Calibration-aware and finite-rate quantization extensions

Develop calibration-aware rounding, coupled finite-rate interfaces, approximate-inverse sketching, and structured ΣΔ noise shaping directed toward low-energy contraction coordinates.

Background

The paper’s exact product-error identity applies to subtractive dither and independent stochastic rounding, while deterministic round-to-nearest is treated through empirical calibration and diagnostics. The authors explicitly identify several unresolved extensions involving calibration-aware rounding, finite-rate coupling, approximate-inverse sketches, and structured noise shaping for contraction coordinates with low energy.

References

Calibration-aware rounding, coupled finite-rate interfaces, approximate-inverse sketching, and structured $\Sigma\Delta$ noise shaping toward low-energy contraction coordinates remain open.

— Contraction-Gauge Preconditioning for Quantized Matrix Multiplication  (2607.18745 - Sao et al., 21 Jul 2026) in Section 10, paragraph “Open problems”