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Life sciences · Preprint
arXiv · August 7, 2026
Early or partial results. Treat as a signal, not a conclusion.
CubicQuant is a parametric non-uniform quantization scheme that reduces reconstruction error on synthetic weight distributions by 3.90–28.14% relative to uniform quantization, with early GPU kernel results showing variable speed trade-offs. The work is technically sound in its formulation and synthetic benchmarks but lacks peer review, real-model quality metrics, and end-to-end performance validation across devices.
Algorithm development with synthetic benchmark and GPU kernel profiling. Synthetic weight distributions (Uniform, Gaussian, Laplace); no real language model weights or inference workloads evaluated.. Intervention: CubicQuant parametric non-uniform quantization with 1–8 bit weight payloads.. Compared with: Uniformly clipped 4-bit integer quantization and enumerated 4-bit floating-point formats..
W4 CubicQuant reduced RMSE by 3.90% on Uniform, 13.49% on Gaussian, and 28.14% on Laplace samples relative to optimally clipped uniform integer quantization. Relative to best enumerated 4-bit floating-point format: 3.90%, 9.44%, and 6.27% RMSE reduction on Uniform, Gaussian, and Laplace distributions. H200 kernel measurements show workload-dependent performance: model-dtype faster for narrow GEMV, Dynamic A8 favorable as row count grows.
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A novel quantization method with demonstrated technical promise on synthetic benchmarks and early GPU kernels, but lacking peer review, end-to-end model quality evaluation, and cross-device validation.
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Weight quantization for large-language-model inference must balance adaptive reconstruction levels with representations regular enough for efficient GPU execution. Uniform integers constrain each group to a linear grid. Low-bit floating-point formats use a fixed exponent-mantissa structure, while learned codebooks gain flexibility at the cost of irregular decoding and additional metadata. We introduce CubicQuant, a parametric non-uniform scalar format that preserves a dense integer code stream while adapting reconstruction levels within each weight group. A monotonic cubic curve, specified by two shape parameters and one scale, maps uniformly spaced magnitude codes to non-uniform levels. The family spans 1-8-bit weight payloads, contains symmetric uniform integer quantization as an exact special case, and has effective width B + 64/G bits per weight for payload width B and group size G. We derive population distortion under Uniform, Gaussian, and Laplace distributions, formulate continuous and Dynamic-A8-carrier-aware fitting objectives, and describe direct packed-weight GPU execution. For finite groups of G=128 with 15,360 samples per distribution, W4 CubicQuant reduced reconstruction RMSE relative to optimally clipped four-bit uniform integer quantization by 3.90% on Uniform, 13.49% on Gaussian, and 28.14% on Laplace samples. Relative to the best enumerated four-bit finite floating-point format, the reductions were 3.90%, 9.44%, and 6.27%. Preliminary H200 kernel measurements show a workload-dependent crossover: model-dtype execution is faster for narrow GEMV, while Dynamic A8 becomes favorable as row count grows. The results establish the format's representational promise and direct executability; downstream model quality and cross-device end-to-end performance remain open evaluation questions.
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