up to +14.0%). The mechanism is supported by quantization error: in Euclidean space head items consistently show lower average error than tail items, while in hyperbolic space the gap narrows or reverses. Recommended lists also contain a systematically higher share of tail items regardless of whether the ground truth is head or tail.
Semantic ID quality caps what a generative recommender can reach, and this paper shows the quantization geometry itself is an unused degree of freedom. For long-tail-heavy catalogs the gains are direct. The migration cost is contained because the change swaps Euclidean operations inside a mature RQ-VAE pipeline for their hyperbolic counterparts, and the appendix shows codebook utilization is naturally more uniform without the regularizers that LC-Rec and LETTER need.
Datasets are small: 2,751 to 20,956 items, orders of magnitude below industrial catalogs, and collision behavior at scale is not discussed. Absolute tail hit rates stay low; doubling a small number is still a small number. The comparison fixes on LLaMA-2-7B, an aging backbone. Numerical stability of exp/log maps and Mobius operations is not covered. And the core claim, that hyperbolic geometry suits hierarchical data, is long-standing; the contribution is compositional, plugging it into generative item indexing.