CurveTQ Preprint Proposes Curvature-Weighted Trellis Quantization Without Rotations
arXiv abstract dated 2026-10-06 introduces CurveTQ, a rotation-free trellis codec for two-bit LLM weights that incorporates Hessian curvature into the Viterbi metric and adds…
- CurveTQ matches full-dimension randomized Hadamard performance to within about one point of downstream accuracy using weighted native-basis search.
- The method leads QTIP and Proteus by 1-3 points in mean downstream accuracy on tested models after both baselines receive the new start-state treatment.
- Without needing to undo rotations, the CurveTQ decoder runs fastest among the three across all tested batch sizes and bit widths.
Preprint Summary
This evidence is an arXiv research preprint abstract-only capture dated 2026-10-06 by authors Ding, Guanhua; Wang, Zi; Li, Ruichao; and Liu, Jack. The work examines limitations in current two-bit weight quantizers for large language models.
Existing approaches such as QTIP and Proteus apply a random orthogonal transform to each weight matrix, requiring inversion at every decoding step. They then apply trellis or lattice coding under Euclidean distance search. The layer Hessian influences results only indirectly through error feedback between coding blocks.
Core Technical Insight
The authors note that error feedback converts the loss into a weighted sum of per-coordinate rounding errors. The weights correspond to the diagonal of the Hessian's LDL factorization, which prior methods compute but do not use directly.
CurveTQ inserts these curvature weights into the Viterbi branch metric. This allows the search to follow within-block curvature in the native basis. The preprint states that this weighted native search performs to within about one point of downstream accuracy compared with a full-dimension randomized Hadamard transform on three models. Weighting after rotation adds little benefit, suggesting the two approaches serve as substitutes.
CurveTQ Codec Features
The new codec uses a factored scale field and closed-form quantile table to address weight amplitude and marginal shape. It stores a start state per coding block so the trellis can adapt to residuals from error feedback.
At two bits, CurveTQ shows higher mean downstream accuracy than QTIP and Proteus on the evaluated 4-8B Instruct models and on a 35B mixture-of-experts model. The authors describe the latter result as the first trellis-coded outcome on a model of that scale. The start-state addition alone improves either baseline by 1-3 points.
Decoder Speed and Open Questions
Because no rotation must be inverted at runtime, the CurveTQ decoder is the fastest of the three methods at all tested batch sizes and bit widths. This may simplify deployment for practitioners working with low-bit open-weight models.
The supplied capture is the abstract only. Full methodological details, exact model names, evaluation conditions, complete numerical results, and any independent replication are unavailable. Claims should be read in that limited context.
