Paper 2607.27042 studies two-sided adaptive rounding, where a residual matrix is measured after multiplication by fixed nonsingular bases on both the left and right. Vectorization reduces the problem to the usual GPTQ, or Babai nearest-plane, procedure under a Kronecker-product metric, but raises the runtime to quartic in the matrix dimension. GPTQ-2D exploits the matrix structure: it processes entries anti-diagonal by anti-diagonal, with entries on one anti-diagonal independent and parallelizable. According to the abstract, it produces the identical rounded matrix in cubic time.
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