复线性映射的谱相位可容许性证明
A Spectral Phase Admissibility Certificate for Complex Linear Maps
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中文总结 AI 辅助
本文将量子引力的Kontsevich-Segal-Witten准则引入机器学习，构建三种可微证明评估复线性映射，该方法可降低处理成本，但存在适用边界，仅适用于处理谱乘积参数的模型。
中文摘要 AI 辅助
本文将量子引力中的Kontsevich-Segal-Witten准则引入机器学习，用于评估复线性映射。标准技术分析幅值或正定性，而本方法专门限制谱的集体相位。研究人员构建了三种不同的可微证明，包括行列式部分、子集乘积包络和完整准则。子集包络可防止所有外幂特征值触及负实轴，该约束与指数子式枚举的接受/拒绝选择完全匹配，同时大幅降低处理成本。团队通过Schur参数化提供了可微执行应用，还确定了该系统适用的关键边界：由于相位预算的限制会损害特征向量的条件数，该约束无法平衡深度线性传播；此外，该技术对基于幅值的目标（如归一化流似然）完全不敏感，因此研究人员必须将此工具专门限制于处理谱乘积参数的模型。
英文摘要
The paper imports the Kontsevich Segal Witten criterion from quantum gravity into machine learning to evaluate complex linear maps Standard techniques analyze magnitude or positive definiteness whereas this method exclusively limits the collective phase of a spectrum The researchers create three distinct differentiable certificates comprising a determinant sector a subset product envelope and the full criterion The subset envelope prevents all exterior power eigenvalues from touching the negative real axis This constraint precisely matches the accept or reject choices of an exponential minor enumeration while reducing processing expenses drastically The team provides a differentiable enforcement application via a Schur parameterization The document also identifies crucial boundaries regarding where this system works The constraint cannot balance deep linear propagation since restricting the phase budget damages eigenvector conditioning Furthermore the technique remains completely blind to magnitude based targets like normalizing flow likelihoods Thus researchers must restrict this tool specifically to models that process the argument of a spectral product
